Removed openssl, and curl, and added mbedded tls.curl-removal

Almost fully removed curl, needs more testing.

Fixed most issues, now trying to cross compile.

Fix?

Sigh.

1 files changed, 3605 insertions, 0 deletions

diff --git a/lib/mbedtls-2.27.0/library/ecp.c b/lib/mbedtls-2.27.0/library/ecp.c
new file mode 100644
index 0000000..ca49f99
--- /dev/null
+++ b/lib/mbedtls-2.27.0/library/ecp.c
@@ -0,0 +1,3605 @@
+/*
+ *  Elliptic curves over GF(p): generic functions
+ *
+ *  Copyright The Mbed TLS Contributors
+ *  SPDX-License-Identifier: Apache-2.0
+ *
+ *  Licensed under the Apache License, Version 2.0 (the "License"); you may
+ *  not use this file except in compliance with the License.
+ *  You may obtain a copy of the License at
+ *
+ *  http://www.apache.org/licenses/LICENSE-2.0
+ *
+ *  Unless required by applicable law or agreed to in writing, software
+ *  distributed under the License is distributed on an "AS IS" BASIS, WITHOUT
+ *  WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.
+ *  See the License for the specific language governing permissions and
+ *  limitations under the License.
+ */
+
+/*
+ * References:
+ *
+ * SEC1 http://www.secg.org/index.php?action=secg,docs_secg
+ * GECC = Guide to Elliptic Curve Cryptography - Hankerson, Menezes, Vanstone
+ * FIPS 186-3 http://csrc.nist.gov/publications/fips/fips186-3/fips_186-3.pdf
+ * RFC 4492 for the related TLS structures and constants
+ * RFC 7748 for the Curve448 and Curve25519 curve definitions
+ *
+ * [Curve25519] http://cr.yp.to/ecdh/curve25519-20060209.pdf
+ *
+ * [2] CORON, Jean-S'ebastien. Resistance against differential power analysis
+ *     for elliptic curve cryptosystems. In : Cryptographic Hardware and
+ *     Embedded Systems. Springer Berlin Heidelberg, 1999. p. 292-302.
+ *     <http://link.springer.com/chapter/10.1007/3-540-48059-5_25>
+ *
+ * [3] HEDABOU, Mustapha, PINEL, Pierre, et B'EN'ETEAU, Lucien. A comb method to
+ *     render ECC resistant against Side Channel Attacks. IACR Cryptology
+ *     ePrint Archive, 2004, vol. 2004, p. 342.
+ *     <http://eprint.iacr.org/2004/342.pdf>
+ */
+
+#include "common.h"
+
+/**
+ * \brief Function level alternative implementation.
+ *
+ * The MBEDTLS_ECP_INTERNAL_ALT macro enables alternative implementations to
+ * replace certain functions in this module. The alternative implementations are
+ * typically hardware accelerators and need to activate the hardware before the
+ * computation starts and deactivate it after it finishes. The
+ * mbedtls_internal_ecp_init() and mbedtls_internal_ecp_free() functions serve
+ * this purpose.
+ *
+ * To preserve the correct functionality the following conditions must hold:
+ *
+ * - The alternative implementation must be activated by
+ *   mbedtls_internal_ecp_init() before any of the replaceable functions is
+ *   called.
+ * - mbedtls_internal_ecp_free() must \b only be called when the alternative
+ *   implementation is activated.
+ * - mbedtls_internal_ecp_init() must \b not be called when the alternative
+ *   implementation is activated.
+ * - Public functions must not return while the alternative implementation is
+ *   activated.
+ * - Replaceable functions are guarded by \c MBEDTLS_ECP_XXX_ALT macros and
+ *   before calling them an \code if( mbedtls_internal_ecp_grp_capable( grp ) )
+ *   \endcode ensures that the alternative implementation supports the current
+ *   group.
+ */
+#if defined(MBEDTLS_ECP_INTERNAL_ALT)
+#endif
+
+#if defined(MBEDTLS_ECP_C)
+
+#include "mbedtls/ecp.h"
+#include "mbedtls/threading.h"
+#include "mbedtls/platform_util.h"
+#include "mbedtls/error.h"
+#include "mbedtls/bn_mul.h"
+
+#include "ecp_invasive.h"
+
+#include <string.h>
+
+#if !defined(MBEDTLS_ECP_ALT)
+
+/* Parameter validation macros based on platform_util.h */
+#define ECP_VALIDATE_RET( cond )    \
+    MBEDTLS_INTERNAL_VALIDATE_RET( cond, MBEDTLS_ERR_ECP_BAD_INPUT_DATA )
+#define ECP_VALIDATE( cond )        \
+    MBEDTLS_INTERNAL_VALIDATE( cond )
+
+#if defined(MBEDTLS_PLATFORM_C)
+#include "mbedtls/platform.h"
+#else
+#include <stdlib.h>
+#include <stdio.h>
+#define mbedtls_printf     printf
+#define mbedtls_calloc    calloc
+#define mbedtls_free       free
+#endif
+
+#include "mbedtls/ecp_internal.h"
+
+#if !defined(MBEDTLS_ECP_NO_INTERNAL_RNG)
+#if defined(MBEDTLS_HMAC_DRBG_C)
+#include "mbedtls/hmac_drbg.h"
+#elif defined(MBEDTLS_CTR_DRBG_C)
+#include "mbedtls/ctr_drbg.h"
+#else
+#error "Invalid configuration detected. Include check_config.h to ensure that the configuration is valid."
+#endif
+#endif /* MBEDTLS_ECP_NO_INTERNAL_RNG */
+
+#if ( defined(__ARMCC_VERSION) || defined(_MSC_VER) ) && \
+    !defined(inline) && !defined(__cplusplus)
+#define inline __inline
+#endif
+
+#if defined(MBEDTLS_SELF_TEST)
+/*
+ * Counts of point addition and doubling, and field multiplications.
+ * Used to test resistance of point multiplication to simple timing attacks.
+ */
+static unsigned long add_count, dbl_count, mul_count;
+#endif
+
+#if !defined(MBEDTLS_ECP_NO_INTERNAL_RNG)
+/*
+ * Currently ecp_mul() takes a RNG function as an argument, used for
+ * side-channel protection, but it can be NULL. The initial reasoning was
+ * that people will pass non-NULL RNG when they care about side-channels, but
+ * unfortunately we have some APIs that call ecp_mul() with a NULL RNG, with
+ * no opportunity for the user to do anything about it.
+ *
+ * The obvious strategies for addressing that include:
+ * - change those APIs so that they take RNG arguments;
+ * - require a global RNG to be available to all crypto modules.
+ *
+ * Unfortunately those would break compatibility. So what we do instead is
+ * have our own internal DRBG instance, seeded from the secret scalar.
+ *
+ * The following is a light-weight abstraction layer for doing that with
+ * HMAC_DRBG (first choice) or CTR_DRBG.
+ */
+
+#if defined(MBEDTLS_HMAC_DRBG_C)
+
+/* DRBG context type */
+typedef mbedtls_hmac_drbg_context ecp_drbg_context;
+
+/* DRBG context init */
+static inline void ecp_drbg_init( ecp_drbg_context *ctx )
+{
+    mbedtls_hmac_drbg_init( ctx );
+}
+
+/* DRBG context free */
+static inline void ecp_drbg_free( ecp_drbg_context *ctx )
+{
+    mbedtls_hmac_drbg_free( ctx );
+}
+
+/* DRBG function */
+static inline int ecp_drbg_random( void *p_rng,
+                                   unsigned char *output, size_t output_len )
+{
+    return( mbedtls_hmac_drbg_random( p_rng, output, output_len ) );
+}
+
+/* DRBG context seeding */
+static int ecp_drbg_seed( ecp_drbg_context *ctx,
+                   const mbedtls_mpi *secret, size_t secret_len )
+{
+    int ret;
+    unsigned char secret_bytes[MBEDTLS_ECP_MAX_BYTES];
+    /* The list starts with strong hashes */
+    const mbedtls_md_type_t md_type = mbedtls_md_list()[0];
+    const mbedtls_md_info_t *md_info = mbedtls_md_info_from_type( md_type );
+
+    if( secret_len > MBEDTLS_ECP_MAX_BYTES )
+    {
+        ret = MBEDTLS_ERR_ECP_RANDOM_FAILED;
+        goto cleanup;
+    }
+
+    MBEDTLS_MPI_CHK( mbedtls_mpi_write_binary( secret,
+                                               secret_bytes, secret_len ) );
+
+    ret = mbedtls_hmac_drbg_seed_buf( ctx, md_info, secret_bytes, secret_len );
+
+cleanup:
+    mbedtls_platform_zeroize( secret_bytes, secret_len );
+
+    return( ret );
+}
+
+#elif defined(MBEDTLS_CTR_DRBG_C)
+
+/* DRBG context type */
+typedef mbedtls_ctr_drbg_context ecp_drbg_context;
+
+/* DRBG context init */
+static inline void ecp_drbg_init( ecp_drbg_context *ctx )
+{
+    mbedtls_ctr_drbg_init( ctx );
+}
+
+/* DRBG context free */
+static inline void ecp_drbg_free( ecp_drbg_context *ctx )
+{
+    mbedtls_ctr_drbg_free( ctx );
+}
+
+/* DRBG function */
+static inline int ecp_drbg_random( void *p_rng,
+                                   unsigned char *output, size_t output_len )
+{
+    return( mbedtls_ctr_drbg_random( p_rng, output, output_len ) );
+}
+
+/*
+ * Since CTR_DRBG doesn't have a seed_buf() function the way HMAC_DRBG does,
+ * we need to pass an entropy function when seeding. So we use a dummy
+ * function for that, and pass the actual entropy as customisation string.
+ * (During seeding of CTR_DRBG the entropy input and customisation string are
+ * concatenated before being used to update the secret state.)
+ */
+static int ecp_ctr_drbg_null_entropy(void *ctx, unsigned char *out, size_t len)
+{
+    (void) ctx;
+    memset( out, 0, len );
+    return( 0 );
+}
+
+/* DRBG context seeding */
+static int ecp_drbg_seed( ecp_drbg_context *ctx,
+                   const mbedtls_mpi *secret, size_t secret_len )
+{
+    int ret;
+    unsigned char secret_bytes[MBEDTLS_ECP_MAX_BYTES];
+
+    if( secret_len > MBEDTLS_ECP_MAX_BYTES )
+    {
+        ret = MBEDTLS_ERR_ECP_RANDOM_FAILED;
+        goto cleanup;
+    }
+
+    MBEDTLS_MPI_CHK( mbedtls_mpi_write_binary( secret,
+                                               secret_bytes, secret_len ) );
+
+    ret = mbedtls_ctr_drbg_seed( ctx, ecp_ctr_drbg_null_entropy, NULL,
+                                 secret_bytes, secret_len );
+
+cleanup:
+    mbedtls_platform_zeroize( secret_bytes, secret_len );
+
+    return( ret );
+}
+
+#else
+#error "Invalid configuration detected. Include check_config.h to ensure that the configuration is valid."
+#endif /* DRBG modules */
+#endif /* MBEDTLS_ECP_NO_INTERNAL_RNG */
+
+#if defined(MBEDTLS_ECP_RESTARTABLE)
+/*
+ * Maximum number of "basic operations" to be done in a row.
+ *
+ * Default value 0 means that ECC operations will not yield.
+ * Note that regardless of the value of ecp_max_ops, always at
+ * least one step is performed before yielding.
+ *
+ * Setting ecp_max_ops=1 can be suitable for testing purposes
+ * as it will interrupt computation at all possible points.
+ */
+static unsigned ecp_max_ops = 0;
+
+/*
+ * Set ecp_max_ops
+ */
+void mbedtls_ecp_set_max_ops( unsigned max_ops )
+{
+    ecp_max_ops = max_ops;
+}
+
+/*
+ * Check if restart is enabled
+ */
+int mbedtls_ecp_restart_is_enabled( void )
+{
+    return( ecp_max_ops != 0 );
+}
+
+/*
+ * Restart sub-context for ecp_mul_comb()
+ */
+struct mbedtls_ecp_restart_mul
+{
+    mbedtls_ecp_point R;    /* current intermediate result                  */
+    size_t i;               /* current index in various loops, 0 outside    */
+    mbedtls_ecp_point *T;   /* table for precomputed points                 */
+    unsigned char T_size;   /* number of points in table T                  */
+    enum {                  /* what were we doing last time we returned?    */
+        ecp_rsm_init = 0,       /* nothing so far, dummy initial state      */
+        ecp_rsm_pre_dbl,        /* precompute 2^n multiples                 */
+        ecp_rsm_pre_norm_dbl,   /* normalize precomputed 2^n multiples      */
+        ecp_rsm_pre_add,        /* precompute remaining points by adding    */
+        ecp_rsm_pre_norm_add,   /* normalize all precomputed points         */
+        ecp_rsm_comb_core,      /* ecp_mul_comb_core()                      */
+        ecp_rsm_final_norm,     /* do the final normalization               */
+    } state;
+#if !defined(MBEDTLS_ECP_NO_INTERNAL_RNG)
+    ecp_drbg_context drbg_ctx;
+    unsigned char drbg_seeded;
+#endif
+};
+
+/*
+ * Init restart_mul sub-context
+ */
+static void ecp_restart_rsm_init( mbedtls_ecp_restart_mul_ctx *ctx )
+{
+    mbedtls_ecp_point_init( &ctx->R );
+    ctx->i = 0;
+    ctx->T = NULL;
+    ctx->T_size = 0;
+    ctx->state = ecp_rsm_init;
+#if !defined(MBEDTLS_ECP_NO_INTERNAL_RNG)
+    ecp_drbg_init( &ctx->drbg_ctx );
+    ctx->drbg_seeded = 0;
+#endif
+}
+
+/*
+ * Free the components of a restart_mul sub-context
+ */
+static void ecp_restart_rsm_free( mbedtls_ecp_restart_mul_ctx *ctx )
+{
+    unsigned char i;
+
+    if( ctx == NULL )
+        return;
+
+    mbedtls_ecp_point_free( &ctx->R );
+
+    if( ctx->T != NULL )
+    {
+        for( i = 0; i < ctx->T_size; i++ )
+            mbedtls_ecp_point_free( ctx->T + i );
+        mbedtls_free( ctx->T );
+    }
+
+#if !defined(MBEDTLS_ECP_NO_INTERNAL_RNG)
+    ecp_drbg_free( &ctx->drbg_ctx );
+#endif
+
+    ecp_restart_rsm_init( ctx );
+}
+
+/*
+ * Restart context for ecp_muladd()
+ */
+struct mbedtls_ecp_restart_muladd
+{
+    mbedtls_ecp_point mP;       /* mP value                             */
+    mbedtls_ecp_point R;        /* R intermediate result                */
+    enum {                      /* what should we do next?              */
+        ecp_rsma_mul1 = 0,      /* first multiplication                 */
+        ecp_rsma_mul2,          /* second multiplication                */
+        ecp_rsma_add,           /* addition                             */
+        ecp_rsma_norm,          /* normalization                        */
+    } state;
+};
+
+/*
+ * Init restart_muladd sub-context
+ */
+static void ecp_restart_ma_init( mbedtls_ecp_restart_muladd_ctx *ctx )
+{
+    mbedtls_ecp_point_init( &ctx->mP );
+    mbedtls_ecp_point_init( &ctx->R );
+    ctx->state = ecp_rsma_mul1;
+}
+
+/*
+ * Free the components of a restart_muladd sub-context
+ */
+static void ecp_restart_ma_free( mbedtls_ecp_restart_muladd_ctx *ctx )
+{
+    if( ctx == NULL )
+        return;
+
+    mbedtls_ecp_point_free( &ctx->mP );
+    mbedtls_ecp_point_free( &ctx->R );
+
+    ecp_restart_ma_init( ctx );
+}
+
+/*
+ * Initialize a restart context
+ */
+void mbedtls_ecp_restart_init( mbedtls_ecp_restart_ctx *ctx )
+{
+    ECP_VALIDATE( ctx != NULL );
+    ctx->ops_done = 0;
+    ctx->depth = 0;
+    ctx->rsm = NULL;
+    ctx->ma = NULL;
+}
+
+/*
+ * Free the components of a restart context
+ */
+void mbedtls_ecp_restart_free( mbedtls_ecp_restart_ctx *ctx )
+{
+    if( ctx == NULL )
+        return;
+
+    ecp_restart_rsm_free( ctx->rsm );
+    mbedtls_free( ctx->rsm );
+
+    ecp_restart_ma_free( ctx->ma );
+    mbedtls_free( ctx->ma );
+
+    mbedtls_ecp_restart_init( ctx );
+}
+
+/*
+ * Check if we can do the next step
+ */
+int mbedtls_ecp_check_budget( const mbedtls_ecp_group *grp,
+                              mbedtls_ecp_restart_ctx *rs_ctx,
+                              unsigned ops )
+{
+    ECP_VALIDATE_RET( grp != NULL );
+
+    if( rs_ctx != NULL && ecp_max_ops != 0 )
+    {
+        /* scale depending on curve size: the chosen reference is 256-bit,
+         * and multiplication is quadratic. Round to the closest integer. */
+        if( grp->pbits >= 512 )
+            ops *= 4;
+        else if( grp->pbits >= 384 )
+            ops *= 2;
+
+        /* Avoid infinite loops: always allow first step.
+         * Because of that, however, it's not generally true
+         * that ops_done <= ecp_max_ops, so the check
+         * ops_done > ecp_max_ops below is mandatory. */
+        if( ( rs_ctx->ops_done != 0 ) &&
+            ( rs_ctx->ops_done > ecp_max_ops ||
+              ops > ecp_max_ops - rs_ctx->ops_done ) )
+        {
+            return( MBEDTLS_ERR_ECP_IN_PROGRESS );
+        }
+
+        /* update running count */
+        rs_ctx->ops_done += ops;
+    }
+
+    return( 0 );
+}
+
+/* Call this when entering a function that needs its own sub-context */
+#define ECP_RS_ENTER( SUB )   do {                                      \
+    /* reset ops count for this call if top-level */                    \
+    if( rs_ctx != NULL && rs_ctx->depth++ == 0 )                        \
+        rs_ctx->ops_done = 0;                                           \
+                                                                        \
+    /* set up our own sub-context if needed */                          \
+    if( mbedtls_ecp_restart_is_enabled() &&                             \
+        rs_ctx != NULL && rs_ctx->SUB == NULL )                         \
+    {                                                                   \
+        rs_ctx->SUB = mbedtls_calloc( 1, sizeof( *rs_ctx->SUB ) );      \
+        if( rs_ctx->SUB == NULL )                                       \
+            return( MBEDTLS_ERR_ECP_ALLOC_FAILED );                     \
+                                                                        \
+        ecp_restart_## SUB ##_init( rs_ctx->SUB );                      \
+    }                                                                   \
+} while( 0 )
+
+/* Call this when leaving a function that needs its own sub-context */
+#define ECP_RS_LEAVE( SUB )   do {                                      \
+    /* clear our sub-context when not in progress (done or error) */    \
+    if( rs_ctx != NULL && rs_ctx->SUB != NULL &&                        \
+        ret != MBEDTLS_ERR_ECP_IN_PROGRESS )                            \
+    {                                                                   \
+        ecp_restart_## SUB ##_free( rs_ctx->SUB );                      \
+        mbedtls_free( rs_ctx->SUB );                                    \
+        rs_ctx->SUB = NULL;                                             \
+    }                                                                   \
+                                                                        \
+    if( rs_ctx != NULL )                                                \
+        rs_ctx->depth--;                                                \
+} while( 0 )
+
+#else /* MBEDTLS_ECP_RESTARTABLE */
+
+#define ECP_RS_ENTER( sub )     (void) rs_ctx;
+#define ECP_RS_LEAVE( sub )     (void) rs_ctx;
+
+#endif /* MBEDTLS_ECP_RESTARTABLE */
+
+/*
+ * List of supported curves:
+ *  - internal ID
+ *  - TLS NamedCurve ID (RFC 4492 sec. 5.1.1, RFC 7071 sec. 2, RFC 8446 sec. 4.2.7)
+ *  - size in bits
+ *  - readable name
+ *
+ * Curves are listed in order: largest curves first, and for a given size,
+ * fastest curves first. This provides the default order for the SSL module.
+ *
+ * Reminder: update profiles in x509_crt.c when adding a new curves!
