diff --git a/library/ecp.c b/library/ecp.c
index f04b6fe..6019500 100644
--- a/library/ecp.c
+++ b/library/ecp.c
@@ -41,26 +41,26 @@
  *     <http://eprint.iacr.org/2004/342.pdf>
  */
 
-#if !defined(POLARSSL_CONFIG_FILE)
+#if !defined(MBEDTLS_CONFIG_FILE)
 #include "mbedtls/config.h"
 #else
-#include POLARSSL_CONFIG_FILE
+#include MBEDTLS_CONFIG_FILE
 #endif
 
-#if defined(POLARSSL_ECP_C)
+#if defined(MBEDTLS_ECP_C)
 
 #include "mbedtls/ecp.h"
 
 #include <string.h>
 
-#if defined(POLARSSL_PLATFORM_C)
+#if defined(MBEDTLS_PLATFORM_C)
 #include "mbedtls/platform.h"
 #else
 #include <stdlib.h>
 #include <stdio.h>
-#define polarssl_printf     printf
-#define polarssl_malloc     malloc
-#define polarssl_free       free
+#define mbedtls_printf     printf
+#define mbedtls_malloc     malloc
+#define mbedtls_free       free
 #endif
 
 #if defined(_MSC_VER) && !defined strcasecmp && !defined(EFIX64) && \
@@ -77,11 +77,11 @@
 #endif /*_MSC_VER */
 
 /* Implementation that should never be optimized out by the compiler */
-static void polarssl_zeroize( void *v, size_t n ) {
+static void mbedtls_zeroize( void *v, size_t n ) {
     volatile unsigned char *p = v; while( n-- ) *p++ = 0;
 }
 
-#if defined(POLARSSL_SELF_TEST)
+#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.
@@ -89,25 +89,25 @@
 static unsigned long add_count, dbl_count, mul_count;
 #endif
 
-#if defined(POLARSSL_ECP_DP_SECP192R1_ENABLED) ||   \
-    defined(POLARSSL_ECP_DP_SECP224R1_ENABLED) ||   \
-    defined(POLARSSL_ECP_DP_SECP256R1_ENABLED) ||   \
-    defined(POLARSSL_ECP_DP_SECP384R1_ENABLED) ||   \
-    defined(POLARSSL_ECP_DP_SECP521R1_ENABLED) ||   \
-    defined(POLARSSL_ECP_DP_BP256R1_ENABLED)   ||   \
-    defined(POLARSSL_ECP_DP_BP384R1_ENABLED)   ||   \
-    defined(POLARSSL_ECP_DP_BP512R1_ENABLED)   ||   \
-    defined(POLARSSL_ECP_DP_SECP192K1_ENABLED) ||   \
-    defined(POLARSSL_ECP_DP_SECP224K1_ENABLED) ||   \
-    defined(POLARSSL_ECP_DP_SECP256K1_ENABLED)
-#define POLARSSL_ECP_SHORT_WEIERSTRASS
+#if defined(MBEDTLS_ECP_DP_SECP192R1_ENABLED) ||   \
+    defined(MBEDTLS_ECP_DP_SECP224R1_ENABLED) ||   \
+    defined(MBEDTLS_ECP_DP_SECP256R1_ENABLED) ||   \
+    defined(MBEDTLS_ECP_DP_SECP384R1_ENABLED) ||   \
+    defined(MBEDTLS_ECP_DP_SECP521R1_ENABLED) ||   \
+    defined(MBEDTLS_ECP_DP_BP256R1_ENABLED)   ||   \
+    defined(MBEDTLS_ECP_DP_BP384R1_ENABLED)   ||   \
+    defined(MBEDTLS_ECP_DP_BP512R1_ENABLED)   ||   \
+    defined(MBEDTLS_ECP_DP_SECP192K1_ENABLED) ||   \
+    defined(MBEDTLS_ECP_DP_SECP224K1_ENABLED) ||   \
+    defined(MBEDTLS_ECP_DP_SECP256K1_ENABLED)
+#define MBEDTLS_ECP_SHORT_WEIERSTRASS
 #endif
 