+ */
+static const mbedtls_ecp_curve_info ecp_supported_curves[] =
+{
+#if defined(MBEDTLS_ECP_DP_SECP521R1_ENABLED)
+    { MBEDTLS_ECP_DP_SECP521R1,    25,     521,    "secp521r1"         },
+#endif
+#if defined(MBEDTLS_ECP_DP_BP512R1_ENABLED)
+    { MBEDTLS_ECP_DP_BP512R1,      28,     512,    "brainpoolP512r1"   },
+#endif
+#if defined(MBEDTLS_ECP_DP_SECP384R1_ENABLED)
+    { MBEDTLS_ECP_DP_SECP384R1,    24,     384,    "secp384r1"         },
+#endif
+#if defined(MBEDTLS_ECP_DP_BP384R1_ENABLED)
+    { MBEDTLS_ECP_DP_BP384R1,      27,     384,    "brainpoolP384r1"   },
+#endif
+#if defined(MBEDTLS_ECP_DP_SECP256R1_ENABLED)
+    { MBEDTLS_ECP_DP_SECP256R1,    23,     256,    "secp256r1"         },
+#endif
+#if defined(MBEDTLS_ECP_DP_SECP256K1_ENABLED)
+    { MBEDTLS_ECP_DP_SECP256K1,    22,     256,    "secp256k1"         },
+#endif
+#if defined(MBEDTLS_ECP_DP_BP256R1_ENABLED)
+    { MBEDTLS_ECP_DP_BP256R1,      26,     256,    "brainpoolP256r1"   },
+#endif
+#if defined(MBEDTLS_ECP_DP_SECP224R1_ENABLED)
+    { MBEDTLS_ECP_DP_SECP224R1,    21,     224,    "secp224r1"         },
+#endif
+#if defined(MBEDTLS_ECP_DP_SECP224K1_ENABLED)
+    { MBEDTLS_ECP_DP_SECP224K1,    20,     224,    "secp224k1"         },
+#endif
+#if defined(MBEDTLS_ECP_DP_SECP192R1_ENABLED)
+    { MBEDTLS_ECP_DP_SECP192R1,    19,     192,    "secp192r1"         },
+#endif
+#if defined(MBEDTLS_ECP_DP_SECP192K1_ENABLED)
+    { MBEDTLS_ECP_DP_SECP192K1,    18,     192,    "secp192k1"         },
+#endif
+#if defined(MBEDTLS_ECP_DP_CURVE25519_ENABLED)
+    { MBEDTLS_ECP_DP_CURVE25519,   29,     256,    "x25519"            },
+#endif
+#if defined(MBEDTLS_ECP_DP_CURVE448_ENABLED)
+    { MBEDTLS_ECP_DP_CURVE448,     30,     448,    "x448"              },
+#endif
+    { MBEDTLS_ECP_DP_NONE,          0,     0,      NULL                },
+};
+
+#define ECP_NB_CURVES   sizeof( ecp_supported_curves ) /    \
+                        sizeof( ecp_supported_curves[0] )
+
+static mbedtls_ecp_group_id ecp_supported_grp_id[ECP_NB_CURVES];
+
+/*
+ * List of supported curves and associated info
+ */
+const mbedtls_ecp_curve_info *mbedtls_ecp_curve_list( void )
+{
+    return( ecp_supported_curves );
+}
+
+/*
+ * List of supported curves, group ID only
+ */
+const mbedtls_ecp_group_id *mbedtls_ecp_grp_id_list( void )
+{
+    static int init_done = 0;
+
+    if( ! init_done )
+    {
+        size_t i = 0;
+        const mbedtls_ecp_curve_info *curve_info;
+
+        for( curve_info = mbedtls_ecp_curve_list();
+             curve_info->grp_id != MBEDTLS_ECP_DP_NONE;
+             curve_info++ )
+        {
+            ecp_supported_grp_id[i++] = curve_info->grp_id;
+        }
+        ecp_supported_grp_id[i] = MBEDTLS_ECP_DP_NONE;
+
+        init_done = 1;
+    }
+
+    return( ecp_supported_grp_id );
+}
+
+/*
+ * Get the curve info for the internal identifier
+ */
+const mbedtls_ecp_curve_info *mbedtls_ecp_curve_info_from_grp_id( mbedtls_ecp_group_id grp_id )
+{
+    const mbedtls_ecp_curve_info *curve_info;
+
+    for( curve_info = mbedtls_ecp_curve_list();
+         curve_info->grp_id != MBEDTLS_ECP_DP_NONE;
+         curve_info++ )
+    {
+        if( curve_info->grp_id == grp_id )
+            return( curve_info );
+    }
+
+    return( NULL );
+}
+
+/*
+ * Get the curve info from the TLS identifier
+ */
+const mbedtls_ecp_curve_info *mbedtls_ecp_curve_info_from_tls_id( uint16_t tls_id )
+{
+    const mbedtls_ecp_curve_info *curve_info;
+
+    for( curve_info = mbedtls_ecp_curve_list();
+         curve_info->grp_id != MBEDTLS_ECP_DP_NONE;
+         curve_info++ )
+    {
+        if( curve_info->tls_id == tls_id )
+            return( curve_info );
+    }
+
+    return( NULL );
+}
+
+/*
+ * Get the curve info from the name
+ */
+const mbedtls_ecp_curve_info *mbedtls_ecp_curve_info_from_name( const char *name )
+{
+    const mbedtls_ecp_curve_info *curve_info;
+
+    if( name == NULL )
+        return( NULL );
+
+    for( curve_info = mbedtls_ecp_curve_list();
+         curve_info->grp_id != MBEDTLS_ECP_DP_NONE;
+         curve_info++ )
+    {
+        if( strcmp( curve_info->name, name ) == 0 )
+            return( curve_info );
+    }
+
+    return( NULL );
+}
+
+/*
+ * Get the type of a curve
+ */
+mbedtls_ecp_curve_type mbedtls_ecp_get_type( const mbedtls_ecp_group *grp )
+{
+    if( grp->G.X.p == NULL )
+        return( MBEDTLS_ECP_TYPE_NONE );
+
+    if( grp->G.Y.p == NULL )
+        return( MBEDTLS_ECP_TYPE_MONTGOMERY );
+    else
+        return( MBEDTLS_ECP_TYPE_SHORT_WEIERSTRASS );
+}
+
+/*
+ * Initialize (the components of) a point
+ */
+void mbedtls_ecp_point_init( mbedtls_ecp_point *pt )
+{
+    ECP_VALIDATE( pt != NULL );
+
+    mbedtls_mpi_init( &pt->X );
+    mbedtls_mpi_init( &pt->Y );
+    mbedtls_mpi_init( &pt->Z );
+}
+
+/*
+ * Initialize (the components of) a group
+ */
+void mbedtls_ecp_group_init( mbedtls_ecp_group *grp )
+{
+    ECP_VALIDATE( grp != NULL );
+
+    grp->id = MBEDTLS_ECP_DP_NONE;
+    mbedtls_mpi_init( &grp->P );
+    mbedtls_mpi_init( &grp->A );
+    mbedtls_mpi_init( &grp->B );
+    mbedtls_ecp_point_init( &grp->G );
+    mbedtls_mpi_init( &grp->N );
+    grp->pbits = 0;
+    grp->nbits = 0;
+    grp->h = 0;
+    grp->modp = NULL;
+    grp->t_pre = NULL;
+    grp->t_post = NULL;
+    grp->t_data = NULL;
+    grp->T = NULL;
+    grp->T_size = 0;
+}
+
+/*
+ * Initialize (the components of) a key pair
+ */
+void mbedtls_ecp_keypair_init( mbedtls_ecp_keypair *key )
+{
+    ECP_VALIDATE( key != NULL );
+
+    mbedtls_ecp_group_init( &key->grp );
+    mbedtls_mpi_init( &key->d );
+    mbedtls_ecp_point_init( &key->Q );
+}
+
+/*
+ * Unallocate (the components of) a point
+ */
+void mbedtls_ecp_point_free( mbedtls_ecp_point *pt )
+{
+    if( pt == NULL )
+        return;
+
+    mbedtls_mpi_free( &( pt->X ) );
+    mbedtls_mpi_free( &( pt->Y ) );
+    mbedtls_mpi_free( &( pt->Z ) );
+}
+
+/*
+ * Unallocate (the components of) a group
+ */
+void mbedtls_ecp_group_free( mbedtls_ecp_group *grp )
+{
+    size_t i;
+
+    if( grp == NULL )
+        return;
+
+    if( grp->h != 1 )
+    {
+        mbedtls_mpi_free( &grp->P );
+        mbedtls_mpi_free( &grp->A );
+        mbedtls_mpi_free( &grp->B );
+        mbedtls_ecp_point_free( &grp->G );
+        mbedtls_mpi_free( &grp->N );
+    }
+
+    if( grp->T != NULL )
+    {
+        for( i = 0; i < grp->T_size; i++ )
+            mbedtls_ecp_point_free( &grp->T[i] );
+        mbedtls_free( grp->T );
+    }
+
+    mbedtls_platform_zeroize( grp, sizeof( mbedtls_ecp_group ) );
+}
+
+/*
+ * Unallocate (the components of) a key pair
+ */
+void mbedtls_ecp_keypair_free( mbedtls_ecp_keypair *key )
+{
+    if( key == NULL )
+        return;
+
+    mbedtls_ecp_group_free( &key->grp );
+    mbedtls_mpi_free( &key->d );
+    mbedtls_ecp_point_free( &key->Q );
+}
+
+/*
+ * Copy the contents of a point
+ */
+int mbedtls_ecp_copy( mbedtls_ecp_point *P, const mbedtls_ecp_point *Q )
+{
+    int ret = MBEDTLS_ERR_ERROR_CORRUPTION_DETECTED;
+    ECP_VALIDATE_RET( P != NULL );
+    ECP_VALIDATE_RET( Q != NULL );
+
+    MBEDTLS_MPI_CHK( mbedtls_mpi_copy( &P->X, &Q->X ) );
+    MBEDTLS_MPI_CHK( mbedtls_mpi_copy( &P->Y, &Q->Y ) );
+    MBEDTLS_MPI_CHK( mbedtls_mpi_copy( &P->Z, &Q->Z ) );
+
+cleanup:
+    return( ret );
+}
+
+/*
+ * Copy the contents of a group object
+ */
+int mbedtls_ecp_group_copy( mbedtls_ecp_group *dst, const mbedtls_ecp_group *src )
+{
+    ECP_VALIDATE_RET( dst != NULL );
+    ECP_VALIDATE_RET( src != NULL );
+
+    return( mbedtls_ecp_group_load( dst, src->id ) );
+}
+
+/*
+ * Set point to zero
+ */
+int mbedtls_ecp_set_zero( mbedtls_ecp_point *pt )
+{
+    int ret = MBEDTLS_ERR_ERROR_CORRUPTION_DETECTED;
+    ECP_VALIDATE_RET( pt != NULL );
+
+    MBEDTLS_MPI_CHK( mbedtls_mpi_lset( &pt->X , 1 ) );
+    MBEDTLS_MPI_CHK( mbedtls_mpi_lset( &pt->Y , 1 ) );
+    MBEDTLS_MPI_CHK( mbedtls_mpi_lset( &pt->Z , 0 ) );
+
+cleanup:
+    return( ret );
+}
+
+/*
+ * Tell if a point is zero
+ */
+int mbedtls_ecp_is_zero( mbedtls_ecp_point *pt )
+{
+    ECP_VALIDATE_RET( pt != NULL );
+
+    return( mbedtls_mpi_cmp_int( &pt->Z, 0 ) == 0 );
+}
+
+/*
+ * Compare two points lazily
+ */
+int mbedtls_ecp_point_cmp( const mbedtls_ecp_point *P,
+                           const mbedtls_ecp_point *Q )
+{
+    ECP_VALIDATE_RET( P != NULL );
+    ECP_VALIDATE_RET( Q != NULL );
+
+    if( mbedtls_mpi_cmp_mpi( &P->X, &Q->X ) == 0 &&
+        mbedtls_mpi_cmp_mpi( &P->Y, &Q->Y ) == 0 &&
+        mbedtls_mpi_cmp_mpi( &P->Z, &Q->Z ) == 0 )
+    {
+        return( 0 );
+    }
+
+    return( MBEDTLS_ERR_ECP_BAD_INPUT_DATA );
+}
+
+/*
+ * Import a non-zero point from ASCII strings
+ */
+int mbedtls_ecp_point_read_string( mbedtls_ecp_point *P, int radix,
+                           const char *x, const char *y )
+{
+    int ret = MBEDTLS_ERR_ERROR_CORRUPTION_DETECTED;
+    ECP_VALIDATE_RET( P != NULL );
+    ECP_VALIDATE_RET( x != NULL );
+    ECP_VALIDATE_RET( y != NULL );
+
+    MBEDTLS_MPI_CHK( mbedtls_mpi_read_string( &P->X, radix, x ) );
+    MBEDTLS_MPI_CHK( mbedtls_mpi_read_string( &P->Y, radix, y ) );
+    MBEDTLS_MPI_CHK( mbedtls_mpi_lset( &P->Z, 1 ) );
+
+cleanup:
+    return( ret );
+}
+
+/*
+ * Export a point into unsigned binary data (SEC1 2.3.3 and RFC7748)
+ */
+int mbedtls_ecp_point_write_binary( const mbedtls_ecp_group *grp,
+                                    const mbedtls_ecp_point *P,
+                                    int format, size_t *olen,
+                                    unsigned char *buf, size_t buflen )
+{
+    int ret = MBEDTLS_ERR_ECP_FEATURE_UNAVAILABLE;
+    size_t plen;
+    ECP_VALIDATE_RET( grp  != NULL );
+    ECP_VALIDATE_RET( P    != NULL );
+    ECP_VALIDATE_RET( olen != NULL );
+    ECP_VALIDATE_RET( buf  != NULL );
+    ECP_VALIDATE_RET( format == MBEDTLS_ECP_PF_UNCOMPRESSED ||
+                      format == MBEDTLS_ECP_PF_COMPRESSED );
+
+    plen = mbedtls_mpi_size( &grp->P );
+
+#if defined(MBEDTLS_ECP_MONTGOMERY_ENABLED)
+    (void) format; /* Montgomery curves always use the same point format */
+    if( mbedtls_ecp_get_type( grp ) == MBEDTLS_ECP_TYPE_MONTGOMERY )
+    {
+        *olen = plen;
+        if( buflen < *olen )
+            return( MBEDTLS_ERR_ECP_BUFFER_TOO_SMALL );
+
+        MBEDTLS_MPI_CHK( mbedtls_mpi_write_binary_le( &P->X, buf, plen ) );
+    }
+#endif
+#if defined(MBEDTLS_ECP_SHORT_WEIERSTRASS_ENABLED)
+    if( mbedtls_ecp_get_type( grp ) == MBEDTLS_ECP_TYPE_SHORT_WEIERSTRASS )
+    {
+        /*
+         * Common case: P == 0
+         */
+        if( mbedtls_mpi_cmp_int( &P->Z, 0 ) == 0 )
+        {
+            if( buflen < 1 )
+                return( MBEDTLS_ERR_ECP_BUFFER_TOO_SMALL );
+
+            buf[0] = 0x00;
+            *olen = 1;
+
+            return( 0 );
+        }
+
+        if( format == MBEDTLS_ECP_PF_UNCOMPRESSED )
+        {
+            *olen = 2 * plen + 1;
+
+            if( buflen < *olen )
+                return( MBEDTLS_ERR_ECP_BUFFER_TOO_SMALL );
+
+            buf[0] = 0x04;
+            MBEDTLS_MPI_CHK( mbedtls_mpi_write_binary( &P->X, buf + 1, plen ) );
+            MBEDTLS_MPI_CHK( mbedtls_mpi_write_binary( &P->Y, buf + 1 + plen, plen ) );
+        }
+        else if( format == MBEDTLS_ECP_PF_COMPRESSED )
+        {
+            *olen = plen + 1;
+
+            if( buflen < *olen )
+                return( MBEDTLS_ERR_ECP_BUFFER_TOO_SMALL );
+
+            buf[0] = 0x02 + mbedtls_mpi_get_bit( &P->Y, 0 );
+            MBEDTLS_MPI_CHK( mbedtls_mpi_write_binary( &P->X, buf + 1, plen ) );
+        }
+    }
+#endif
+
+cleanup:
+    return( ret );
+}
+
+/*
+ * Import a point from unsigned binary data (SEC1 2.3.4 and RFC7748)
+ */
+int mbedtls_ecp_point_read_binary( const mbedtls_ecp_group *grp,
+                                   mbedtls_ecp_point *pt,
+                                   const unsigned char *buf, size_t ilen )
+{
+    int ret = MBEDTLS_ERR_ECP_FEATURE_UNAVAILABLE;
+    size_t plen;
+    ECP_VALIDATE_RET( grp != NULL );
+    ECP_VALIDATE_RET( pt  != NULL );
+    ECP_VALIDATE_RET( buf != NULL );
+
+    if( ilen < 1 )
+        return( MBEDTLS_ERR_ECP_BAD_INPUT_DATA );
+
+    plen = mbedtls_mpi_size( &grp->P );
+
+#if defined(MBEDTLS_ECP_MONTGOMERY_ENABLED)
+    if( mbedtls_ecp_get_type( grp ) == MBEDTLS_ECP_TYPE_MONTGOMERY )
+    {
+        if( plen != ilen )
+            return( MBEDTLS_ERR_ECP_BAD_INPUT_DATA );
+
+        MBEDTLS_MPI_CHK( mbedtls_mpi_read_binary_le( &pt->X, buf, plen ) );
+        mbedtls_mpi_free( &pt->Y );
+
+        if( grp->id == MBEDTLS_ECP_DP_CURVE25519 )
+            /* Set most significant bit to 0 as prescribed in RFC7748 §5 */
+            MBEDTLS_MPI_CHK( mbedtls_mpi_set_bit( &pt->X, plen * 8 - 1, 0 ) );
+
+        MBEDTLS_MPI_CHK( mbedtls_mpi_lset( &pt->Z, 1 ) );
+    }
+#endif
+#if defined(MBEDTLS_ECP_SHORT_WEIERSTRASS_ENABLED)
+    if( mbedtls_ecp_get_type( grp ) == MBEDTLS_ECP_TYPE_SHORT_WEIERSTRASS )
+    {
+        if( buf[0] == 0x00 )
+        {
+            if( ilen == 1 )
+                return( mbedtls_ecp_set_zero( pt ) );
+            else
+                return( MBEDTLS_ERR_ECP_BAD_INPUT_DATA );
+        }
+
+        if( buf[0] != 0x04 )
+            return( MBEDTLS_ERR_ECP_FEATURE_UNAVAILABLE );
+
+        if( ilen != 2 * plen + 1 )
+            return( MBEDTLS_ERR_ECP_BAD_INPUT_DATA );
+
+        MBEDTLS_MPI_CHK( mbedtls_mpi_read_binary( &pt->X, buf + 1, plen ) );
+        MBEDTLS_MPI_CHK( mbedtls_mpi_read_binary( &pt->Y,
+                                                  buf + 1 + plen, plen ) );
+        MBEDTLS_MPI_CHK( mbedtls_mpi_lset( &pt->Z, 1 ) );
+    }
+#endif
+
+cleanup:
+    return( ret );
+}
+
+/*
+ * Import a point from a TLS ECPoint record (RFC 4492)
+ *      struct {
+ *          opaque point <1..2^8-1>;
+ *      } ECPoint;
+ */
+int mbedtls_ecp_tls_read_point( const mbedtls_ecp_group *grp,
+                                mbedtls_ecp_point *pt,
+                                const unsigned char **buf, size_t buf_len )
+{
+    unsigned char data_len;
+    const unsigned char *buf_start;
+    ECP_VALIDATE_RET( grp != NULL );
+    ECP_VALIDATE_RET( pt  != NULL );
+    ECP_VALIDATE_RET( buf != NULL );
+    ECP_VALIDATE_RET( *buf != NULL );
+
+    /*
+     * We must have at least two bytes (1 for length, at least one for data)
+     */
+    if( buf_len < 2 )
+        return( MBEDTLS_ERR_ECP_BAD_INPUT_DATA );
+
+    data_len = *(*buf)++;
+    if( data_len < 1 || data_len > buf_len - 1 )
+        return( MBEDTLS_ERR_ECP_BAD_INPUT_DATA );
+
+    /*
+     * Save buffer start for read_binary and update buf
+     */
+    buf_start = *buf;
+    *buf += data_len;
+
+    return( mbedtls_ecp_point_read_binary( grp, pt, buf_start, data_len ) );
+}
+
+/*
+ * Export a point as a TLS ECPoint record (RFC 4492)
+ *      struct {
+ *          opaque point <1..2^8-1>;
+ *      } ECPoint;
+ */
+int mbedtls_ecp_tls_write_point( const mbedtls_ecp_group *grp, const mbedtls_ecp_point *pt,
+                         int format, size_t *olen,
+                         unsigned char *buf, size_t blen )
+{
+    int ret = MBEDTLS_ERR_ERROR_CORRUPTION_DETECTED;
+    ECP_VALIDATE_RET( grp  != NULL );
+    ECP_VALIDATE_RET( pt   != NULL );
+    ECP_VALIDATE_RET( olen != NULL );
+    ECP_VALIDATE_RET( buf  != NULL );
+    ECP_VALIDATE_RET( format == MBEDTLS_ECP_PF_UNCOMPRESSED ||
+                      format == MBEDTLS_ECP_PF_COMPRESSED );
+
+    /*
+     * buffer length must be at least one, for our length byte
+     */
+    if( blen < 1 )
+        return( MBEDTLS_ERR_ECP_BAD_INPUT_DATA );
+
+    if( ( ret = mbedtls_ecp_point_write_binary( grp, pt, format,
+                    olen, buf + 1, blen - 1) ) != 0 )
+        return( ret );
+
+    /*
+     * write length to the first byte and update total length
+     */
+    buf[0] = (unsigned char) *olen;
+    ++*olen;
+
+    return( 0 );
+}
+
+/*
+ * Set a group from an ECParameters record (RFC 4492)
+ */
+int mbedtls_ecp_tls_read_group( mbedtls_ecp_group *grp,
+                                const unsigned char **buf, size_t len )
+{
+    int ret = MBEDTLS_ERR_ERROR_CORRUPTION_DETECTED;
+    mbedtls_ecp_group_id grp_id;
+    ECP_VALIDATE_RET( grp  != NULL );
+    ECP_VALIDATE_RET( buf  != NULL );
+    ECP_VALIDATE_RET( *buf != NULL );
+
+    if( ( ret = mbedtls_ecp_tls_read_group_id( &grp_id, buf, len ) ) != 0 )
+        return( ret );
+
+    return( mbedtls_ecp_group_load( grp, grp_id ) );
+}
+
+/*
+ * Read a group id from an ECParameters record (RFC 4492) and convert it to
+ * mbedtls_ecp_group_id.