-#if defined(POLARSSL_ECP_DP_M221_ENABLED) ||   \
-    defined(POLARSSL_ECP_DP_M255_ENABLED) ||   \
-    defined(POLARSSL_ECP_DP_M383_ENABLED) ||   \
-    defined(POLARSSL_ECP_DP_M511_ENABLED)
-#define POLARSSL_ECP_MONTGOMERY
+#if defined(MBEDTLS_ECP_DP_M221_ENABLED) ||   \
+    defined(MBEDTLS_ECP_DP_M255_ENABLED) ||   \
+    defined(MBEDTLS_ECP_DP_M383_ENABLED) ||   \
+    defined(MBEDTLS_ECP_DP_M511_ENABLED)
+#define MBEDTLS_ECP_MONTGOMERY
 #endif
 
 /*
@@ -115,9 +115,9 @@
  */
 typedef enum
 {
-    POLARSSL_ECP_TYPE_NONE = 0,
-    POLARSSL_ECP_TYPE_SHORT_WEIERSTRASS,    /* y^2 = x^3 + a x + b      */
-    POLARSSL_ECP_TYPE_MONTGOMERY,           /* y^2 = x^3 + a x^2 + x    */
+    MBEDTLS_ECP_TYPE_NONE = 0,
+    MBEDTLS_ECP_TYPE_SHORT_WEIERSTRASS,    /* y^2 = x^3 + a x + b      */
+    MBEDTLS_ECP_TYPE_MONTGOMERY,           /* y^2 = x^3 + a x^2 + x    */
 } ecp_curve_type;
 
 /*
@@ -130,53 +130,53 @@
  * 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.
  */
-static const ecp_curve_info ecp_supported_curves[] =
+static const mbedtls_ecp_curve_info ecp_supported_curves[] =
 {
-#if defined(POLARSSL_ECP_DP_SECP521R1_ENABLED)
-    { POLARSSL_ECP_DP_SECP521R1,    25,     521,    "secp521r1"         },
+#if defined(MBEDTLS_ECP_DP_SECP521R1_ENABLED)
+    { MBEDTLS_ECP_DP_SECP521R1,    25,     521,    "secp521r1"         },
 #endif
-#if defined(POLARSSL_ECP_DP_BP512R1_ENABLED)
-    { POLARSSL_ECP_DP_BP512R1,      28,     512,    "brainpoolP512r1"   },
+#if defined(MBEDTLS_ECP_DP_BP512R1_ENABLED)
+    { MBEDTLS_ECP_DP_BP512R1,      28,     512,    "brainpoolP512r1"   },
 #endif
-#if defined(POLARSSL_ECP_DP_SECP384R1_ENABLED)
-    { POLARSSL_ECP_DP_SECP384R1,    24,     384,    "secp384r1"         },
+#if defined(MBEDTLS_ECP_DP_SECP384R1_ENABLED)
+    { MBEDTLS_ECP_DP_SECP384R1,    24,     384,    "secp384r1"         },
 #endif
-#if defined(POLARSSL_ECP_DP_BP384R1_ENABLED)
-    { POLARSSL_ECP_DP_BP384R1,      27,     384,    "brainpoolP384r1"   },
+#if defined(MBEDTLS_ECP_DP_BP384R1_ENABLED)
+    { MBEDTLS_ECP_DP_BP384R1,      27,     384,    "brainpoolP384r1"   },
 #endif
-#if defined(POLARSSL_ECP_DP_SECP256R1_ENABLED)
-    { POLARSSL_ECP_DP_SECP256R1,    23,     256,    "secp256r1"         },
+#if defined(MBEDTLS_ECP_DP_SECP256R1_ENABLED)
+    { MBEDTLS_ECP_DP_SECP256R1,    23,     256,    "secp256r1"         },
 #endif
-#if defined(POLARSSL_ECP_DP_SECP256K1_ENABLED)
-    { POLARSSL_ECP_DP_SECP256K1,    22,     256,    "secp256k1"         },
+#if defined(MBEDTLS_ECP_DP_SECP256K1_ENABLED)
+    { MBEDTLS_ECP_DP_SECP256K1,    22,     256,    "secp256k1"         },
 #endif
-#if defined(POLARSSL_ECP_DP_BP256R1_ENABLED)
-    { POLARSSL_ECP_DP_BP256R1,      26,     256,    "brainpoolP256r1"   },
+#if defined(MBEDTLS_ECP_DP_BP256R1_ENABLED)
+    { MBEDTLS_ECP_DP_BP256R1,      26,     256,    "brainpoolP256r1"   },
 #endif
-#if defined(POLARSSL_ECP_DP_SECP224R1_ENABLED)
-    { POLARSSL_ECP_DP_SECP224R1,    21,     224,    "secp224r1"         },
+#if defined(MBEDTLS_ECP_DP_SECP224R1_ENABLED)
+    { MBEDTLS_ECP_DP_SECP224R1,    21,     224,    "secp224r1"         },
 #endif
-#if defined(POLARSSL_ECP_DP_SECP224K1_ENABLED)
-    { POLARSSL_ECP_DP_SECP224K1,    20,     224,    "secp224k1"         },
+#if defined(MBEDTLS_ECP_DP_SECP224K1_ENABLED)
+    { MBEDTLS_ECP_DP_SECP224K1,    20,     224,    "secp224k1"         },
 #endif
-#if defined(POLARSSL_ECP_DP_SECP192R1_ENABLED)
-    { POLARSSL_ECP_DP_SECP192R1,    19,     192,    "secp192r1"         },
+#if defined(MBEDTLS_ECP_DP_SECP192R1_ENABLED)
+    { MBEDTLS_ECP_DP_SECP192R1,    19,     192,    "secp192r1"         },
 #endif
-#if defined(POLARSSL_ECP_DP_SECP192K1_ENABLED)
-    { POLARSSL_ECP_DP_SECP192K1,    18,     192,    "secp192k1"         },
+#if defined(MBEDTLS_ECP_DP_SECP192K1_ENABLED)
+    { MBEDTLS_ECP_DP_SECP192K1,    18,     192,    "secp192k1"         },
 #endif
-    { POLARSSL_ECP_DP_NONE,          0,     0,      NULL                },
+    { MBEDTLS_ECP_DP_NONE,          0,     0,      NULL                },
 };
 