+ */
+int mbedtls_ecp_tls_read_group_id( mbedtls_ecp_group_id *grp,
+                                   const unsigned char **buf, size_t len )
+{
+    uint16_t tls_id;
+    const mbedtls_ecp_curve_info *curve_info;
+    ECP_VALIDATE_RET( grp  != NULL );
+    ECP_VALIDATE_RET( buf  != NULL );
+    ECP_VALIDATE_RET( *buf != NULL );
+
+    /*
+     * We expect at least three bytes (see below)
+     */
+    if( len < 3 )
+        return( MBEDTLS_ERR_ECP_BAD_INPUT_DATA );
+
+    /*
+     * First byte is curve_type; only named_curve is handled
+     */
+    if( *(*buf)++ != MBEDTLS_ECP_TLS_NAMED_CURVE )
+        return( MBEDTLS_ERR_ECP_BAD_INPUT_DATA );
+
+    /*
+     * Next two bytes are the namedcurve value
+     */
+    tls_id = *(*buf)++;
+    tls_id <<= 8;
+    tls_id |= *(*buf)++;
+
+    if( ( curve_info = mbedtls_ecp_curve_info_from_tls_id( tls_id ) ) == NULL )
+        return( MBEDTLS_ERR_ECP_FEATURE_UNAVAILABLE );
+
+    *grp = curve_info->grp_id;
+
+    return( 0 );
+}
+
+/*
+ * Write the ECParameters record corresponding to a group (RFC 4492)
+ */
+int mbedtls_ecp_tls_write_group( const mbedtls_ecp_group *grp, size_t *olen,
+                         unsigned char *buf, size_t blen )
+{
+    const mbedtls_ecp_curve_info *curve_info;
+    ECP_VALIDATE_RET( grp  != NULL );
+    ECP_VALIDATE_RET( buf  != NULL );
+    ECP_VALIDATE_RET( olen != NULL );
+
+    if( ( curve_info = mbedtls_ecp_curve_info_from_grp_id( grp->id ) ) == NULL )
+        return( MBEDTLS_ERR_ECP_BAD_INPUT_DATA );
+
+    /*
+     * We are going to write 3 bytes (see below)
+     */
+    *olen = 3;
+    if( blen < *olen )
+        return( MBEDTLS_ERR_ECP_BUFFER_TOO_SMALL );
+
+    /*
+     * First byte is curve_type, always named_curve
+     */
+    *buf++ = MBEDTLS_ECP_TLS_NAMED_CURVE;
+
+    /*
+     * Next two bytes are the namedcurve value
+     */
+    buf[0] = curve_info->tls_id >> 8;
+    buf[1] = curve_info->tls_id & 0xFF;
+
+    return( 0 );
+}
+
+/*
+ * Wrapper around fast quasi-modp functions, with fall-back to mbedtls_mpi_mod_mpi.
+ * See the documentation of struct mbedtls_ecp_group.
+ *
+ * This function is in the critial loop for mbedtls_ecp_mul, so pay attention to perf.
+ */
+static int ecp_modp( mbedtls_mpi *N, const mbedtls_ecp_group *grp )
+{
+    int ret = MBEDTLS_ERR_ERROR_CORRUPTION_DETECTED;
+
+    if( grp->modp == NULL )
+        return( mbedtls_mpi_mod_mpi( N, N, &grp->P ) );
+
+    /* N->s < 0 is a much faster test, which fails only if N is 0 */
+    if( ( N->s < 0 && mbedtls_mpi_cmp_int( N, 0 ) != 0 ) ||
+        mbedtls_mpi_bitlen( N ) > 2 * grp->pbits )
+    {
+        return( MBEDTLS_ERR_ECP_BAD_INPUT_DATA );
+    }
+
+    MBEDTLS_MPI_CHK( grp->modp( N ) );
+
+    /* N->s < 0 is a much faster test, which fails only if N is 0 */
+    while( N->s < 0 && mbedtls_mpi_cmp_int( N, 0 ) != 0 )
+        MBEDTLS_MPI_CHK( mbedtls_mpi_add_mpi( N, N, &grp->P ) );
+
+    while( mbedtls_mpi_cmp_mpi( N, &grp->P ) >= 0 )
+        /* we known P, N and the result are positive */
+        MBEDTLS_MPI_CHK( mbedtls_mpi_sub_abs( N, N, &grp->P ) );
+
+cleanup:
+    return( ret );
+}
+
+/*
+ * Fast mod-p functions expect their argument to be in the 0..p^2 range.
+ *
+ * In order to guarantee that, we need to ensure that operands of
+ * mbedtls_mpi_mul_mpi are in the 0..p range. So, after each operation we will
+ * bring the result back to this range.
+ *
+ * The following macros are shortcuts for doing that.
+ */
+
+/*
+ * Reduce a mbedtls_mpi mod p in-place, general case, to use after mbedtls_mpi_mul_mpi
+ */
+#if defined(MBEDTLS_SELF_TEST)
+#define INC_MUL_COUNT   mul_count++;
+#else
+#define INC_MUL_COUNT
+#endif
+
+#define MOD_MUL( N )                                                    \
+    do                                                                  \
+    {                                                                   \
+        MBEDTLS_MPI_CHK( ecp_modp( &(N), grp ) );                       \
+        INC_MUL_COUNT                                                   \
+    } while( 0 )
+
+static inline int mbedtls_mpi_mul_mod( const mbedtls_ecp_group *grp,
+                                       mbedtls_mpi *X,
+                                       const mbedtls_mpi *A,
+                                       const mbedtls_mpi *B )
+{
+    int ret = MBEDTLS_ERR_ERROR_CORRUPTION_DETECTED;
+    MBEDTLS_MPI_CHK( mbedtls_mpi_mul_mpi( X, A, B ) );
+    MOD_MUL( *X );
+cleanup:
+    return( ret );
+}
+
+/*
+ * Reduce a mbedtls_mpi mod p in-place, to use after mbedtls_mpi_sub_mpi
+ * N->s < 0 is a very fast test, which fails only if N is 0
+ */
+#define MOD_SUB( N )                                                    \
+    while( (N).s < 0 && mbedtls_mpi_cmp_int( &(N), 0 ) != 0 )           \
+        MBEDTLS_MPI_CHK( mbedtls_mpi_add_mpi( &(N), &(N), &grp->P ) )
+
+#if ( defined(MBEDTLS_ECP_SHORT_WEIERSTRASS_ENABLED) && \
+      !( defined(MBEDTLS_ECP_NO_FALLBACK) && \
+         defined(MBEDTLS_ECP_DOUBLE_JAC_ALT) && \
+         defined(MBEDTLS_ECP_ADD_MIXED_ALT) ) ) || \
+    ( defined(MBEDTLS_ECP_MONTGOMERY_ENABLED) && \
+      !( defined(MBEDTLS_ECP_NO_FALLBACK) && \
+         defined(MBEDTLS_ECP_DOUBLE_ADD_MXZ_ALT) ) )
+static inline int mbedtls_mpi_sub_mod( const mbedtls_ecp_group *grp,
+                                       mbedtls_mpi *X,
+                                       const mbedtls_mpi *A,
+                                       const mbedtls_mpi *B )
+{
+    int ret = MBEDTLS_ERR_ERROR_CORRUPTION_DETECTED;
+    MBEDTLS_MPI_CHK( mbedtls_mpi_sub_mpi( X, A, B ) );
+    MOD_SUB( *X );
+cleanup:
+    return( ret );
+}
+#endif /* All functions referencing mbedtls_mpi_sub_mod() are alt-implemented without fallback */
+
+/*
+ * Reduce a mbedtls_mpi mod p in-place, to use after mbedtls_mpi_add_mpi and mbedtls_mpi_mul_int.
+ * We known P, N and the result are positive, so sub_abs is correct, and
+ * a bit faster.
+ */
+#define MOD_ADD( N )                                                    \
+    while( mbedtls_mpi_cmp_mpi( &(N), &grp->P ) >= 0 )                  \
+        MBEDTLS_MPI_CHK( mbedtls_mpi_sub_abs( &(N), &(N), &grp->P ) )
+
+static inline int mbedtls_mpi_add_mod( const mbedtls_ecp_group *grp,
+                                       mbedtls_mpi *X,
+                                       const mbedtls_mpi *A,
+                                       const mbedtls_mpi *B )
+{
+    int ret = MBEDTLS_ERR_ERROR_CORRUPTION_DETECTED;
+    MBEDTLS_MPI_CHK( mbedtls_mpi_add_mpi( X, A, B ) );
+    MOD_ADD( *X );
+cleanup:
+    return( ret );
+}
+
+#if defined(MBEDTLS_ECP_SHORT_WEIERSTRASS_ENABLED) && \
+    !( defined(MBEDTLS_ECP_NO_FALLBACK) && \
+       defined(MBEDTLS_ECP_DOUBLE_JAC_ALT) && \
+       defined(MBEDTLS_ECP_ADD_MIXED_ALT) )
+static inline int mbedtls_mpi_shift_l_mod( const mbedtls_ecp_group *grp,
+                                           mbedtls_mpi *X,
+                                           size_t count )
+{
+    int ret = MBEDTLS_ERR_ERROR_CORRUPTION_DETECTED;
+    MBEDTLS_MPI_CHK( mbedtls_mpi_shift_l( X, count ) );
+    MOD_ADD( *X );
+cleanup:
+    return( ret );
+}
+#endif /* All functions referencing mbedtls_mpi_shift_l_mod() are alt-implemented without fallback */
+
+#if defined(MBEDTLS_ECP_SHORT_WEIERSTRASS_ENABLED)
+/*
+ * For curves in short Weierstrass form, we do all the internal operations in
+ * Jacobian coordinates.
+ *
+ * For multiplication, we'll use a comb method with coutermeasueres against
+ * SPA, hence timing attacks.
+ */
+
+/*
+ * Normalize jacobian coordinates so that Z == 0 || Z == 1  (GECC 3.2.1)
+ * Cost: 1N := 1I + 3M + 1S
+ */
+static int ecp_normalize_jac( const mbedtls_ecp_group *grp, mbedtls_ecp_point *pt )
+{
+    if( mbedtls_mpi_cmp_int( &pt->Z, 0 ) == 0 )
+        return( 0 );
+
+#if defined(MBEDTLS_ECP_NORMALIZE_JAC_ALT)
+    if( mbedtls_internal_ecp_grp_capable( grp ) )
+        return( mbedtls_internal_ecp_normalize_jac( grp, pt ) );
+#endif /* MBEDTLS_ECP_NORMALIZE_JAC_ALT */
+
+#if defined(MBEDTLS_ECP_NO_FALLBACK) && defined(MBEDTLS_ECP_NORMALIZE_JAC_ALT)
+    return( MBEDTLS_ERR_ECP_FEATURE_UNAVAILABLE );
+#else
+    int ret = MBEDTLS_ERR_ERROR_CORRUPTION_DETECTED;
+    mbedtls_mpi Zi, ZZi;
+    mbedtls_mpi_init( &Zi ); mbedtls_mpi_init( &ZZi );
+
+    /*
+     * X = X / Z^2  mod p
+     */
+    MBEDTLS_MPI_CHK( mbedtls_mpi_inv_mod( &Zi,      &pt->Z,     &grp->P ) );
+    MBEDTLS_MPI_CHK( mbedtls_mpi_mul_mod( grp, &ZZi,     &Zi,        &Zi     ) );
+    MBEDTLS_MPI_CHK( mbedtls_mpi_mul_mod( grp, &pt->X,   &pt->X,     &ZZi    ) );
+
+    /*
+     * Y = Y / Z^3  mod p
+     */
+    MBEDTLS_MPI_CHK( mbedtls_mpi_mul_mod( grp, &pt->Y,   &pt->Y,     &ZZi    ) );
+    MBEDTLS_MPI_CHK( mbedtls_mpi_mul_mod( grp, &pt->Y,   &pt->Y,     &Zi     ) );
+
+    /*
+     * Z = 1
+     */
+    MBEDTLS_MPI_CHK( mbedtls_mpi_lset( &pt->Z, 1 ) );
+
+cleanup:
+
+    mbedtls_mpi_free( &Zi ); mbedtls_mpi_free( &ZZi );
+
+    return( ret );
+#endif /* !defined(MBEDTLS_ECP_NO_FALLBACK) || !defined(MBEDTLS_ECP_NORMALIZE_JAC_ALT) */
+}
+
+/*
+ * Normalize jacobian coordinates of an array of (pointers to) points,
+ * using Montgomery's trick to perform only one inversion mod P.
+ * (See for example Cohen's "A Course in Computational Algebraic Number
+ * Theory", Algorithm 10.3.4.)
+ *
+ * Warning: fails (returning an error) if one of the points is zero!
+ * This should never happen, see choice of w in ecp_mul_comb().
+ *
+ * Cost: 1N(t) := 1I + (6t - 3)M + 1S
+ */
+static int ecp_normalize_jac_many( const mbedtls_ecp_group *grp,
+                                   mbedtls_ecp_point *T[], size_t T_size )
+{
+    if( T_size < 2 )
+        return( ecp_normalize_jac( grp, *T ) );
+
+#if defined(MBEDTLS_ECP_NORMALIZE_JAC_MANY_ALT)
+    if( mbedtls_internal_ecp_grp_capable( grp ) )
+        return( mbedtls_internal_ecp_normalize_jac_many( grp, T, T_size ) );
+#endif
+
+#if defined(MBEDTLS_ECP_NO_FALLBACK) && defined(MBEDTLS_ECP_NORMALIZE_JAC_MANY_ALT)
+    return( MBEDTLS_ERR_ECP_FEATURE_UNAVAILABLE );
+#else
+    int ret = MBEDTLS_ERR_ERROR_CORRUPTION_DETECTED;
+    size_t i;
+    mbedtls_mpi *c, u, Zi, ZZi;
+
+    if( ( c = mbedtls_calloc( T_size, sizeof( mbedtls_mpi ) ) ) == NULL )
+        return( MBEDTLS_ERR_ECP_ALLOC_FAILED );
+
+    for( i = 0; i < T_size; i++ )
+        mbedtls_mpi_init( &c[i] );
+
+    mbedtls_mpi_init( &u ); mbedtls_mpi_init( &Zi ); mbedtls_mpi_init( &ZZi );
+
+    /*
+     * c[i] = Z_0 * ... * Z_i
+     */
+    MBEDTLS_MPI_CHK( mbedtls_mpi_copy( &c[0], &T[0]->Z ) );
+    for( i = 1; i < T_size; i++ )
+    {
+        MBEDTLS_MPI_CHK( mbedtls_mpi_mul_mod( grp, &c[i], &c[i-1], &T[i]->Z ) );
+    }
+
+    /*
+     * u = 1 / (Z_0 * ... * Z_n) mod P
+     */
+    MBEDTLS_MPI_CHK( mbedtls_mpi_inv_mod( &u, &c[T_size-1], &grp->P ) );
+
+    for( i = T_size - 1; ; i-- )
+    {
+        /*
+         * Zi = 1 / Z_i mod p
+         * u = 1 / (Z_0 * ... * Z_i) mod P
+         */
+        if( i == 0 ) {
+            MBEDTLS_MPI_CHK( mbedtls_mpi_copy( &Zi, &u ) );
+        }
+        else
+        {
+            MBEDTLS_MPI_CHK( mbedtls_mpi_mul_mod( grp, &Zi, &u, &c[i-1]  ) );
+            MBEDTLS_MPI_CHK( mbedtls_mpi_mul_mod( grp, &u,  &u, &T[i]->Z ) );
+        }
+
+        /*
+         * proceed as in normalize()
+         */
+        MBEDTLS_MPI_CHK( mbedtls_mpi_mul_mod( grp, &ZZi,     &Zi,      &Zi  ) );
+        MBEDTLS_MPI_CHK( mbedtls_mpi_mul_mod( grp, &T[i]->X, &T[i]->X, &ZZi ) );
+        MBEDTLS_MPI_CHK( mbedtls_mpi_mul_mod( grp, &T[i]->Y, &T[i]->Y, &ZZi ) );
+        MBEDTLS_MPI_CHK( mbedtls_mpi_mul_mod( grp, &T[i]->Y, &T[i]->Y, &Zi  ) );
+
+        /*
+         * Post-precessing: reclaim some memory by shrinking coordinates
+         * - not storing Z (always 1)
+         * - shrinking other coordinates, but still keeping the same number of
+         *   limbs as P, as otherwise it will too likely be regrown too fast.
+         */
+        MBEDTLS_MPI_CHK( mbedtls_mpi_shrink( &T[i]->X, grp->P.n ) );
+        MBEDTLS_MPI_CHK( mbedtls_mpi_shrink( &T[i]->Y, grp->P.n ) );
+        mbedtls_mpi_free( &T[i]->Z );
+
+        if( i == 0 )
+            break;
+    }
+
+cleanup:
+
+    mbedtls_mpi_free( &u ); mbedtls_mpi_free( &Zi ); mbedtls_mpi_free( &ZZi );
+    for( i = 0; i < T_size; i++ )
+        mbedtls_mpi_free( &c[i] );
+    mbedtls_free( c );
+
+    return( ret );
+#endif /* !defined(MBEDTLS_ECP_NO_FALLBACK) || !defined(MBEDTLS_ECP_NORMALIZE_JAC_MANY_ALT) */
+}
+
+/*
+ * Conditional point inversion: Q -> -Q = (Q.X, -Q.Y, Q.Z) without leak.
+ * "inv" must be 0 (don't invert) or 1 (invert) or the result will be invalid
+ */
+static int ecp_safe_invert_jac( const mbedtls_ecp_group *grp,
+                            mbedtls_ecp_point *Q,
+                            unsigned char inv )
+{
+    int ret = MBEDTLS_ERR_ERROR_CORRUPTION_DETECTED;
+    unsigned char nonzero;
+    mbedtls_mpi mQY;
+
+    mbedtls_mpi_init( &mQY );
+
+    /* Use the fact that -Q.Y mod P = P - Q.Y unless Q.Y == 0 */
+    MBEDTLS_MPI_CHK( mbedtls_mpi_sub_mpi( &mQY, &grp->P, &Q->Y ) );
+    nonzero = mbedtls_mpi_cmp_int( &Q->Y, 0 ) != 0;
+    MBEDTLS_MPI_CHK( mbedtls_mpi_safe_cond_assign( &Q->Y, &mQY, inv & nonzero ) );
+
+cleanup:
+    mbedtls_mpi_free( &mQY );
+
+    return( ret );
+}
+
+/*
+ * Point doubling R = 2 P, Jacobian coordinates
+ *
+ * Based on http://www.hyperelliptic.org/EFD/g1p/auto-shortw-jacobian.html#doubling-dbl-1998-cmo-2 .
+ *
+ * We follow the variable naming fairly closely. The formula variations that trade a MUL for a SQR
+ * (plus a few ADDs) aren't useful as our bignum implementation doesn't distinguish squaring.
+ *
+ * Standard optimizations are applied when curve parameter A is one of { 0, -3 }.
+ *
+ * Cost: 1D := 3M + 4S          (A ==  0)
+ *             4M + 4S          (A == -3)
+ *             3M + 6S + 1a     otherwise
+ */
+static int ecp_double_jac( const mbedtls_ecp_group *grp, mbedtls_ecp_point *R,
+                           const mbedtls_ecp_point *P )
+{
+#if defined(MBEDTLS_SELF_TEST)
+    dbl_count++;
+#endif
+
+#if defined(MBEDTLS_ECP_DOUBLE_JAC_ALT)
+    if( mbedtls_internal_ecp_grp_capable( grp ) )
+        return( mbedtls_internal_ecp_double_jac( grp, R, P ) );
+#endif /* MBEDTLS_ECP_DOUBLE_JAC_ALT */
+
+#if defined(MBEDTLS_ECP_NO_FALLBACK) && defined(MBEDTLS_ECP_DOUBLE_JAC_ALT)
+    return( MBEDTLS_ERR_ECP_FEATURE_UNAVAILABLE );
+#else
+    int ret = MBEDTLS_ERR_ERROR_CORRUPTION_DETECTED;
+    mbedtls_mpi M, S, T, U;
+
+    mbedtls_mpi_init( &M ); mbedtls_mpi_init( &S ); mbedtls_mpi_init( &T ); mbedtls_mpi_init( &U );
+
+    /* Special case for A = -3 */
+    if( grp->A.p == NULL )
+    {
+        /* M = 3(X + Z^2)(X - Z^2) */
+        MBEDTLS_MPI_CHK( mbedtls_mpi_mul_mod( grp, &S,  &P->Z,  &P->Z   ) );
+        MBEDTLS_MPI_CHK( mbedtls_mpi_add_mod( grp, &T,  &P->X,  &S      ) );
+        MBEDTLS_MPI_CHK( mbedtls_mpi_sub_mod( grp, &U,  &P->X,  &S      ) );
+        MBEDTLS_MPI_CHK( mbedtls_mpi_mul_mod( grp, &S,  &T,     &U      ) );
+        MBEDTLS_MPI_CHK( mbedtls_mpi_mul_int( &M,  &S,     3       ) ); MOD_ADD( M );
+    }
+    else
+    {
+        /* M = 3.X^2 */
+        MBEDTLS_MPI_CHK( mbedtls_mpi_mul_mod( grp, &S,  &P->X,  &P->X   ) );
+        MBEDTLS_MPI_CHK( mbedtls_mpi_mul_int( &M,  &S,     3       ) ); MOD_ADD( M );
+
+        /* Optimize away for "koblitz" curves with A = 0 */
+        if( mbedtls_mpi_cmp_int( &grp->A, 0 ) != 0 )
+        {
+            /* M += A.Z^4 */
+            MBEDTLS_MPI_CHK( mbedtls_mpi_mul_mod( grp, &S,  &P->Z,  &P->Z   ) );
+            MBEDTLS_MPI_CHK( mbedtls_mpi_mul_mod( grp, &T,  &S,     &S      ) );
+            MBEDTLS_MPI_CHK( mbedtls_mpi_mul_mod( grp, &S,  &T,     &grp->A ) );
+            MBEDTLS_MPI_CHK( mbedtls_mpi_add_mod( grp, &M,  &M,     &S      ) );
+        }
+    }
+
+    /* S = 4.X.Y^2 */
+    MBEDTLS_MPI_CHK( mbedtls_mpi_mul_mod( grp, &T,  &P->Y,  &P->Y   ) );
+    MBEDTLS_MPI_CHK( mbedtls_mpi_shift_l_mod( grp, &T,  1               ) );
+    MBEDTLS_MPI_CHK( mbedtls_mpi_mul_mod( grp, &S,  &P->X,  &T      ) );
+    MBEDTLS_MPI_CHK( mbedtls_mpi_shift_l_mod( grp, &S,  1               ) );
+
+    /* U = 8.Y^4 */
+    MBEDTLS_MPI_CHK( mbedtls_mpi_mul_mod( grp, &U,  &T,     &T      ) );
+    MBEDTLS_MPI_CHK( mbedtls_mpi_shift_l_mod( grp, &U,  1               ) );
+
+    /* T = M^2 - 2.S */
+    MBEDTLS_MPI_CHK( mbedtls_mpi_mul_mod( grp, &T,  &M,     &M      ) );
+    MBEDTLS_MPI_CHK( mbedtls_mpi_sub_mod( grp, &T,  &T,     &S      ) );
+    MBEDTLS_MPI_CHK( mbedtls_mpi_sub_mod( grp, &T,  &T,     &S      ) );
+
+    /* S = M(S - T) - U */
+    MBEDTLS_MPI_CHK( mbedtls_mpi_sub_mod( grp, &S,  &S,     &T      ) );
+    MBEDTLS_MPI_CHK( mbedtls_mpi_mul_mod( grp, &S,  &S,     &M      ) );
+    MBEDTLS_MPI_CHK( mbedtls_mpi_sub_mod( grp, &S,  &S,     &U      ) );
+
+    /* U = 2.Y.Z */
+    MBEDTLS_MPI_CHK( mbedtls_mpi_mul_mod( grp, &U,  &P->Y,  &P->Z   ) );
+    MBEDTLS_MPI_CHK( mbedtls_mpi_shift_l_mod( grp, &U,  1               ) );
+
+    MBEDTLS_MPI_CHK( mbedtls_mpi_copy( &R->X, &T ) );
+    MBEDTLS_MPI_CHK( mbedtls_mpi_copy( &R->Y, &S ) );
+    MBEDTLS_MPI_CHK( mbedtls_mpi_copy( &R->Z, &U ) );
+
+cleanup:
+    mbedtls_mpi_free( &M ); mbedtls_mpi_free( &S ); mbedtls_mpi_free( &T ); mbedtls_mpi_free( &U );
+
+    return( ret );
+#endif /* !defined(MBEDTLS_ECP_NO_FALLBACK) || !defined(MBEDTLS_ECP_DOUBLE_JAC_ALT) */
+}
+
+/*
+ * Addition: R = P + Q, mixed affine-Jacobian coordinates (GECC 3.22)
+ *
+ * The coordinates of Q must be normalized (= affine),
+ * but those of P don't need to. R is not normalized.
+ *
+ * Special cases: (1) P or Q is zero, (2) R is zero, (3) P == Q.
+ * None of these cases can happen as intermediate step in ecp_mul_comb():
+ * - at each step, P, Q and R are multiples of the base point, the factor
+ *   being less than its order, so none of them is zero;
+ * - Q is an odd multiple of the base point, P an even multiple,
+ *   due to the choice of precomputed points in the modified comb method.
+ * So branches for these cases do not leak secret information.
+ *
+ * We accept Q->Z being unset (saving memory in tables) as meaning 1.
+ *
+ * Cost: 1A := 8M + 3S
+ */
+static int ecp_add_mixed( const mbedtls_ecp_group *grp, mbedtls_ecp_point *R,
+                          const mbedtls_ecp_point *P, const mbedtls_ecp_point *Q )
+{
+#if defined(MBEDTLS_SELF_TEST)
+    add_count++;
+#endif
+
+#if defined(MBEDTLS_ECP_ADD_MIXED_ALT)
+    if( mbedtls_internal_ecp_grp_capable( grp ) )
+        return( mbedtls_internal_ecp_add_mixed( grp, R, P, Q ) );
+#endif /* MBEDTLS_ECP_ADD_MIXED_ALT */
+
+#if defined(MBEDTLS_ECP_NO_FALLBACK) && defined(MBEDTLS_ECP_ADD_MIXED_ALT)
+    return( MBEDTLS_ERR_ECP_FEATURE_UNAVAILABLE );
+#else
+    int ret = MBEDTLS_ERR_ERROR_CORRUPTION_DETECTED;
+    mbedtls_mpi T1, T2, T3, T4, X, Y, Z;
+
+    /*
+     * Trivial cases: P == 0 or Q == 0 (case 1)
+     */
+    if( mbedtls_mpi_cmp_int( &P->Z, 0 ) == 0 )
+        return( mbedtls_ecp_copy( R, Q ) );
+
+    if( Q->Z.p != NULL && mbedtls_mpi_cmp_int( &Q->Z, 0 ) == 0 )
+        return( mbedtls_ecp_copy( R, P ) );
+
+    /*
+     * Make sure Q coordinates are normalized
+     */
+    if( Q->Z.p != NULL && mbedtls_mpi_cmp_int( &Q->Z, 1 ) != 0 )
+        return( MBEDTLS_ERR_ECP_BAD_INPUT_DATA );
+
+    mbedtls_mpi_init( &T1 ); mbedtls_mpi_init( &T2 ); mbedtls_mpi_init( &T3 ); mbedtls_mpi_init( &T4 );
+    mbedtls_mpi_init( &X ); mbedtls_mpi_init( &Y ); mbedtls_mpi_init( &Z );
+
+    MBEDTLS_MPI_CHK( mbedtls_mpi_mul_mod( grp, &T1,  &P->Z,  &P->Z ) );
+    MBEDTLS_MPI_CHK( mbedtls_mpi_mul_mod( grp, &T2,  &T1,    &P->Z ) );
+    MBEDTLS_MPI_CHK( mbedtls_mpi_mul_mod( grp, &T1,  &T1,    &Q->X ) );
+    MBEDTLS_MPI_CHK( mbedtls_mpi_mul_mod( grp, &T2,  &T2,    &Q->Y ) );
+    MBEDTLS_MPI_CHK( mbedtls_mpi_sub_mod( grp, &T1,  &T1,    &P->X ) );
+    MBEDTLS_MPI_CHK( mbedtls_mpi_sub_mod( grp, &T2,  &T2,    &P->Y ) );
+
+    /* Special cases (2) and (3) */
+    if( mbedtls_mpi_cmp_int( &T1, 0 ) == 0 )
+    {
+        if( mbedtls_mpi_cmp_int( &T2, 0 ) == 0 )
+        {
+            ret = ecp_double_jac( grp, R, P );
+            goto cleanup;
+        }
+        else
+        {
+            ret = mbedtls_ecp_set_zero( R );
+            goto cleanup;
+        }
+    }
+
+    MBEDTLS_MPI_CHK( mbedtls_mpi_mul_mod( grp, &Z,   &P->Z,  &T1   ) );
+    MBEDTLS_MPI_CHK( mbedtls_mpi_mul_mod( grp, &T3,  &T1,    &T1   ) );
+    MBEDTLS_MPI_CHK( mbedtls_mpi_mul_mod( grp, &T4,  &T3,    &T1   ) );
+    MBEDTLS_MPI_CHK( mbedtls_mpi_mul_mod( grp, &T3,  &T3,    &P->X ) );
+    MBEDTLS_MPI_CHK( mbedtls_mpi_copy( &T1, &T3 ) );
+    MBEDTLS_MPI_CHK( mbedtls_mpi_shift_l_mod( grp, &T1,  1     ) );
+    MBEDTLS_MPI_CHK( mbedtls_mpi_mul_mod( grp, &X,   &T2,    &T2   ) );
+    MBEDTLS_MPI_CHK( mbedtls_mpi_sub_mod( grp, &X,   &X,     &T1   ) );
+    MBEDTLS_MPI_CHK( mbedtls_mpi_sub_mod( grp, &X,   &X,     &T4   ) );
+    MBEDTLS_MPI_CHK( mbedtls_mpi_sub_mod( grp, &T3,  &T3,    &X    ) );
+    MBEDTLS_MPI_CHK( mbedtls_mpi_mul_mod( grp, &T3,  &T3,    &T2   ) );
+    MBEDTLS_MPI_CHK( mbedtls_mpi_mul_mod( grp, &T4,  &T4,    &P->Y ) );
+    MBEDTLS_MPI_CHK( mbedtls_mpi_sub_mod( grp, &Y,   &T3,    &T4   ) );
+
+    MBEDTLS_MPI_CHK( mbedtls_mpi_copy( &R->X, &X ) );
+    MBEDTLS_MPI_CHK( mbedtls_mpi_copy( &R->Y, &Y ) );
+    MBEDTLS_MPI_CHK( mbedtls_mpi_copy( &R->Z, &Z ) );
+
+cleanup:
+
+    mbedtls_mpi_free( &T1 ); mbedtls_mpi_free( &T2 ); mbedtls_mpi_free( &T3 ); mbedtls_mpi_free( &T4 );
+    mbedtls_mpi_free( &X ); mbedtls_mpi_free( &Y ); mbedtls_mpi_free( &Z );
+
+    return( ret );
+#endif /* !defined(MBEDTLS_ECP_NO_FALLBACK) || !defined(MBEDTLS_ECP_ADD_MIXED_ALT) */
+}
+
+/*
+ * Randomize jacobian coordinates:
+ * (X, Y, Z) -> (l^2 X, l^3 Y, l Z) for random l
+ * This is sort of the reverse operation of ecp_normalize_jac().
+ *
+ * This countermeasure was first suggested in [2].
+ */
+static int ecp_randomize_jac( const mbedtls_ecp_group *grp, mbedtls_ecp_point *pt,
+                int (*f_rng)(void *, unsigned char *, size_t), void *p_rng )
+{
+#if defined(MBEDTLS_ECP_RANDOMIZE_JAC_ALT)
+    if( mbedtls_internal_ecp_grp_capable( grp ) )
+        return( mbedtls_internal_ecp_randomize_jac( grp, pt, f_rng, p_rng ) );
+#endif /* MBEDTLS_ECP_RANDOMIZE_JAC_ALT */
+
+#if defined(MBEDTLS_ECP_NO_FALLBACK) && defined(MBEDTLS_ECP_RANDOMIZE_JAC_ALT)
+    return( MBEDTLS_ERR_ECP_FEATURE_UNAVAILABLE );
+#else
+    int ret = MBEDTLS_ERR_ERROR_CORRUPTION_DETECTED;
+    mbedtls_mpi l, ll;
+
+    mbedtls_mpi_init( &l ); mbedtls_mpi_init( &ll );
+
+    /* Generate l such that 1 < l < p */
+    MBEDTLS_MPI_CHK( mbedtls_mpi_random( &l, 2, &grp->P, f_rng, p_rng ) );
+
+    /* Z = l * Z */
+    MBEDTLS_MPI_CHK( mbedtls_mpi_mul_mod( grp, &pt->Z,   &pt->Z,     &l  ) );
+
+    /* X = l^2 * X */
+    MBEDTLS_MPI_CHK( mbedtls_mpi_mul_mod( grp, &ll,      &l,         &l  ) );
+    MBEDTLS_MPI_CHK( mbedtls_mpi_mul_mod( grp, &pt->X,   &pt->X,     &ll ) );
+
+    /* Y = l^3 * Y */
+    MBEDTLS_MPI_CHK( mbedtls_mpi_mul_mod( grp, &ll,      &ll,        &l  ) );
+    MBEDTLS_MPI_CHK( mbedtls_mpi_mul_mod( grp, &pt->Y,   &pt->Y,     &ll ) );
+
+cleanup:
+    mbedtls_mpi_free( &l ); mbedtls_mpi_free( &ll );
+
+    if( ret == MBEDTLS_ERR_MPI_NOT_ACCEPTABLE )
+        ret = MBEDTLS_ERR_ECP_RANDOM_FAILED;
+    return( ret );
+#endif /* !defined(MBEDTLS_ECP_NO_FALLBACK) || !defined(MBEDTLS_ECP_RANDOMIZE_JAC_ALT) */
+}
+
+/*
+ * Check and define parameters used by the comb method (see below for details)
+ */
+#if MBEDTLS_ECP_WINDOW_SIZE < 2 || MBEDTLS_ECP_WINDOW_SIZE > 7
+#error "MBEDTLS_ECP_WINDOW_SIZE out of bounds"
+#endif
+
+/* d = ceil( n / w ) */
+#define COMB_MAX_D      ( MBEDTLS_ECP_MAX_BITS + 1 ) / 2
+
+/* number of precomputed points */
+#define COMB_MAX_PRE    ( 1 << ( MBEDTLS_ECP_WINDOW_SIZE - 1 ) )
+
+/*
+ * Compute the representation of m that will be used with our comb method.
+ *
+ * The basic comb method is described in GECC 3.44 for example. We use a
+ * modified version that provides resistance to SPA by avoiding zero
+ * digits in the representation as in [3]. We modify the method further by
+ * requiring that all K_i be odd, which has the small cost that our
+ * representation uses one more K_i, due to carries, but saves on the size of
+ * the precomputed table.
+ *
+ * Summary of the comb method and its modifications:
+ *
+ * - The goal is to compute m*P for some w*d-bit integer m.
+ *
+ * - The basic comb method splits m into the w-bit integers
+ *   x[0] .. x[d-1] where x[i] consists of the bits in m whose
+ *   index has residue i modulo d, and computes m * P as
+ *   S[x[0]] + 2 * S[x[1]] + .. + 2^(d-1) S[x[d-1]], where
+ *   S[i_{w-1} .. i_0] := i_{w-1} 2^{(w-1)d} P + ... + i_1 2^d P + i_0 P.
+ *
+ * - If it happens that, say, x[i+1]=0 (=> S[x[i+1]]=0), one can replace the sum by
+ *    .. + 2^{i-1} S[x[i-1]] - 2^i S[x[i]] + 2^{i+1} S[x[i]] + 2^{i+2} S[x[i+2]] ..,
+ *   thereby successively converting it into a form where all summands
+ *   are nonzero, at the cost of negative summands. This is the basic idea of [3].
+ *
+ * - More generally, even if x[i+1] != 0, we can first transform the sum as
+ *   .. - 2^i S[x[i]] + 2^{i+1} ( S[x[i]] + S[x[i+1]] ) + 2^{i+2} S[x[i+2]] ..,
+ *   and then replace S[x[i]] + S[x[i+1]] = S[x[i] ^ x[i+1]] + 2 S[x[i] & x[i+1]].
+ *   Performing and iterating this procedure for those x[i] that are even
+ *   (keeping track of carry), we can transform the original sum into one of the form
+ *   S[x'[0]] +- 2 S[x'[1]] +- .. +- 2^{d-1} S[x'[d-1]] + 2^d S[x'[d]]
+ *   with all x'[i] odd. It is therefore only necessary to know S at odd indices,
+ *   which is why we are only computing half of it in the first place in
+ *   ecp_precompute_comb and accessing it with index abs(i) / 2 in ecp_select_comb.
+ *
+ * - For the sake of compactness, only the seven low-order bits of x[i]
+ *   are used to represent its absolute value (K_i in the paper), and the msb
+ *   of x[i] encodes the sign (s_i in the paper): it is set if and only if
+ *   if s_i == -1;
+ *
+ * Calling conventions:
+ * - x is an array of size d + 1
+ * - w is the size, ie number of teeth, of the comb, and must be between
+ *   2 and 7 (in practice, between 2 and MBEDTLS_ECP_WINDOW_SIZE)
+ * - m is the MPI, expected to be odd and such that bitlength(m) <= w * d
+ *   (the result will be incorrect if these assumptions are not satisfied)
+ */
+static void ecp_comb_recode_core( unsigned char x[], size_t d,
+                                  unsigned char w, const mbedtls_mpi *m )
+{
+    size_t i, j;
+    unsigned char c, cc, adjust;
+
+    memset( x, 0, d+1 );
+
+    /* First get the classical comb values (except for x_d = 0) */
+    for( i = 0; i < d; i++ )
+        for( j = 0; j < w; j++ )
+            x[i] |= mbedtls_mpi_get_bit( m, i + d * j ) << j;
+
+    /* Now make sure x_1 .. x_d are odd */
+    c = 0;
+    for( i = 1; i <= d; i++ )
+    {
+        /* Add carry and update it */
+        cc   = x[i] & c;
+        x[i] = x[i] ^ c;
+        c = cc;
+
+        /* Adjust if needed, avoiding branches */
+        adjust = 1 - ( x[i] & 0x01 );
+        c   |= x[i] & ( x[i-1] * adjust );
+        x[i] = x[i] ^ ( x[i-1] * adjust );
+        x[i-1] |= adjust << 7;
+    }
+}
+
+/*
+ * Precompute points for the adapted comb method
+ *
+ * Assumption: T must be able to hold 2^{w - 1} elements.
+ *
+ * Operation: If i = i_{w-1} ... i_1 is the binary representation of i,
+ *            sets T[i] = i_{w-1} 2^{(w-1)d} P + ... + i_1 2^d P + P.
+ *
+ * Cost: d(w-1) D + (2^{w-1} - 1) A + 1 N(w-1) + 1 N(2^{w-1} - 1)
+ *
+ * Note: Even comb values (those where P would be omitted from the
+ *       sum defining T[i] above) are not needed in our adaption
+ *       the comb method. See ecp_comb_recode_core().
+ *
+ * This function currently works in four steps:
+ * (1) [dbl]      Computation of intermediate T[i] for 2-power values of i
+ * (2) [norm_dbl] Normalization of coordinates of these T[i]
+ * (3) [add]      Computation of all T[i]
+ * (4) [norm_add] Normalization of all T[i]
+ *
+ * Step 1 can be interrupted but not the others; together with the final
+ * coordinate normalization they are the largest steps done at once, depending
+ * on the window size. Here are operation counts for P-256:
+ *
+ * step     (2)     (3)     (4)
+ * w = 5    142     165     208
+ * w = 4    136      77     160
+ * w = 3    130      33     136
+ * w = 2    124      11     124
+ *
+ * So if ECC operations are blocking for too long even with a low max_ops
+ * value, it's useful to set MBEDTLS_ECP_WINDOW_SIZE to a lower value in order
+ * to minimize maximum blocking time.