 #define ECP_NB_CURVES   sizeof( ecp_supported_curves ) /    \
                         sizeof( ecp_supported_curves[0] )
 
-static ecp_group_id ecp_supported_grp_id[ECP_NB_CURVES];
+static mbedtls_ecp_group_id ecp_supported_grp_id[ECP_NB_CURVES];
 
 /*
  * List of supported curves and associated info
  */
-const ecp_curve_info *ecp_curve_list( void )
+const mbedtls_ecp_curve_info *mbedtls_ecp_curve_list( void )
 {
     return( ecp_supported_curves );
 }
@@ -184,22 +184,22 @@
 /*
  * List of supported curves, group ID only
  */
-const ecp_group_id *ecp_grp_id_list( void )
+const mbedtls_ecp_group_id *mbedtls_ecp_grp_id_list( void )
 {
     static int init_done = 0;
 
     if( ! init_done )
     {
         size_t i = 0;
-        const ecp_curve_info *curve_info;
+        const mbedtls_ecp_curve_info *curve_info;
 
-        for( curve_info = ecp_curve_list();
-             curve_info->grp_id != POLARSSL_ECP_DP_NONE;
+        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] = POLARSSL_ECP_DP_NONE;
+        ecp_supported_grp_id[i] = MBEDTLS_ECP_DP_NONE;
 
         init_done = 1;
     }
@@ -210,12 +210,12 @@
 /*
  * Get the curve info for the internal identifier
  */
-const ecp_curve_info *ecp_curve_info_from_grp_id( ecp_group_id grp_id )
+const mbedtls_ecp_curve_info *mbedtls_ecp_curve_info_from_grp_id( mbedtls_ecp_group_id grp_id )
 {
-    const ecp_curve_info *curve_info;
+    const mbedtls_ecp_curve_info *curve_info;
 