+ */
+static int ecp_precompute_comb( const mbedtls_ecp_group *grp,
+                                mbedtls_ecp_point T[], const mbedtls_ecp_point *P,
+                                unsigned char w, size_t d,
+                                mbedtls_ecp_restart_ctx *rs_ctx )
+{
+    int ret = MBEDTLS_ERR_ERROR_CORRUPTION_DETECTED;
+    unsigned char i;
+    size_t j = 0;
+    const unsigned char T_size = 1U << ( w - 1 );
+    mbedtls_ecp_point *cur, *TT[COMB_MAX_PRE - 1];
+
+#if defined(MBEDTLS_ECP_RESTARTABLE)
+    if( rs_ctx != NULL && rs_ctx->rsm != NULL )
+    {
+        if( rs_ctx->rsm->state == ecp_rsm_pre_dbl )
+            goto dbl;
+        if( rs_ctx->rsm->state == ecp_rsm_pre_norm_dbl )
+            goto norm_dbl;
+        if( rs_ctx->rsm->state == ecp_rsm_pre_add )
+            goto add;
+        if( rs_ctx->rsm->state == ecp_rsm_pre_norm_add )
+            goto norm_add;
+    }
+#else
+    (void) rs_ctx;
+#endif
+
+#if defined(MBEDTLS_ECP_RESTARTABLE)
+    if( rs_ctx != NULL && rs_ctx->rsm != NULL )
+    {
+        rs_ctx->rsm->state = ecp_rsm_pre_dbl;
+
+        /* initial state for the loop */
+        rs_ctx->rsm->i = 0;
+    }
+
+dbl:
+#endif
+    /*
+     * Set T[0] = P and
+     * T[2^{l-1}] = 2^{dl} P for l = 1 .. w-1 (this is not the final value)
+     */
+    MBEDTLS_MPI_CHK( mbedtls_ecp_copy( &T[0], P ) );
+
+#if defined(MBEDTLS_ECP_RESTARTABLE)
+    if( rs_ctx != NULL && rs_ctx->rsm != NULL && rs_ctx->rsm->i != 0 )
+        j = rs_ctx->rsm->i;
+    else
+#endif
+        j = 0;
+
+    for( ; j < d * ( w - 1 ); j++ )
+    {
+        MBEDTLS_ECP_BUDGET( MBEDTLS_ECP_OPS_DBL );
+
+        i = 1U << ( j / d );
+        cur = T + i;
+
+        if( j % d == 0 )
+            MBEDTLS_MPI_CHK( mbedtls_ecp_copy( cur, T + ( i >> 1 ) ) );
+
+        MBEDTLS_MPI_CHK( ecp_double_jac( grp, cur, cur ) );
+    }
+
+#if defined(MBEDTLS_ECP_RESTARTABLE)
+    if( rs_ctx != NULL && rs_ctx->rsm != NULL )
+        rs_ctx->rsm->state = ecp_rsm_pre_norm_dbl;
+
+norm_dbl:
+#endif
+    /*
+     * Normalize current elements in T. As T has holes,
+     * use an auxiliary array of pointers to elements in T.
+     */
+    j = 0;
+    for( i = 1; i < T_size; i <<= 1 )
+        TT[j++] = T + i;
+
+    MBEDTLS_ECP_BUDGET( MBEDTLS_ECP_OPS_INV + 6 * j - 2 );
+
+    MBEDTLS_MPI_CHK( ecp_normalize_jac_many( grp, TT, j ) );
+
+#if defined(MBEDTLS_ECP_RESTARTABLE)
+    if( rs_ctx != NULL && rs_ctx->rsm != NULL )
+        rs_ctx->rsm->state = ecp_rsm_pre_add;
+
+add:
+#endif
+    /*
+     * Compute the remaining ones using the minimal number of additions
+     * Be careful to update T[2^l] only after using it!
+     */
+    MBEDTLS_ECP_BUDGET( ( T_size - 1 ) * MBEDTLS_ECP_OPS_ADD );
+
+    for( i = 1; i < T_size; i <<= 1 )
+    {
+        j = i;
+        while( j-- )
+            MBEDTLS_MPI_CHK( ecp_add_mixed( grp, &T[i + j], &T[j], &T[i] ) );
+    }
+
+#if defined(MBEDTLS_ECP_RESTARTABLE)
+    if( rs_ctx != NULL && rs_ctx->rsm != NULL )
+        rs_ctx->rsm->state = ecp_rsm_pre_norm_add;
+
+norm_add:
+#endif
+    /*
+     * Normalize final elements in T. Even though there are no holes now, we
+     * still need the auxiliary array for homogeneity with the previous
+     * call. Also, skip T[0] which is already normalised, being a copy of P.
+     */
+    for( j = 0; j + 1 < T_size; j++ )
+        TT[j] = T + j + 1;
+
+    MBEDTLS_ECP_BUDGET( MBEDTLS_ECP_OPS_INV + 6 * j - 2 );
+
+    MBEDTLS_MPI_CHK( ecp_normalize_jac_many( grp, TT, j ) );
+
+cleanup:
+#if defined(MBEDTLS_ECP_RESTARTABLE)
+    if( rs_ctx != NULL && rs_ctx->rsm != NULL &&
+        ret == MBEDTLS_ERR_ECP_IN_PROGRESS )
+    {
+        if( rs_ctx->rsm->state == ecp_rsm_pre_dbl )
+            rs_ctx->rsm->i = j;
+    }
+#endif
+
+    return( ret );
+}
+
+/*
+ * Select precomputed point: R = sign(i) * T[ abs(i) / 2 ]
+ *
+ * See ecp_comb_recode_core() for background
+ */
+static int ecp_select_comb( const mbedtls_ecp_group *grp, mbedtls_ecp_point *R,
+                            const mbedtls_ecp_point T[], unsigned char T_size,
+                            unsigned char i )
+{
+    int ret = MBEDTLS_ERR_ERROR_CORRUPTION_DETECTED;
+    unsigned char ii, j;
+
+    /* Ignore the "sign" bit and scale down */
+    ii =  ( i & 0x7Fu ) >> 1;
+
+    /* Read the whole table to thwart cache-based timing attacks */
+    for( j = 0; j < T_size; j++ )
+    {
+        MBEDTLS_MPI_CHK( mbedtls_mpi_safe_cond_assign( &R->X, &T[j].X, j == ii ) );
+        MBEDTLS_MPI_CHK( mbedtls_mpi_safe_cond_assign( &R->Y, &T[j].Y, j == ii ) );
+    }
+
+    /* Safely invert result if i is "negative" */
+    MBEDTLS_MPI_CHK( ecp_safe_invert_jac( grp, R, i >> 7 ) );
+
+cleanup:
+    return( ret );
+}
+
+/*
+ * Core multiplication algorithm for the (modified) comb method.
+ * This part is actually common with the basic comb method (GECC 3.44)
+ *
+ * Cost: d A + d D + 1 R
+ */
+static int ecp_mul_comb_core( const mbedtls_ecp_group *grp, mbedtls_ecp_point *R,
+                              const mbedtls_ecp_point T[], unsigned char T_size,
+                              const unsigned char x[], size_t d,
+                              int (*f_rng)(void *, unsigned char *, size_t),
+                              void *p_rng,
+                              mbedtls_ecp_restart_ctx *rs_ctx )
+{
+    int ret = MBEDTLS_ERR_ERROR_CORRUPTION_DETECTED;
+    mbedtls_ecp_point Txi;
+    size_t i;
+
+    mbedtls_ecp_point_init( &Txi );
+
+#if !defined(MBEDTLS_ECP_RESTARTABLE)
+    (void) rs_ctx;
+#endif
+
+#if defined(MBEDTLS_ECP_RESTARTABLE)
+    if( rs_ctx != NULL && rs_ctx->rsm != NULL &&
+        rs_ctx->rsm->state != ecp_rsm_comb_core )
+    {
+        rs_ctx->rsm->i = 0;
+        rs_ctx->rsm->state = ecp_rsm_comb_core;
+    }
+
+    /* new 'if' instead of nested for the sake of the 'else' branch */
+    if( rs_ctx != NULL && rs_ctx->rsm != NULL && rs_ctx->rsm->i != 0 )
+    {
+        /* restore current index (R already pointing to rs_ctx->rsm->R) */
+        i = rs_ctx->rsm->i;
+    }
+    else
+#endif
+    {
+        /* Start with a non-zero point and randomize its coordinates */
+        i = d;
+        MBEDTLS_MPI_CHK( ecp_select_comb( grp, R, T, T_size, x[i] ) );
+        MBEDTLS_MPI_CHK( mbedtls_mpi_lset( &R->Z, 1 ) );
+#if defined(MBEDTLS_ECP_NO_INTERNAL_RNG)
+        if( f_rng != 0 )
+#endif
+            MBEDTLS_MPI_CHK( ecp_randomize_jac( grp, R, f_rng, p_rng ) );
+    }
+
+    while( i != 0 )
+    {
+        MBEDTLS_ECP_BUDGET( MBEDTLS_ECP_OPS_DBL + MBEDTLS_ECP_OPS_ADD );
+        --i;
+
+        MBEDTLS_MPI_CHK( ecp_double_jac( grp, R, R ) );
+        MBEDTLS_MPI_CHK( ecp_select_comb( grp, &Txi, T, T_size, x[i] ) );
+        MBEDTLS_MPI_CHK( ecp_add_mixed( grp, R, R, &Txi ) );
+    }
+
+cleanup:
+
+    mbedtls_ecp_point_free( &Txi );
+
+#if defined(MBEDTLS_ECP_RESTARTABLE)
+    if( rs_ctx != NULL && rs_ctx->rsm != NULL &&
+        ret == MBEDTLS_ERR_ECP_IN_PROGRESS )
+    {
+        rs_ctx->rsm->i = i;
+        /* no need to save R, already pointing to rs_ctx->rsm->R */
+    }
+#endif
+
+    return( ret );
+}
+
+/*
+ * Recode the scalar to get constant-time comb multiplication
+ *
+ * As the actual scalar recoding needs an odd scalar as a starting point,
+ * this wrapper ensures that by replacing m by N - m if necessary, and
+ * informs the caller that the result of multiplication will be negated.
+ *
+ * This works because we only support large prime order for Short Weierstrass
+ * curves, so N is always odd hence either m or N - m is.
+ *
+ * See ecp_comb_recode_core() for background.
+ */
+static int ecp_comb_recode_scalar( const mbedtls_ecp_group *grp,
+                                   const mbedtls_mpi *m,
+                                   unsigned char k[COMB_MAX_D + 1],
+                                   size_t d,
+                                   unsigned char w,
+                                   unsigned char *parity_trick )
+{
+    int ret = MBEDTLS_ERR_ERROR_CORRUPTION_DETECTED;
+    mbedtls_mpi M, mm;
+
+    mbedtls_mpi_init( &M );
+    mbedtls_mpi_init( &mm );
+
+    /* N is always odd (see above), just make extra sure */
+    if( mbedtls_mpi_get_bit( &grp->N, 0 ) != 1 )
+        return( MBEDTLS_ERR_ECP_BAD_INPUT_DATA );
+
+    /* do we need the parity trick? */
+    *parity_trick = ( mbedtls_mpi_get_bit( m, 0 ) == 0 );
+
+    /* execute parity fix in constant time */
+    MBEDTLS_MPI_CHK( mbedtls_mpi_copy( &M, m ) );
+    MBEDTLS_MPI_CHK( mbedtls_mpi_sub_mpi( &mm, &grp->N, m ) );
+    MBEDTLS_MPI_CHK( mbedtls_mpi_safe_cond_assign( &M, &mm, *parity_trick ) );
+
+    /* actual scalar recoding */
+    ecp_comb_recode_core( k, d, w, &M );
+
+cleanup:
+    mbedtls_mpi_free( &mm );
+    mbedtls_mpi_free( &M );
+
+    return( ret );
+}
+
+/*
+ * Perform comb multiplication (for short Weierstrass curves)
+ * once the auxiliary table has been pre-computed.
+ *
+ * Scalar recoding may use a parity trick that makes us compute -m * P,
+ * if that is the case we'll need to recover m * P at the end.
+ */
+static int ecp_mul_comb_after_precomp( const mbedtls_ecp_group *grp,
+                                mbedtls_ecp_point *R,
+                                const mbedtls_mpi *m,
+                                const mbedtls_ecp_point *T,
+                                unsigned char T_size,
+                                unsigned char w,
+                                size_t d,
+                                int (*f_rng)(void *, unsigned char *, size_t),
+                                void *p_rng,
+                                mbedtls_ecp_restart_ctx *rs_ctx )
+{
+    int ret = MBEDTLS_ERR_ERROR_CORRUPTION_DETECTED;
+    unsigned char parity_trick;
+    unsigned char k[COMB_MAX_D + 1];
+    mbedtls_ecp_point *RR = R;
+
+#if defined(MBEDTLS_ECP_RESTARTABLE)
+    if( rs_ctx != NULL && rs_ctx->rsm != NULL )
+    {
+        RR = &rs_ctx->rsm->R;
+
+        if( rs_ctx->rsm->state == ecp_rsm_final_norm )
+            goto final_norm;
+    }
+#endif
+
+    MBEDTLS_MPI_CHK( ecp_comb_recode_scalar( grp, m, k, d, w,
+                                            &parity_trick ) );
+    MBEDTLS_MPI_CHK( ecp_mul_comb_core( grp, RR, T, T_size, k, d,
+                                        f_rng, p_rng, rs_ctx ) );
+    MBEDTLS_MPI_CHK( ecp_safe_invert_jac( grp, RR, parity_trick ) );
+
+#if defined(MBEDTLS_ECP_RESTARTABLE)
+    if( rs_ctx != NULL && rs_ctx->rsm != NULL )
+        rs_ctx->rsm->state = ecp_rsm_final_norm;
+
+final_norm:
+    MBEDTLS_ECP_BUDGET( MBEDTLS_ECP_OPS_INV );
+#endif
+    /*
+     * Knowledge of the jacobian coordinates may leak the last few bits of the
+     * scalar [1], and since our MPI implementation isn't constant-flow,
+     * inversion (used for coordinate normalization) may leak the full value
+     * of its input via side-channels [2].
+     *
+     * [1] https://eprint.iacr.org/2003/191
+     * [2] https://eprint.iacr.org/2020/055
+     *
+     * Avoid the leak by randomizing coordinates before we normalize them.
+     */
+#if defined(MBEDTLS_ECP_NO_INTERNAL_RNG)
+    if( f_rng != 0 )
+#endif
+        MBEDTLS_MPI_CHK( ecp_randomize_jac( grp, RR, f_rng, p_rng ) );
+
+    MBEDTLS_MPI_CHK( ecp_normalize_jac( grp, RR ) );
+
+#if defined(MBEDTLS_ECP_RESTARTABLE)
+    if( rs_ctx != NULL && rs_ctx->rsm != NULL )
+        MBEDTLS_MPI_CHK( mbedtls_ecp_copy( R, RR ) );
+#endif
+
+cleanup:
+    return( ret );
+}
+
+/*
+ * Pick window size based on curve size and whether we optimize for base point
+ */
+static unsigned char ecp_pick_window_size( const mbedtls_ecp_group *grp,
+                                           unsigned char p_eq_g )
+{
+    unsigned char w;
+
+    /*
+     * Minimize the number of multiplications, that is minimize
+     * 10 * d * w + 18 * 2^(w-1) + 11 * d + 7 * w, with d = ceil( nbits / w )
+     * (see costs of the various parts, with 1S = 1M)
+     */
+    w = grp->nbits >= 384 ? 5 : 4;
+
+    /*
+     * If P == G, pre-compute a bit more, since this may be re-used later.
+     * Just adding one avoids upping the cost of the first mul too much,
+     * and the memory cost too.
+     */
+    if( p_eq_g )
+        w++;
+
+    /*
+     * Make sure w is within bounds.
+     * (The last test is useful only for very small curves in the test suite.)
+     */
+#if( MBEDTLS_ECP_WINDOW_SIZE < 6 )
+    if( w > MBEDTLS_ECP_WINDOW_SIZE )
+        w = MBEDTLS_ECP_WINDOW_SIZE;
+#endif
+    if( w >= grp->nbits )
+        w = 2;
+
+    return( w );
+}
+
+/*
+ * Multiplication using the comb method - for curves in short Weierstrass form
+ *
+ * This function is mainly responsible for administrative work:
+ * - managing the restart context if enabled
+ * - managing the table of precomputed points (passed between the below two
+ *   functions): allocation, computation, ownership tranfer, freeing.
+ *
+ * It delegates the actual arithmetic work to:
+ *      ecp_precompute_comb() and ecp_mul_comb_with_precomp()
+ *
+ * See comments on ecp_comb_recode_core() regarding the computation strategy.
+ */
+static int ecp_mul_comb( mbedtls_ecp_group *grp, mbedtls_ecp_point *R,
+                         const mbedtls_mpi *m, const mbedtls_ecp_point *P,
+                         int (*f_rng)(void *, unsigned char *, size_t),
+                         void *p_rng,
+                         mbedtls_ecp_restart_ctx *rs_ctx )
+{
+    int ret = MBEDTLS_ERR_ERROR_CORRUPTION_DETECTED;
+    unsigned char w, p_eq_g, i;
+    size_t d;
+    unsigned char T_size = 0, T_ok = 0;
+    mbedtls_ecp_point *T = NULL;
+#if !defined(MBEDTLS_ECP_NO_INTERNAL_RNG)
+    ecp_drbg_context drbg_ctx;
+
+    ecp_drbg_init( &drbg_ctx );
+#endif
+
+    ECP_RS_ENTER( rsm );
+
+#if !defined(MBEDTLS_ECP_NO_INTERNAL_RNG)
+    if( f_rng == NULL )
+    {
+        /* Adjust pointers */
+        f_rng = &ecp_drbg_random;
+#if defined(MBEDTLS_ECP_RESTARTABLE)
+        if( rs_ctx != NULL && rs_ctx->rsm != NULL )
+            p_rng = &rs_ctx->rsm->drbg_ctx;
+        else
+#endif
+            p_rng = &drbg_ctx;
+
+        /* Initialize internal DRBG if necessary */
+#if defined(MBEDTLS_ECP_RESTARTABLE)
+        if( rs_ctx == NULL || rs_ctx->rsm == NULL ||
+            rs_ctx->rsm->drbg_seeded == 0 )
+#endif
+        {
+            const size_t m_len = ( grp->nbits + 7 ) / 8;
+            MBEDTLS_MPI_CHK( ecp_drbg_seed( p_rng, m, m_len ) );
+        }
+#if defined(MBEDTLS_ECP_RESTARTABLE)
+        if( rs_ctx != NULL && rs_ctx->rsm != NULL )
+            rs_ctx->rsm->drbg_seeded = 1;
+#endif
+    }
+#endif /* !MBEDTLS_ECP_NO_INTERNAL_RNG */
+
+    /* Is P the base point ? */
+#if MBEDTLS_ECP_FIXED_POINT_OPTIM == 1
+    p_eq_g = ( mbedtls_mpi_cmp_mpi( &P->Y, &grp->G.Y ) == 0 &&
+               mbedtls_mpi_cmp_mpi( &P->X, &grp->G.X ) == 0 );
+#else
+    p_eq_g = 0;
+#endif
+
+    /* Pick window size and deduce related sizes */
+    w = ecp_pick_window_size( grp, p_eq_g );
+    T_size = 1U << ( w - 1 );
+    d = ( grp->nbits + w - 1 ) / w;
+
+    /* Pre-computed table: do we have it already for the base point? */
+    if( p_eq_g && grp->T != NULL )
+    {
+        /* second pointer to the same table, will be deleted on exit */
+        T = grp->T;
+        T_ok = 1;
+    }
+    else
+#if defined(MBEDTLS_ECP_RESTARTABLE)
+    /* Pre-computed table: do we have one in progress? complete? */
+    if( rs_ctx != NULL && rs_ctx->rsm != NULL && rs_ctx->rsm->T != NULL )
+    {
+        /* transfer ownership of T from rsm to local function */
+        T = rs_ctx->rsm->T;
+        rs_ctx->rsm->T = NULL;
+        rs_ctx->rsm->T_size = 0;
+
+        /* This effectively jumps to the call to mul_comb_after_precomp() */
+        T_ok = rs_ctx->rsm->state >= ecp_rsm_comb_core;
+    }
+    else
+#endif
+    /* Allocate table if we didn't have any */
+    {
+        T = mbedtls_calloc( T_size, sizeof( mbedtls_ecp_point ) );
+        if( T == NULL )
+        {
+            ret = MBEDTLS_ERR_ECP_ALLOC_FAILED;
+            goto cleanup;
+        }
+
+        for( i = 0; i < T_size; i++ )
+            mbedtls_ecp_point_init( &T[i] );
+
+        T_ok = 0;
+    }
+
+    /* Compute table (or finish computing it) if not done already */
+    if( !T_ok )
+    {
+        MBEDTLS_MPI_CHK( ecp_precompute_comb( grp, T, P, w, d, rs_ctx ) );
+
+        if( p_eq_g )
+        {
+            /* almost transfer ownership of T to the group, but keep a copy of
+             * the pointer to use for calling the next function more easily */
+            grp->T = T;
+            grp->T_size = T_size;
+        }
+    }
+
+    /* Actual comb multiplication using precomputed points */
+    MBEDTLS_MPI_CHK( ecp_mul_comb_after_precomp( grp, R, m,
+                                                 T, T_size, w, d,
+                                                 f_rng, p_rng, rs_ctx ) );
+
+cleanup:
+
+#if !defined(MBEDTLS_ECP_NO_INTERNAL_RNG)
+    ecp_drbg_free( &drbg_ctx );
+#endif
+
+    /* does T belong to the group? */
+    if( T == grp->T )
+        T = NULL;
+
+    /* does T belong to the restart context? */
+#if defined(MBEDTLS_ECP_RESTARTABLE)
+    if( rs_ctx != NULL && rs_ctx->rsm != NULL && ret == MBEDTLS_ERR_ECP_IN_PROGRESS && T != NULL )
+    {
+        /* transfer ownership of T from local function to rsm */
+        rs_ctx->rsm->T_size = T_size;
+        rs_ctx->rsm->T = T;
+        T = NULL;
+    }
+#endif
+
+    /* did T belong to us? then let's destroy it! */
+    if( T != NULL )
+    {
+        for( i = 0; i < T_size; i++ )
+            mbedtls_ecp_point_free( &T[i] );
+        mbedtls_free( T );
+    }
+
+    /* don't free R while in progress in case R == P */
+#if defined(MBEDTLS_ECP_RESTARTABLE)
+    if( ret != MBEDTLS_ERR_ECP_IN_PROGRESS )
+#endif
+    /* prevent caller from using invalid value */
+    if( ret != 0 )
+        mbedtls_ecp_point_free( R );
+
+    ECP_RS_LEAVE( rsm );
+
+    return( ret );
+}
+
+#endif /* MBEDTLS_ECP_SHORT_WEIERSTRASS_ENABLED */
+
+#if defined(MBEDTLS_ECP_MONTGOMERY_ENABLED)
+/*
+ * For Montgomery curves, we do all the internal arithmetic in projective
+ * coordinates. Import/export of points uses only the x coordinates, which is
+ * internaly represented as X / Z.
+ *
+ * For scalar multiplication, we'll use a Montgomery ladder.
+ */
+
+/*
+ * Normalize Montgomery x/z coordinates: X = X/Z, Z = 1
+ * Cost: 1M + 1I
+ */
+static int ecp_normalize_mxz( const mbedtls_ecp_group *grp, mbedtls_ecp_point *P )
+{
+#if defined(MBEDTLS_ECP_NORMALIZE_MXZ_ALT)
+    if( mbedtls_internal_ecp_grp_capable( grp ) )
+        return( mbedtls_internal_ecp_normalize_mxz( grp, P ) );
+#endif /* MBEDTLS_ECP_NORMALIZE_MXZ_ALT */
+
+#if defined(MBEDTLS_ECP_NO_FALLBACK) && defined(MBEDTLS_ECP_NORMALIZE_MXZ_ALT)
+    return( MBEDTLS_ERR_ECP_FEATURE_UNAVAILABLE );
+#else
+    int ret = MBEDTLS_ERR_ERROR_CORRUPTION_DETECTED;
+    MBEDTLS_MPI_CHK( mbedtls_mpi_inv_mod( &P->Z, &P->Z, &grp->P ) );
+    MBEDTLS_MPI_CHK( mbedtls_mpi_mul_mod( grp, &P->X, &P->X, &P->Z ) );
+    MBEDTLS_MPI_CHK( mbedtls_mpi_lset( &P->Z, 1 ) );
+
+cleanup:
+    return( ret );
+#endif /* !defined(MBEDTLS_ECP_NO_FALLBACK) || !defined(MBEDTLS_ECP_NORMALIZE_MXZ_ALT) */
+}
+
+/*
+ * Randomize projective x/z coordinates:
+ * (X, Z) -> (l X, l Z) for random l
+ * This is sort of the reverse operation of ecp_normalize_mxz().
+ *
+ * This countermeasure was first suggested in [2].
+ * Cost: 2M
+ */
+static int ecp_randomize_mxz( const mbedtls_ecp_group *grp, mbedtls_ecp_point *P,
+                int (*f_rng)(void *, unsigned char *, size_t), void *p_rng )
+{
+#if defined(MBEDTLS_ECP_RANDOMIZE_MXZ_ALT)
+    if( mbedtls_internal_ecp_grp_capable( grp ) )
+        return( mbedtls_internal_ecp_randomize_mxz( grp, P, f_rng, p_rng ) );
+#endif /* MBEDTLS_ECP_RANDOMIZE_MXZ_ALT */
+
+#if defined(MBEDTLS_ECP_NO_FALLBACK) && defined(MBEDTLS_ECP_RANDOMIZE_MXZ_ALT)
+    return( MBEDTLS_ERR_ECP_FEATURE_UNAVAILABLE );
+#else
+    int ret = MBEDTLS_ERR_ERROR_CORRUPTION_DETECTED;
+    mbedtls_mpi l;
+    mbedtls_mpi_init( &l );
+
+    /* Generate l such that 1 < l < p */
+    MBEDTLS_MPI_CHK( mbedtls_mpi_random( &l, 2, &grp->P, f_rng, p_rng ) );
+
+    MBEDTLS_MPI_CHK( mbedtls_mpi_mul_mod( grp, &P->X, &P->X, &l ) );
+    MBEDTLS_MPI_CHK( mbedtls_mpi_mul_mod( grp, &P->Z, &P->Z, &l ) );
+
+cleanup:
+    mbedtls_mpi_free( &l );
+
+    if( ret == MBEDTLS_ERR_MPI_NOT_ACCEPTABLE )
+        ret = MBEDTLS_ERR_ECP_RANDOM_FAILED;
+    return( ret );
+#endif /* !defined(MBEDTLS_ECP_NO_FALLBACK) || !defined(MBEDTLS_ECP_RANDOMIZE_MXZ_ALT) */
+}
+
+/*
+ * Double-and-add: R = 2P, S = P + Q, with d = X(P - Q),
+ * for Montgomery curves in x/z coordinates.
+ *
+ * http://www.hyperelliptic.org/EFD/g1p/auto-code/montgom/xz/ladder/mladd-1987-m.op3
+ * with
+ * d =  X1
+ * P = (X2, Z2)
+ * Q = (X3, Z3)
+ * R = (X4, Z4)
+ * S = (X5, Z5)
+ * and eliminating temporary variables tO, ..., t4.
+ *
+ * Cost: 5M + 4S
+ */
+static int ecp_double_add_mxz( const mbedtls_ecp_group *grp,
+                               mbedtls_ecp_point *R, mbedtls_ecp_point *S,
+                               const mbedtls_ecp_point *P, const mbedtls_ecp_point *Q,
+                               const mbedtls_mpi *d )
+{
+#if defined(MBEDTLS_ECP_DOUBLE_ADD_MXZ_ALT)
+    if( mbedtls_internal_ecp_grp_capable( grp ) )
+        return( mbedtls_internal_ecp_double_add_mxz( grp, R, S, P, Q, d ) );
+#endif /* MBEDTLS_ECP_DOUBLE_ADD_MXZ_ALT */
+
+#if defined(MBEDTLS_ECP_NO_FALLBACK) && defined(MBEDTLS_ECP_DOUBLE_ADD_MXZ_ALT)
+    return( MBEDTLS_ERR_ECP_FEATURE_UNAVAILABLE );
+#else
+    int ret = MBEDTLS_ERR_ERROR_CORRUPTION_DETECTED;
+    mbedtls_mpi A, AA, B, BB, E, C, D, DA, CB;
+
+    mbedtls_mpi_init( &A ); mbedtls_mpi_init( &AA ); mbedtls_mpi_init( &B );
+    mbedtls_mpi_init( &BB ); mbedtls_mpi_init( &E ); mbedtls_mpi_init( &C );
+    mbedtls_mpi_init( &D ); mbedtls_mpi_init( &DA ); mbedtls_mpi_init( &CB );
+
+    MBEDTLS_MPI_CHK( mbedtls_mpi_add_mod( grp, &A,    &P->X,   &P->Z ) );
+    MBEDTLS_MPI_CHK( mbedtls_mpi_mul_mod( grp, &AA,   &A,      &A    ) );
+    MBEDTLS_MPI_CHK( mbedtls_mpi_sub_mod( grp, &B,    &P->X,   &P->Z ) );
+    MBEDTLS_MPI_CHK( mbedtls_mpi_mul_mod( grp, &BB,   &B,      &B    ) );
+    MBEDTLS_MPI_CHK( mbedtls_mpi_sub_mod( grp, &E,    &AA,     &BB   ) );
+    MBEDTLS_MPI_CHK( mbedtls_mpi_add_mod( grp, &C,    &Q->X,   &Q->Z ) );
+    MBEDTLS_MPI_CHK( mbedtls_mpi_sub_mod( grp, &D,    &Q->X,   &Q->Z ) );
+    MBEDTLS_MPI_CHK( mbedtls_mpi_mul_mod( grp, &DA,   &D,      &A    ) );
+    MBEDTLS_MPI_CHK( mbedtls_mpi_mul_mod( grp, &CB,   &C,      &B    ) );
+    MBEDTLS_MPI_CHK( mbedtls_mpi_add_mod( grp, &S->X, &DA,     &CB   ) );
+    MBEDTLS_MPI_CHK( mbedtls_mpi_mul_mod( grp, &S->X, &S->X,   &S->X ) );
+    MBEDTLS_MPI_CHK( mbedtls_mpi_sub_mod( grp, &S->Z, &DA,     &CB   ) );
+    MBEDTLS_MPI_CHK( mbedtls_mpi_mul_mod( grp, &S->Z, &S->Z,   &S->Z ) );
+    MBEDTLS_MPI_CHK( mbedtls_mpi_mul_mod( grp, &S->Z, d,       &S->Z ) );
+    MBEDTLS_MPI_CHK( mbedtls_mpi_mul_mod( grp, &R->X, &AA,     &BB   ) );
+    MBEDTLS_MPI_CHK( mbedtls_mpi_mul_mod( grp, &R->Z, &grp->A, &E    ) );
+    MBEDTLS_MPI_CHK( mbedtls_mpi_add_mod( grp, &R->Z, &BB,     &R->Z ) );
+    MBEDTLS_MPI_CHK( mbedtls_mpi_mul_mod( grp, &R->Z, &E,      &R->Z ) );
+
+cleanup:
+    mbedtls_mpi_free( &A ); mbedtls_mpi_free( &AA ); mbedtls_mpi_free( &B );
+    mbedtls_mpi_free( &BB ); mbedtls_mpi_free( &E ); mbedtls_mpi_free( &C );
+    mbedtls_mpi_free( &D ); mbedtls_mpi_free( &DA ); mbedtls_mpi_free( &CB );
+
+    return( ret );
+#endif /* !defined(MBEDTLS_ECP_NO_FALLBACK) || !defined(MBEDTLS_ECP_DOUBLE_ADD_MXZ_ALT) */
+}
+
+/*
+ * Multiplication with Montgomery ladder in x/z coordinates,
+ * for curves in Montgomery form
+ */
+static int ecp_mul_mxz( mbedtls_ecp_group *grp, mbedtls_ecp_point *R,
+                        const mbedtls_mpi *m, const mbedtls_ecp_point *P,
+                        int (*f_rng)(void *, unsigned char *, size_t),
+                        void *p_rng )
+{
+    int ret = MBEDTLS_ERR_ERROR_CORRUPTION_DETECTED;
+    size_t i;
+    unsigned char b;
+    mbedtls_ecp_point RP;
+    mbedtls_mpi PX;
+#if !defined(MBEDTLS_ECP_NO_INTERNAL_RNG)
+    ecp_drbg_context drbg_ctx;
+
+    ecp_drbg_init( &drbg_ctx );
+#endif
+    mbedtls_ecp_point_init( &RP ); mbedtls_mpi_init( &PX );
+
+#if !defined(MBEDTLS_ECP_NO_INTERNAL_RNG)
+    if( f_rng == NULL )
+    {
+        const size_t m_len = ( grp->nbits + 7 ) / 8;
+        MBEDTLS_MPI_CHK( ecp_drbg_seed( &drbg_ctx, m, m_len ) );
+        f_rng = &ecp_drbg_random;
+        p_rng = &drbg_ctx;
+    }
+#endif /* !MBEDTLS_ECP_NO_INTERNAL_RNG */
+
+    /* Save PX and read from P before writing to R, in case P == R */
+    MBEDTLS_MPI_CHK( mbedtls_mpi_copy( &PX, &P->X ) );
+    MBEDTLS_MPI_CHK( mbedtls_ecp_copy( &RP, P ) );
+
+    /* Set R to zero in modified x/z coordinates */
+    MBEDTLS_MPI_CHK( mbedtls_mpi_lset( &R->X, 1 ) );
+    MBEDTLS_MPI_CHK( mbedtls_mpi_lset( &R->Z, 0 ) );
+    mbedtls_mpi_free( &R->Y );
+
+    /* RP.X might be sligtly larger than P, so reduce it */
+    MOD_ADD( RP.X );
+
+    /* Randomize coordinates of the starting point */
+#if defined(MBEDTLS_ECP_NO_INTERNAL_RNG)
+    if( f_rng != NULL )
+#endif
+        MBEDTLS_MPI_CHK( ecp_randomize_mxz( grp, &RP, f_rng, p_rng ) );
+
+    /* Loop invariant: R = result so far, RP = R + P */
+    i = mbedtls_mpi_bitlen( m ); /* one past the (zero-based) most significant bit */
+    while( i-- > 0 )
+    {
+        b = mbedtls_mpi_get_bit( m, i );
+        /*
+         *  if (b) R = 2R + P else R = 2R,
+         * which is:
+         *  if (b) double_add( RP, R, RP, R )
+         *  else   double_add( R, RP, R, RP )
+         * but using safe conditional swaps to avoid leaks
+         */
+        MBEDTLS_MPI_CHK( mbedtls_mpi_safe_cond_swap( &R->X, &RP.X, b ) );
+        MBEDTLS_MPI_CHK( mbedtls_mpi_safe_cond_swap( &R->Z, &RP.Z, b ) );
+        MBEDTLS_MPI_CHK( ecp_double_add_mxz( grp, R, &RP, R, &RP, &PX ) );
+        MBEDTLS_MPI_CHK( mbedtls_mpi_safe_cond_swap( &R->X, &RP.X, b ) );
+        MBEDTLS_MPI_CHK( mbedtls_mpi_safe_cond_swap( &R->Z, &RP.Z, b ) );
+    }
+
+    /*
+     * Knowledge of the projective coordinates may leak the last few bits of the
+     * scalar [1], and since our MPI implementation isn't constant-flow,
+     * inversion (used for coordinate normalization) may leak the full value
+     * of its input via side-channels [2].
+     *
+     * [1] https://eprint.iacr.org/2003/191
+     * [2] https://eprint.iacr.org/2020/055
+     *
+     * Avoid the leak by randomizing coordinates before we normalize them.
+     */
+#if defined(MBEDTLS_ECP_NO_INTERNAL_RNG)
+    if( f_rng != NULL )
+#endif
+        MBEDTLS_MPI_CHK( ecp_randomize_mxz( grp, R, f_rng, p_rng ) );
+
+    MBEDTLS_MPI_CHK( ecp_normalize_mxz( grp, R ) );
+
+cleanup:
+#if !defined(MBEDTLS_ECP_NO_INTERNAL_RNG)
+    ecp_drbg_free( &drbg_ctx );
+#endif
+
+    mbedtls_ecp_point_free( &RP ); mbedtls_mpi_free( &PX );
+
+    return( ret );
+}
+
+#endif /* MBEDTLS_ECP_MONTGOMERY_ENABLED */
+
+/*
+ * Restartable multiplication R = m * P
+ */
+int mbedtls_ecp_mul_restartable( mbedtls_ecp_group *grp, mbedtls_ecp_point *R,
+             const mbedtls_mpi *m, const mbedtls_ecp_point *P,
+             int (*f_rng)(void *, unsigned char *, size_t), void *p_rng,
+             mbedtls_ecp_restart_ctx *rs_ctx )
+{
+    int ret = MBEDTLS_ERR_ECP_BAD_INPUT_DATA;
+#if defined(MBEDTLS_ECP_INTERNAL_ALT)
+    char is_grp_capable = 0;
+#endif
+    ECP_VALIDATE_RET( grp != NULL );
+    ECP_VALIDATE_RET( R   != NULL );
+    ECP_VALIDATE_RET( m   != NULL );
+    ECP_VALIDATE_RET( P   != NULL );
+
+#if defined(MBEDTLS_ECP_RESTARTABLE)
+    /* reset ops count for this call if top-level */
+    if( rs_ctx != NULL && rs_ctx->depth++ == 0 )
+        rs_ctx->ops_done = 0;
+#else
+    (void) rs_ctx;
+#endif
+
+#if defined(MBEDTLS_ECP_INTERNAL_ALT)
+    if( ( is_grp_capable = mbedtls_internal_ecp_grp_capable( grp ) ) )
+        MBEDTLS_MPI_CHK( mbedtls_internal_ecp_init( grp ) );
+#endif /* MBEDTLS_ECP_INTERNAL_ALT */
+
+#if defined(MBEDTLS_ECP_RESTARTABLE)
+    /* skip argument check when restarting */
+    if( rs_ctx == NULL || rs_ctx->rsm == NULL )
+#endif
+    {
+        /* check_privkey is free */
+        MBEDTLS_ECP_BUDGET( MBEDTLS_ECP_OPS_CHK );
+
+        /* Common sanity checks */
+        MBEDTLS_MPI_CHK( mbedtls_ecp_check_privkey( grp, m ) );
+        MBEDTLS_MPI_CHK( mbedtls_ecp_check_pubkey( grp, P ) );
+    }
+
+    ret = MBEDTLS_ERR_ECP_BAD_INPUT_DATA;
+#if defined(MBEDTLS_ECP_MONTGOMERY_ENABLED)
+    if( mbedtls_ecp_get_type( grp ) == MBEDTLS_ECP_TYPE_MONTGOMERY )
+        MBEDTLS_MPI_CHK( ecp_mul_mxz( grp, R, m, P, f_rng, p_rng ) );
+#endif
+#if defined(MBEDTLS_ECP_SHORT_WEIERSTRASS_ENABLED)
+    if( mbedtls_ecp_get_type( grp ) == MBEDTLS_ECP_TYPE_SHORT_WEIERSTRASS )
+        MBEDTLS_MPI_CHK( ecp_mul_comb( grp, R, m, P, f_rng, p_rng, rs_ctx ) );
+#endif
+
+cleanup:
+
+#if defined(MBEDTLS_ECP_INTERNAL_ALT)
+    if( is_grp_capable )
+        mbedtls_internal_ecp_free( grp );
+#endif /* MBEDTLS_ECP_INTERNAL_ALT */
+
+#if defined(MBEDTLS_ECP_RESTARTABLE)
+    if( rs_ctx != NULL )
+        rs_ctx->depth--;
+#endif
+
+    return( ret );
+}
+
+/*
+ * Multiplication R = m * P
+ */
+int mbedtls_ecp_mul( mbedtls_ecp_group *grp, mbedtls_ecp_point *R,
+             const mbedtls_mpi *m, const mbedtls_ecp_point *P,
+             int (*f_rng)(void *, unsigned char *, size_t), void *p_rng )
+{
+    ECP_VALIDATE_RET( grp != NULL );
+    ECP_VALIDATE_RET( R   != NULL );
+    ECP_VALIDATE_RET( m   != NULL );
+    ECP_VALIDATE_RET( P   != NULL );
+    return( mbedtls_ecp_mul_restartable( grp, R, m, P, f_rng, p_rng, NULL ) );
+}
+
+#if defined(MBEDTLS_ECP_SHORT_WEIERSTRASS_ENABLED)
+/*
+ * Check that an affine point is valid as a public key,
+ * short weierstrass curves (SEC1 3.2.3.1)
+ */
+static int ecp_check_pubkey_sw( const mbedtls_ecp_group *grp, const mbedtls_ecp_point *pt )
+{
+    int ret = MBEDTLS_ERR_ERROR_CORRUPTION_DETECTED;
+    mbedtls_mpi YY, RHS;
+
+    /* pt coordinates must be normalized for our checks */
+    if( mbedtls_mpi_cmp_int( &pt->X, 0 ) < 0 ||
+        mbedtls_mpi_cmp_int( &pt->Y, 0 ) < 0 ||
+        mbedtls_mpi_cmp_mpi( &pt->X, &grp->P ) >= 0 ||
+        mbedtls_mpi_cmp_mpi( &pt->Y, &grp->P ) >= 0 )
+        return( MBEDTLS_ERR_ECP_INVALID_KEY );
+
+    mbedtls_mpi_init( &YY ); mbedtls_mpi_init( &RHS );
+
+    /*
+     * YY = Y^2
+     * RHS = X (X^2 + A) + B = X^3 + A X + B
+     */
+    MBEDTLS_MPI_CHK( mbedtls_mpi_mul_mod( grp, &YY,  &pt->Y,   &pt->Y  ) );
+    MBEDTLS_MPI_CHK( mbedtls_mpi_mul_mod( grp, &RHS, &pt->X,   &pt->X  ) );
+
+    /* Special case for A = -3 */
+    if( grp->A.p == NULL )
+    {
+        MBEDTLS_MPI_CHK( mbedtls_mpi_sub_int( &RHS, &RHS, 3       ) );  MOD_SUB( RHS );
+    }
+    else
+    {
+        MBEDTLS_MPI_CHK( mbedtls_mpi_add_mod( grp, &RHS, &RHS, &grp->A ) );
+    }
+
+    MBEDTLS_MPI_CHK( mbedtls_mpi_mul_mod( grp, &RHS, &RHS,     &pt->X  ) );
+    MBEDTLS_MPI_CHK( mbedtls_mpi_add_mod( grp, &RHS, &RHS,     &grp->B ) );
+
+    if( mbedtls_mpi_cmp_mpi( &YY, &RHS ) != 0 )
+        ret = MBEDTLS_ERR_ECP_INVALID_KEY;
+
+cleanup:
+
+    mbedtls_mpi_free( &YY ); mbedtls_mpi_free( &RHS );
+
+    return( ret );
+}
+#endif /* MBEDTLS_ECP_SHORT_WEIERSTRASS_ENABLED */
+
+#if defined(MBEDTLS_ECP_SHORT_WEIERSTRASS_ENABLED)
+/*
+ * R = m * P with shortcuts for m == 0, m == 1 and m == -1
+ * NOT constant-time - ONLY for short Weierstrass!
+ */
+static int mbedtls_ecp_mul_shortcuts( mbedtls_ecp_group *grp,
+                                      mbedtls_ecp_point *R,
+                                      const mbedtls_mpi *m,
+                                      const mbedtls_ecp_point *P,
+                                      mbedtls_ecp_restart_ctx *rs_ctx )
+{
+    int ret = MBEDTLS_ERR_ERROR_CORRUPTION_DETECTED;
+
+    if( mbedtls_mpi_cmp_int( m, 0 ) == 0 )
+    {
+        MBEDTLS_MPI_CHK( mbedtls_ecp_set_zero( R ) );
+    }
+    else if( mbedtls_mpi_cmp_int( m, 1 ) == 0 )
+    {
+        MBEDTLS_MPI_CHK( mbedtls_ecp_copy( R, P ) );
+    }
+    else if( mbedtls_mpi_cmp_int( m, -1 ) == 0 )
+    {
+        MBEDTLS_MPI_CHK( mbedtls_ecp_copy( R, P ) );
+        if( mbedtls_mpi_cmp_int( &R->Y, 0 ) != 0 )
+            MBEDTLS_MPI_CHK( mbedtls_mpi_sub_mpi( &R->Y, &grp->P, &R->Y ) );
+    }
+    else
+    {
+        MBEDTLS_MPI_CHK( mbedtls_ecp_mul_restartable( grp, R, m, P,
+                                                      NULL, NULL, rs_ctx ) );
+    }
+
+cleanup:
+    return( ret );
+}
+
+/*
+ * Restartable linear combination
+ * NOT constant-time
+ */
+int mbedtls_ecp_muladd_restartable(
+             mbedtls_ecp_group *grp, mbedtls_ecp_point *R,
+             const mbedtls_mpi *m, const mbedtls_ecp_point *P,
+             const mbedtls_mpi *n, const mbedtls_ecp_point *Q,
+             mbedtls_ecp_restart_ctx *rs_ctx )
+{
+    int ret = MBEDTLS_ERR_ERROR_CORRUPTION_DETECTED;
+    mbedtls_ecp_point mP;
+    mbedtls_ecp_point *pmP = &mP;
+    mbedtls_ecp_point *pR = R;
+#if defined(MBEDTLS_ECP_INTERNAL_ALT)
+    char is_grp_capable = 0;
+#endif
+    ECP_VALIDATE_RET( grp != NULL );
+    ECP_VALIDATE_RET( R   != NULL );
+    ECP_VALIDATE_RET( m   != NULL );
+    ECP_VALIDATE_RET( P   != NULL );
+    ECP_VALIDATE_RET( n   != NULL );
+    ECP_VALIDATE_RET( Q   != NULL );
+
+    if( mbedtls_ecp_get_type( grp ) != MBEDTLS_ECP_TYPE_SHORT_WEIERSTRASS )
+        return( MBEDTLS_ERR_ECP_FEATURE_UNAVAILABLE );
+
+    mbedtls_ecp_point_init( &mP );
+
+    ECP_RS_ENTER( ma );
+
+#if defined(MBEDTLS_ECP_RESTARTABLE)
+    if( rs_ctx != NULL && rs_ctx->ma != NULL )
+    {
+        /* redirect intermediate results to restart context */
+        pmP = &rs_ctx->ma->mP;
+        pR  = &rs_ctx->ma->R;
+
+        /* jump to next operation */
+        if( rs_ctx->ma->state == ecp_rsma_mul2 )
+            goto mul2;
+        if( rs_ctx->ma->state == ecp_rsma_add )
+            goto add;
+        if( rs_ctx->ma->state == ecp_rsma_norm )
+            goto norm;
+    }
+#endif /* MBEDTLS_ECP_RESTARTABLE */
+
+    MBEDTLS_MPI_CHK( mbedtls_ecp_mul_shortcuts( grp, pmP, m, P, rs_ctx ) );
+#if defined(MBEDTLS_ECP_RESTARTABLE)
+    if( rs_ctx != NULL && rs_ctx->ma != NULL )
+        rs_ctx->ma->state = ecp_rsma_mul2;
+
+mul2:
+#endif
+    MBEDTLS_MPI_CHK( mbedtls_ecp_mul_shortcuts( grp, pR,  n, Q, rs_ctx ) );
+
+#if defined(MBEDTLS_ECP_INTERNAL_ALT)
+    if( ( is_grp_capable = mbedtls_internal_ecp_grp_capable( grp ) ) )
+        MBEDTLS_MPI_CHK( mbedtls_internal_ecp_init( grp ) );
+#endif /* MBEDTLS_ECP_INTERNAL_ALT */
+
+#if defined(MBEDTLS_ECP_RESTARTABLE)
+    if( rs_ctx != NULL && rs_ctx->ma != NULL )
+        rs_ctx->ma->state = ecp_rsma_add;
+
+add:
+#endif
+    MBEDTLS_ECP_BUDGET( MBEDTLS_ECP_OPS_ADD );
+    MBEDTLS_MPI_CHK( ecp_add_mixed( grp, pR, pmP, pR ) );
+#if defined(MBEDTLS_ECP_RESTARTABLE)
+    if( rs_ctx != NULL && rs_ctx->ma != NULL )
+        rs_ctx->ma->state = ecp_rsma_norm;
+
+norm:
+#endif
+    MBEDTLS_ECP_BUDGET( MBEDTLS_ECP_OPS_INV );
+    MBEDTLS_MPI_CHK( ecp_normalize_jac( grp, pR ) );
+
+#if defined(MBEDTLS_ECP_RESTARTABLE)
+    if( rs_ctx != NULL && rs_ctx->ma != NULL )
+        MBEDTLS_MPI_CHK( mbedtls_ecp_copy( R, pR ) );
+#endif
+
+cleanup:
+#if defined(MBEDTLS_ECP_INTERNAL_ALT)
+    if( is_grp_capable )
+        mbedtls_internal_ecp_free( grp );
+#endif /* MBEDTLS_ECP_INTERNAL_ALT */
+
+    mbedtls_ecp_point_free( &mP );
+
+    ECP_RS_LEAVE( ma );
+
+    return( ret );
+}
+
+/*
+ * Linear combination
+ * NOT constant-time
+ */
+int mbedtls_ecp_muladd( mbedtls_ecp_group *grp, mbedtls_ecp_point *R,
+             const mbedtls_mpi *m, const mbedtls_ecp_point *P,
+             const mbedtls_mpi *n, const mbedtls_ecp_point *Q )
+{
+    ECP_VALIDATE_RET( grp != NULL );
+    ECP_VALIDATE_RET( R   != NULL );
+    ECP_VALIDATE_RET( m   != NULL );
+    ECP_VALIDATE_RET( P   != NULL );
+    ECP_VALIDATE_RET( n   != NULL );
+    ECP_VALIDATE_RET( Q   != NULL );
+    return( mbedtls_ecp_muladd_restartable( grp, R, m, P, n, Q, NULL ) );
+}
+#endif /* MBEDTLS_ECP_SHORT_WEIERSTRASS_ENABLED */
+
+#if defined(MBEDTLS_ECP_MONTGOMERY_ENABLED)
+#if defined(MBEDTLS_ECP_DP_CURVE25519_ENABLED)
+#define ECP_MPI_INIT(s, n, p) {s, (n), (mbedtls_mpi_uint *)(p)}
+#define ECP_MPI_INIT_ARRAY(x)   \
+    ECP_MPI_INIT(1, sizeof(x) / sizeof(mbedtls_mpi_uint), x)
+/*
+ * Constants for the two points other than 0, 1, -1 (mod p) in
+ * https://cr.yp.to/ecdh.html#validate
+ * See ecp_check_pubkey_x25519().
+ */
+static const mbedtls_mpi_uint x25519_bad_point_1[] = {
+    MBEDTLS_BYTES_TO_T_UINT_8( 0xe0, 0xeb, 0x7a, 0x7c, 0x3b, 0x41, 0xb8, 0xae ),
+    MBEDTLS_BYTES_TO_T_UINT_8( 0x16, 0x56, 0xe3, 0xfa, 0xf1, 0x9f, 0xc4, 0x6a ),
+    MBEDTLS_BYTES_TO_T_UINT_8( 0xda, 0x09, 0x8d, 0xeb, 0x9c, 0x32, 0xb1, 0xfd ),
+    MBEDTLS_BYTES_TO_T_UINT_8( 0x86, 0x62, 0x05, 0x16, 0x5f, 0x49, 0xb8, 0x00 ),
+};
+static const mbedtls_mpi_uint x25519_bad_point_2[] = {
+    MBEDTLS_BYTES_TO_T_UINT_8( 0x5f, 0x9c, 0x95, 0xbc, 0xa3, 0x50, 0x8c, 0x24 ),
+    MBEDTLS_BYTES_TO_T_UINT_8( 0xb1, 0xd0, 0xb1, 0x55, 0x9c, 0x83, 0xef, 0x5b ),
+    MBEDTLS_BYTES_TO_T_UINT_8( 0x04, 0x44, 0x5c, 0xc4, 0x58, 0x1c, 0x8e, 0x86 ),
+    MBEDTLS_BYTES_TO_T_UINT_8( 0xd8, 0x22, 0x4e, 0xdd, 0xd0, 0x9f, 0x11, 0x57 ),
+};
+static const mbedtls_mpi ecp_x25519_bad_point_1 = ECP_MPI_INIT_ARRAY(
+        x25519_bad_point_1 );
+static const mbedtls_mpi ecp_x25519_bad_point_2 = ECP_MPI_INIT_ARRAY(
+        x25519_bad_point_2 );
+#endif /* MBEDTLS_ECP_DP_CURVE25519_ENABLED */
+
+/*
+ * Check that the input point is not one of the low-order points.
+ * This is recommended by the "May the Fourth" paper:
+ * https://eprint.iacr.org/2017/806.pdf
+ * Those points are never sent by an honest peer.
+ */
+static int ecp_check_bad_points_mx( const mbedtls_mpi *X, const mbedtls_mpi *P,
+                                    const mbedtls_ecp_group_id grp_id )
+{
+    int ret;
+    mbedtls_mpi XmP;
+
+    mbedtls_mpi_init( &XmP );
+
+    /* Reduce X mod P so that we only need to check values less than P.
+     * We know X < 2^256 so we can proceed by subtraction. */
+    MBEDTLS_MPI_CHK( mbedtls_mpi_copy( &XmP, X ) );
+    while( mbedtls_mpi_cmp_mpi( &XmP, P ) >= 0 )
+        MBEDTLS_MPI_CHK( mbedtls_mpi_sub_mpi( &XmP, &XmP, P ) );
+
+    /* Check against the known bad values that are less than P. For Curve448
+     * these are 0, 1 and -1. For Curve25519 we check the values less than P
+     * from the following list: https://cr.yp.to/ecdh.html#validate */
+    if( mbedtls_mpi_cmp_int( &XmP, 1 ) <= 0 ) /* takes care of 0 and 1 */
+    {
+        ret = MBEDTLS_ERR_ECP_INVALID_KEY;
+        goto cleanup;
+    }
+
+#if defined(MBEDTLS_ECP_DP_CURVE25519_ENABLED)
+    if( grp_id == MBEDTLS_ECP_DP_CURVE25519 )
+    {
+        if( mbedtls_mpi_cmp_mpi( &XmP, &ecp_x25519_bad_point_1 ) == 0 )
+        {
+            ret = MBEDTLS_ERR_ECP_INVALID_KEY;
+            goto cleanup;
+        }
+
+        if( mbedtls_mpi_cmp_mpi( &XmP, &ecp_x25519_bad_point_2 ) == 0 )
+        {
+            ret = MBEDTLS_ERR_ECP_INVALID_KEY;
+            goto cleanup;
+        }
+    }
+#else
+    (void) grp_id;
+#endif
+
+    /* Final check: check if XmP + 1 is P (final because it changes XmP!) */
+    MBEDTLS_MPI_CHK( mbedtls_mpi_add_int( &XmP, &XmP, 1 ) );
+    if( mbedtls_mpi_cmp_mpi( &XmP, P ) == 0 )
+    {
+        ret = MBEDTLS_ERR_ECP_INVALID_KEY;
+        goto cleanup;
+    }
+
+    ret = 0;
+
+cleanup:
+    mbedtls_mpi_free( &XmP );
+
+    return( ret );
+}
+
+/*
+ * Check validity of a public key for Montgomery curves with x-only schemes
+ */
+static int ecp_check_pubkey_mx( const mbedtls_ecp_group *grp, const mbedtls_ecp_point *pt )
+{
+    /* [Curve25519 p. 5] Just check X is the correct number of bytes */
+    /* Allow any public value, if it's too big then we'll just reduce it mod p
+     * (RFC 7748 sec. 5 para. 3). */
+    if( mbedtls_mpi_size( &pt->X ) > ( grp->nbits + 7 ) / 8 )
+        return( MBEDTLS_ERR_ECP_INVALID_KEY );
+
+    /* Implicit in all standards (as they don't consider negative numbers):
+     * X must be non-negative. This is normally ensured by the way it's
+     * encoded for transmission, but let's be extra sure. */
+    if( mbedtls_mpi_cmp_int( &pt->X, 0 ) < 0 )
+        return( MBEDTLS_ERR_ECP_INVALID_KEY );
+
+    return( ecp_check_bad_points_mx( &pt->X, &grp->P, grp->id ) );
+}
+#endif /* MBEDTLS_ECP_MONTGOMERY_ENABLED */
+
+/*
+ * Check that a point is valid as a public key
+ */
+int mbedtls_ecp_check_pubkey( const mbedtls_ecp_group *grp,
+                              const mbedtls_ecp_point *pt )
+{
+    ECP_VALIDATE_RET( grp != NULL );
+    ECP_VALIDATE_RET( pt  != NULL );
+
+    /* Must use affine coordinates */
+    if( mbedtls_mpi_cmp_int( &pt->Z, 1 ) != 0 )
+        return( MBEDTLS_ERR_ECP_INVALID_KEY );
+
+#if defined(MBEDTLS_ECP_MONTGOMERY_ENABLED)
+    if( mbedtls_ecp_get_type( grp ) == MBEDTLS_ECP_TYPE_MONTGOMERY )
+        return( ecp_check_pubkey_mx( grp, pt ) );
+#endif
+#if defined(MBEDTLS_ECP_SHORT_WEIERSTRASS_ENABLED)
+    if( mbedtls_ecp_get_type( grp ) == MBEDTLS_ECP_TYPE_SHORT_WEIERSTRASS )
+        return( ecp_check_pubkey_sw( grp, pt ) );
+#endif
+    return( MBEDTLS_ERR_ECP_BAD_INPUT_DATA );
+}
+
+/*
+ * Check that an mbedtls_mpi is valid as a private key
+ */
+int mbedtls_ecp_check_privkey( const mbedtls_ecp_group *grp,
+                               const mbedtls_mpi *d )
+{
+    ECP_VALIDATE_RET( grp != NULL );
+    ECP_VALIDATE_RET( d   != NULL );
+
+#if defined(MBEDTLS_ECP_MONTGOMERY_ENABLED)
+    if( mbedtls_ecp_get_type( grp ) == MBEDTLS_ECP_TYPE_MONTGOMERY )
+    {
+        /* see RFC 7748 sec. 5 para. 5 */
+        if( mbedtls_mpi_get_bit( d, 0 ) != 0 ||
+            mbedtls_mpi_get_bit( d, 1 ) != 0 ||
+            mbedtls_mpi_bitlen( d ) - 1 != grp->nbits ) /* mbedtls_mpi_bitlen is one-based! */
+            return( MBEDTLS_ERR_ECP_INVALID_KEY );
+
+        /* see [Curve25519] page 5 */
+        if( grp->nbits == 254 && mbedtls_mpi_get_bit( d, 2 ) != 0 )
+            return( MBEDTLS_ERR_ECP_INVALID_KEY );
+
+        return( 0 );
+    }
+#endif /* MBEDTLS_ECP_MONTGOMERY_ENABLED */
+#if defined(MBEDTLS_ECP_SHORT_WEIERSTRASS_ENABLED)
+    if( mbedtls_ecp_get_type( grp ) == MBEDTLS_ECP_TYPE_SHORT_WEIERSTRASS )
+    {
+        /* see SEC1 3.2 */
+        if( mbedtls_mpi_cmp_int( d, 1 ) < 0 ||
+            mbedtls_mpi_cmp_mpi( d, &grp->N ) >= 0 )
+            return( MBEDTLS_ERR_ECP_INVALID_KEY );
+        else
+            return( 0 );
+    }
+#endif /* MBEDTLS_ECP_SHORT_WEIERSTRASS_ENABLED */
+
+    return( MBEDTLS_ERR_ECP_BAD_INPUT_DATA );
+}
+
+#if defined(MBEDTLS_ECP_MONTGOMERY_ENABLED)
+MBEDTLS_STATIC_TESTABLE
+int mbedtls_ecp_gen_privkey_mx( size_t high_bit,
+                                mbedtls_mpi *d,
+                                int (*f_rng)(void *, unsigned char *, size_t),
+                                void *p_rng )
+{
+    int ret = MBEDTLS_ERR_ECP_BAD_INPUT_DATA;
+    size_t n_random_bytes = high_bit / 8 + 1;
+
+    /* [Curve25519] page 5 */
+    /* Generate a (high_bit+1)-bit random number by generating just enough
+     * random bytes, then shifting out extra bits from the top (necessary
+     * when (high_bit+1) is not a multiple of 8). */
+    MBEDTLS_MPI_CHK( mbedtls_mpi_fill_random( d, n_random_bytes,
+                                              f_rng, p_rng ) );
+    MBEDTLS_MPI_CHK( mbedtls_mpi_shift_r( d, 8 * n_random_bytes - high_bit - 1 ) );
+
+    MBEDTLS_MPI_CHK( mbedtls_mpi_set_bit( d, high_bit, 1 ) );
+
+    /* Make sure the last two bits are unset for Curve448, three bits for
+       Curve25519 */
+    MBEDTLS_MPI_CHK( mbedtls_mpi_set_bit( d, 0, 0 ) );
+    MBEDTLS_MPI_CHK( mbedtls_mpi_set_bit( d, 1, 0 ) );
+    if( high_bit == 254 )
+    {
+        MBEDTLS_MPI_CHK( mbedtls_mpi_set_bit( d, 2, 0 ) );
+    }
+
+cleanup:
+    return( ret );
+}
+#endif /* MBEDTLS_ECP_MONTGOMERY_ENABLED */
+
+#if defined(MBEDTLS_ECP_SHORT_WEIERSTRASS_ENABLED)
+static int mbedtls_ecp_gen_privkey_sw(
+    const mbedtls_mpi *N, mbedtls_mpi *d,
+    int (*f_rng)(void *, unsigned char *, size_t), void *p_rng )
+{
+    int ret = mbedtls_mpi_random( d, 1, N, f_rng, p_rng );
+    switch( ret )
+    {
+        case MBEDTLS_ERR_MPI_NOT_ACCEPTABLE:
+            return( MBEDTLS_ERR_ECP_RANDOM_FAILED );
+        default:
+            return( ret );
+    }
+}
+#endif /* MBEDTLS_ECP_SHORT_WEIERSTRASS_ENABLED */
+
+/*
+ * Generate a private key
+ */
+int mbedtls_ecp_gen_privkey( const mbedtls_ecp_group *grp,
+                     mbedtls_mpi *d,
+                     int (*f_rng)(void *, unsigned char *, size_t),
+                     void *p_rng )
+{
+    ECP_VALIDATE_RET( grp   != NULL );
+    ECP_VALIDATE_RET( d     != NULL );
+    ECP_VALIDATE_RET( f_rng != NULL );
+
+#if defined(MBEDTLS_ECP_MONTGOMERY_ENABLED)
+    if( mbedtls_ecp_get_type( grp ) == MBEDTLS_ECP_TYPE_MONTGOMERY )
+        return( mbedtls_ecp_gen_privkey_mx( grp->nbits, d, f_rng, p_rng ) );
+#endif /* MBEDTLS_ECP_MONTGOMERY_ENABLED */
+
+#if defined(MBEDTLS_ECP_SHORT_WEIERSTRASS_ENABLED)
+    if( mbedtls_ecp_get_type( grp ) == MBEDTLS_ECP_TYPE_SHORT_WEIERSTRASS )
+        return( mbedtls_ecp_gen_privkey_sw( &grp->N, d, f_rng, p_rng ) );
+#endif /* MBEDTLS_ECP_SHORT_WEIERSTRASS_ENABLED */
+
+    return( MBEDTLS_ERR_ECP_BAD_INPUT_DATA );
+}
+
+/*
+ * Generate a keypair with configurable base point
+ */
+int mbedtls_ecp_gen_keypair_base( mbedtls_ecp_group *grp,
+                     const mbedtls_ecp_point *G,
+                     mbedtls_mpi *d, mbedtls_ecp_point *Q,
+                     int (*f_rng)(void *, unsigned char *, size_t),
+                     void *p_rng )
+{
+    int ret = MBEDTLS_ERR_ERROR_CORRUPTION_DETECTED;
+    ECP_VALIDATE_RET( grp   != NULL );
+    ECP_VALIDATE_RET( d     != NULL );
+    ECP_VALIDATE_RET( G     != NULL );
+    ECP_VALIDATE_RET( Q     != NULL );
+    ECP_VALIDATE_RET( f_rng != NULL );
+
+    MBEDTLS_MPI_CHK( mbedtls_ecp_gen_privkey( grp, d, f_rng, p_rng ) );
+    MBEDTLS_MPI_CHK( mbedtls_ecp_mul( grp, Q, d, G, f_rng, p_rng ) );
+
+cleanup:
+    return( ret );
+}
+
+/*
+ * Generate key pair, wrapper for conventional base point
+ */
+int mbedtls_ecp_gen_keypair( mbedtls_ecp_group *grp,
+                             mbedtls_mpi *d, mbedtls_ecp_point *Q,
+                             int (*f_rng)(void *, unsigned char *, size_t),
+                             void *p_rng )
+{
+    ECP_VALIDATE_RET( grp   != NULL );
+    ECP_VALIDATE_RET( d     != NULL );
+    ECP_VALIDATE_RET( Q     != NULL );
+    ECP_VALIDATE_RET( f_rng != NULL );
+
+    return( mbedtls_ecp_gen_keypair_base( grp, &grp->G, d, Q, f_rng, p_rng ) );
+}
+
+/*
+ * Generate a keypair, prettier wrapper
+ */
+int mbedtls_ecp_gen_key( mbedtls_ecp_group_id grp_id, mbedtls_ecp_keypair *key,
+                int (*f_rng)(void *, unsigned char *, size_t), void *p_rng )
+{
+    int ret = MBEDTLS_ERR_ERROR_CORRUPTION_DETECTED;
+    ECP_VALIDATE_RET( key   != NULL );
+    ECP_VALIDATE_RET( f_rng != NULL );
+
+    if( ( ret = mbedtls_ecp_group_load( &key->grp, grp_id ) ) != 0 )
+        return( ret );
+
+    return( mbedtls_ecp_gen_keypair( &key->grp, &key->d, &key->Q, f_rng, p_rng ) );
+}
+
+#define ECP_CURVE25519_KEY_SIZE 32
+/*
+ * Read a private key.
+ */
+int mbedtls_ecp_read_key( mbedtls_ecp_group_id grp_id, mbedtls_ecp_keypair *key,
+                          const unsigned char *buf, size_t buflen )
+{
+    int ret = 0;
+
+    ECP_VALIDATE_RET( key  != NULL );
+    ECP_VALIDATE_RET( buf  != NULL );
+
+    if( ( ret = mbedtls_ecp_group_load( &key->grp, grp_id ) ) != 0 )
+        return( ret );
+
+    ret = MBEDTLS_ERR_ECP_FEATURE_UNAVAILABLE;
+
+#if defined(MBEDTLS_ECP_MONTGOMERY_ENABLED)
+    if( mbedtls_ecp_get_type( &key->grp ) == MBEDTLS_ECP_TYPE_MONTGOMERY )
+    {
+        /*
+         * If it is Curve25519 curve then mask the key as mandated by RFC7748
+         */
+        if( grp_id == MBEDTLS_ECP_DP_CURVE25519 )
+        {
+            if( buflen != ECP_CURVE25519_KEY_SIZE )
+                return MBEDTLS_ERR_ECP_INVALID_KEY;
+
+            MBEDTLS_MPI_CHK( mbedtls_mpi_read_binary_le( &key->d, buf, buflen ) );
+
+            /* Set the three least significant bits to 0 */
+            MBEDTLS_MPI_CHK( mbedtls_mpi_set_bit( &key->d, 0, 0 ) );
+            MBEDTLS_MPI_CHK( mbedtls_mpi_set_bit( &key->d, 1, 0 ) );
+            MBEDTLS_MPI_CHK( mbedtls_mpi_set_bit( &key->d, 2, 0 ) );
+
+            /* Set the most significant bit to 0 */
+            MBEDTLS_MPI_CHK(
+                    mbedtls_mpi_set_bit( &key->d,
+                                         ECP_CURVE25519_KEY_SIZE * 8 - 1, 0 )
+                    );
+
+            /* Set the second most significant bit to 1 */
+            MBEDTLS_MPI_CHK(
+                    mbedtls_mpi_set_bit( &key->d,
+                                         ECP_CURVE25519_KEY_SIZE * 8 - 2, 1 )
+                    );
+        }
+        else
+            ret = MBEDTLS_ERR_ECP_FEATURE_UNAVAILABLE;
+    }
+
+#endif
+#if defined(MBEDTLS_ECP_SHORT_WEIERSTRASS_ENABLED)
+    if( mbedtls_ecp_get_type( &key->grp ) == MBEDTLS_ECP_TYPE_SHORT_WEIERSTRASS )
+    {
+        MBEDTLS_MPI_CHK( mbedtls_mpi_read_binary( &key->d, buf, buflen ) );
+
+        MBEDTLS_MPI_CHK( mbedtls_ecp_check_privkey( &key->grp, &key->d ) );
+    }
+
+#endif
+cleanup:
+
+    if( ret != 0 )
+        mbedtls_mpi_free( &key->d );
+
+    return( ret );
+}
+
+/*
+ * Write a private key.
+ */
+int mbedtls_ecp_write_key( mbedtls_ecp_keypair *key,
+                           unsigned char *buf, size_t buflen )
+{
+    int ret = MBEDTLS_ERR_ECP_FEATURE_UNAVAILABLE;
+
+    ECP_VALIDATE_RET( key != NULL );
+    ECP_VALIDATE_RET( buf != NULL );
+
+#if defined(MBEDTLS_ECP_MONTGOMERY_ENABLED)
+    if( mbedtls_ecp_get_type( &key->grp ) == MBEDTLS_ECP_TYPE_MONTGOMERY )
+    {
+        if( key->grp.id == MBEDTLS_ECP_DP_CURVE25519 )
+        {
+            if( buflen < ECP_CURVE25519_KEY_SIZE )
+                return MBEDTLS_ERR_ECP_BUFFER_TOO_SMALL;
+
+            MBEDTLS_MPI_CHK( mbedtls_mpi_write_binary_le( &key->d, buf, buflen ) );
+        }
+        else
+            ret = MBEDTLS_ERR_ECP_FEATURE_UNAVAILABLE;
+    }
+
+#endif
+#if defined(MBEDTLS_ECP_SHORT_WEIERSTRASS_ENABLED)
+    if( mbedtls_ecp_get_type( &key->grp ) == MBEDTLS_ECP_TYPE_SHORT_WEIERSTRASS )
+    {
+        MBEDTLS_MPI_CHK( mbedtls_mpi_write_binary( &key->d, buf, buflen ) );
+    }
+
+#endif
+cleanup:
+
+    return( ret );
+}
+
+
+/*
+ * Check a public-private key pair
+ */
+int mbedtls_ecp_check_pub_priv( const mbedtls_ecp_keypair *pub, const mbedtls_ecp_keypair *prv )
+{
+    int ret = MBEDTLS_ERR_ERROR_CORRUPTION_DETECTED;
+    mbedtls_ecp_point Q;
+    mbedtls_ecp_group grp;
+    ECP_VALIDATE_RET( pub != NULL );
+    ECP_VALIDATE_RET( prv != NULL );
+
+    if( pub->grp.id == MBEDTLS_ECP_DP_NONE ||
+        pub->grp.id != prv->grp.id ||
+        mbedtls_mpi_cmp_mpi( &pub->Q.X, &prv->Q.X ) ||
+        mbedtls_mpi_cmp_mpi( &pub->Q.Y, &prv->Q.Y ) ||
+        mbedtls_mpi_cmp_mpi( &pub->Q.Z, &prv->Q.Z ) )
+    {
+        return( MBEDTLS_ERR_ECP_BAD_INPUT_DATA );
+    }
+
+    mbedtls_ecp_point_init( &Q );
+    mbedtls_ecp_group_init( &grp );
+
+    /* mbedtls_ecp_mul() needs a non-const group... */
+    mbedtls_ecp_group_copy( &grp, &prv->grp );
+
+    /* Also checks d is valid */
+    MBEDTLS_MPI_CHK( mbedtls_ecp_mul( &grp, &Q, &prv->d, &prv->grp.G, NULL, NULL ) );
+
+    if( mbedtls_mpi_cmp_mpi( &Q.X, &prv->Q.X ) ||
+        mbedtls_mpi_cmp_mpi( &Q.Y, &prv->Q.Y ) ||
+        mbedtls_mpi_cmp_mpi( &Q.Z, &prv->Q.Z ) )
+    {
+        ret = MBEDTLS_ERR_ECP_BAD_INPUT_DATA;
+        goto cleanup;
+    }
+
+cleanup:
+    mbedtls_ecp_point_free( &Q );
+    mbedtls_ecp_group_free( &grp );
+
+    return( ret );
+}
+
+#if defined(MBEDTLS_SELF_TEST)
+
+/* Adjust the exponent to be a valid private point for the specified curve.
+ * This is sometimes necessary because we use a single set of exponents
+ * for all curves but the validity of values depends on the curve. */
+static int self_test_adjust_exponent( const mbedtls_ecp_group *grp,
+                                      mbedtls_mpi *m )
+{
+    int ret = 0;
+    switch( grp->id )
+    {
+        /* If Curve25519 is available, then that's what we use for the
+         * Montgomery test, so we don't need the adjustment code. */
+#if ! defined(MBEDTLS_ECP_DP_CURVE25519_ENABLED)
+#if defined(MBEDTLS_ECP_DP_CURVE448_ENABLED)
+        case MBEDTLS_ECP_DP_CURVE448:
+            /* Move highest bit from 254 to N-1. Setting bit N-1 is
+             * necessary to enforce the highest-bit-set constraint. */
+            MBEDTLS_MPI_CHK( mbedtls_mpi_set_bit( m, 254, 0 ) );
+            MBEDTLS_MPI_CHK( mbedtls_mpi_set_bit( m, grp->nbits, 1 ) );
+            /* Copy second-highest bit from 253 to N-2. This is not
+             * necessary but improves the test variety a bit. */
+            MBEDTLS_MPI_CHK(
+                mbedtls_mpi_set_bit( m, grp->nbits - 1,
+                                     mbedtls_mpi_get_bit( m, 253 ) ) );
+            break;
+#endif
+#endif /* ! defined(MBEDTLS_ECP_DP_CURVE25519_ENABLED) */
+        default:
+            /* Non-Montgomery curves and Curve25519 need no adjustment. */
+            (void) grp;
+            (void) m;
+            goto cleanup;
+    }
+cleanup:
+    return( ret );
+}
+
+/* Calculate R = m.P for each m in exponents. Check that the number of
+ * basic operations doesn't depend on the value of m. */
+static int self_test_point( int verbose,
+                            mbedtls_ecp_group *grp,
+                            mbedtls_ecp_point *R,
+                            mbedtls_mpi *m,
+                            const mbedtls_ecp_point *P,
+                            const char *const *exponents,
+                            size_t n_exponents )
+{
+    int ret = 0;
+    size_t i = 0;
+    unsigned long add_c_prev, dbl_c_prev, mul_c_prev;
+    add_count = 0;
+    dbl_count = 0;
+    mul_count = 0;
+
+    MBEDTLS_MPI_CHK( mbedtls_mpi_read_string( m, 16, exponents[0] ) );
+    MBEDTLS_MPI_CHK( self_test_adjust_exponent( grp, m ) );
+    MBEDTLS_MPI_CHK( mbedtls_ecp_mul( grp, R, m, P, NULL, NULL ) );
+
+    for( i = 1; i < n_exponents; i++ )
+    {
+        add_c_prev = add_count;
+        dbl_c_prev = dbl_count;
+        mul_c_prev = mul_count;
+        add_count = 0;
+        dbl_count = 0;
+        mul_count = 0;
+
+        MBEDTLS_MPI_CHK( mbedtls_mpi_read_string( m, 16, exponents[i] ) );
+        MBEDTLS_MPI_CHK( self_test_adjust_exponent( grp, m ) );
+        MBEDTLS_MPI_CHK( mbedtls_ecp_mul( grp, R, m, P, NULL, NULL ) );
+
+        if( add_count != add_c_prev ||
+            dbl_count != dbl_c_prev ||
+            mul_count != mul_c_prev )
+        {
+            ret = 1;
+            break;
+        }
+    }
+
+cleanup:
+    if( verbose != 0 )
+    {
+        if( ret != 0 )
+            mbedtls_printf( "failed (%u)\n", (unsigned int) i );
+        else
+            mbedtls_printf( "passed\n" );
+    }
+    return( ret );
+}
+
+/*
+ * Checkup routine
+ */
+int mbedtls_ecp_self_test( int verbose )
+{
+    int ret = MBEDTLS_ERR_ERROR_CORRUPTION_DETECTED;
+    mbedtls_ecp_group grp;
+    mbedtls_ecp_point R, P;
+    mbedtls_mpi m;
+
+#if defined(MBEDTLS_ECP_SHORT_WEIERSTRASS_ENABLED)
+    /* Exponents especially adapted for secp192k1, which has the lowest
+     * order n of all supported curves (secp192r1 is in a slightly larger
+     * field but the order of its base point is slightly smaller). */
+    const char *sw_exponents[] =
+    {
+        "000000000000000000000000000000000000000000000001", /* one */
+        "FFFFFFFFFFFFFFFFFFFFFFFE26F2FC170F69466A74DEFD8C", /* n - 1 */
+        "5EA6F389A38B8BC81E767753B15AA5569E1782E30ABE7D25", /* random */
+        "400000000000000000000000000000000000000000000000", /* one and zeros */
+        "7FFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFF", /* all ones */
+        "555555555555555555555555555555555555555555555555", /* 101010... */
+    };
+#endif /* MBEDTLS_ECP_SHORT_WEIERSTRASS_ENABLED */
+#if defined(MBEDTLS_ECP_MONTGOMERY_ENABLED)
+    const char *m_exponents[] =
+    {
+        /* Valid private values for Curve25519. In a build with Curve448
+         * but not Curve25519, they will be adjusted in
+         * self_test_adjust_exponent(). */
+        "4000000000000000000000000000000000000000000000000000000000000000",
+        "5C3C3C3C3C3C3C3C3C3C3C3C3C3C3C3C3C3C3C3C3C3C3C3C3C3C3C3C3C3C3C30",
+        "5715ECCE24583F7A7023C24164390586842E816D7280A49EF6DF4EAE6B280BF8",
+        "41A2B017516F6D254E1F002BCCBADD54BE30F8CEC737A0E912B4963B6BA74460",
+        "5555555555555555555555555555555555555555555555555555555555555550",
+        "7FFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFF8",
+    };
+#endif /* MBEDTLS_ECP_MONTGOMERY_ENABLED */
+
+    mbedtls_ecp_group_init( &grp );
+    mbedtls_ecp_point_init( &R );
+    mbedtls_ecp_point_init( &P );
+    mbedtls_mpi_init( &m );
+
+#if defined(MBEDTLS_ECP_SHORT_WEIERSTRASS_ENABLED)
+    /* Use secp192r1 if available, or any available curve */
+#if defined(MBEDTLS_ECP_DP_SECP192R1_ENABLED)
+    MBEDTLS_MPI_CHK( mbedtls_ecp_group_load( &grp, MBEDTLS_ECP_DP_SECP192R1 ) );
+#else
+    MBEDTLS_MPI_CHK( mbedtls_ecp_group_load( &grp, mbedtls_ecp_curve_list()->grp_id ) );
+#endif
+
+    if( verbose != 0 )
+        mbedtls_printf( "  ECP SW test #1 (constant op_count, base point G): " );
+    /* Do a dummy multiplication first to trigger precomputation */
+    MBEDTLS_MPI_CHK( mbedtls_mpi_lset( &m, 2 ) );
+    MBEDTLS_MPI_CHK( mbedtls_ecp_mul( &grp, &P, &m, &grp.G, NULL, NULL ) );
+    ret = self_test_point( verbose,
+                           &grp, &R, &m, &grp.G,
+                           sw_exponents,
+                           sizeof( sw_exponents ) / sizeof( sw_exponents[0] ));
+    if( ret != 0 )
+        goto cleanup;
+
+    if( verbose != 0 )
+        mbedtls_printf( "  ECP SW test #2 (constant op_count, other point): " );
+    /* We computed P = 2G last time, use it */
+    ret = self_test_point( verbose,
+                           &grp, &R, &m, &P,
+                           sw_exponents,
+                           sizeof( sw_exponents ) / sizeof( sw_exponents[0] ));
+    if( ret != 0 )
+        goto cleanup;
+
+    mbedtls_ecp_group_free( &grp );
+    mbedtls_ecp_point_free( &R );
+#endif /* MBEDTLS_ECP_SHORT_WEIERSTRASS_ENABLED */
+
+#if defined(MBEDTLS_ECP_MONTGOMERY_ENABLED)
+    if( verbose != 0 )
+        mbedtls_printf( "  ECP Montgomery test (constant op_count): " );
+#if defined(MBEDTLS_ECP_DP_CURVE25519_ENABLED)
+    MBEDTLS_MPI_CHK( mbedtls_ecp_group_load( &grp, MBEDTLS_ECP_DP_CURVE25519 ) );
+#elif defined(MBEDTLS_ECP_DP_CURVE448_ENABLED)
+    MBEDTLS_MPI_CHK( mbedtls_ecp_group_load( &grp, MBEDTLS_ECP_DP_CURVE448 ) );
+#else
+#error "MBEDTLS_ECP_MONTGOMERY_ENABLED is defined, but no curve is supported for self-test"
+#endif
+    ret = self_test_point( verbose,
+                           &grp, &R, &m, &grp.G,
+                           m_exponents,
+                           sizeof( m_exponents ) / sizeof( m_exponents[0] ));
+    if( ret != 0 )
+        goto cleanup;
+#endif /* MBEDTLS_ECP_MONTGOMERY_ENABLED */
+
+cleanup:
+
+    if( ret < 0 && verbose != 0 )
+        mbedtls_printf( "Unexpected error, return code = %08X\n", (unsigned int) ret );
+
+    mbedtls_ecp_group_free( &grp );
+    mbedtls_ecp_point_free( &R );
+    mbedtls_ecp_point_free( &P );
+    mbedtls_mpi_free( &m );
+
+    if( verbose != 0 )
+        mbedtls_printf( "\n" );
+
+    return( ret );
+}
+
+#endif /* MBEDTLS_SELF_TEST */
+
+#endif /* !MBEDTLS_ECP_ALT */
+
+#endif /* MBEDTLS_ECP_C */