-    for( curve_info = ecp_curve_list();
-         curve_info->grp_id != POLARSSL_ECP_DP_NONE;
+    for( curve_info = mbedtls_ecp_curve_list();
+         curve_info->grp_id != MBEDTLS_ECP_DP_NONE;
          curve_info++ )
     {
         if( curve_info->grp_id == grp_id )
@@ -228,12 +228,12 @@
 /*
  * Get the curve info from the TLS identifier
  */
-const ecp_curve_info *ecp_curve_info_from_tls_id( uint16_t tls_id )
+const mbedtls_ecp_curve_info *mbedtls_ecp_curve_info_from_tls_id( uint16_t tls_id )
 {
-    const ecp_curve_info *curve_info;
+    const mbedtls_ecp_curve_info *curve_info;
 
-    for( curve_info = ecp_curve_list();
-         curve_info->grp_id != POLARSSL_ECP_DP_NONE;
+    for( curve_info = mbedtls_ecp_curve_list();
+         curve_info->grp_id != MBEDTLS_ECP_DP_NONE;
          curve_info++ )
     {
         if( curve_info->tls_id == tls_id )
@@ -246,12 +246,12 @@
 /*
  * Get the curve info from the name
  */
-const ecp_curve_info *ecp_curve_info_from_name( const char *name )
+const mbedtls_ecp_curve_info *mbedtls_ecp_curve_info_from_name( const char *name )
 {
-    const ecp_curve_info *curve_info;
+    const mbedtls_ecp_curve_info *curve_info;
 
-    for( curve_info = ecp_curve_list();
-         curve_info->grp_id != POLARSSL_ECP_DP_NONE;
+    for( curve_info = mbedtls_ecp_curve_list();
+         curve_info->grp_id != MBEDTLS_ECP_DP_NONE;
          curve_info++ )
     {
         if( strcasecmp( curve_info->name, name ) == 0 )
@@ -264,71 +264,71 @@
 /*
  * Get the type of a curve
  */
-static inline ecp_curve_type ecp_get_type( const ecp_group *grp )
+static inline ecp_curve_type ecp_get_type( const mbedtls_ecp_group *grp )
 {
     if( grp->G.X.p == NULL )
-        return( POLARSSL_ECP_TYPE_NONE );
+        return( MBEDTLS_ECP_TYPE_NONE );
 
     if( grp->G.Y.p == NULL )
-        return( POLARSSL_ECP_TYPE_MONTGOMERY );
+        return( MBEDTLS_ECP_TYPE_MONTGOMERY );
     else
-        return( POLARSSL_ECP_TYPE_SHORT_WEIERSTRASS );
+        return( MBEDTLS_ECP_TYPE_SHORT_WEIERSTRASS );
 }
 
 /*
  * Initialize (the components of) a point
  */
-void ecp_point_init( ecp_point *pt )
+void mbedtls_ecp_point_init( mbedtls_ecp_point *pt )
 {
     if( pt == NULL )
         return;
 
-    mpi_init( &pt->X );
-    mpi_init( &pt->Y );
-    mpi_init( &pt->Z );
+    mbedtls_mpi_init( &pt->X );
+    mbedtls_mpi_init( &pt->Y );
+    mbedtls_mpi_init( &pt->Z );
 }
 
 /*
  * Initialize (the components of) a group
  */
-void ecp_group_init( ecp_group *grp )
+void mbedtls_ecp_group_init( mbedtls_ecp_group *grp )
 {
     if( grp == NULL )
         return;
 
-    memset( grp, 0, sizeof( ecp_group ) );
+    memset( grp, 0, sizeof( mbedtls_ecp_group ) );
 }
 
 /*
  * Initialize (the components of) a key pair
  */
-void ecp_keypair_init( ecp_keypair *key )
+void mbedtls_ecp_keypair_init( mbedtls_ecp_keypair *key )
 {
     if( key == NULL )
         return;
 
-    ecp_group_init( &key->grp );
-    mpi_init( &key->d );
-    ecp_point_init( &key->Q );
+    mbedtls_ecp_group_init( &key->grp );
+    mbedtls_mpi_init( &key->d );
+    mbedtls_ecp_point_init( &key->Q );
 }
 
 /*
  * Unallocate (the components of) a point
  */
-void ecp_point_free( ecp_point *pt )
+void mbedtls_ecp_point_free( mbedtls_ecp_point *pt )
 {
     if( pt == NULL )
         return;
 
-    mpi_free( &( pt->X ) );
-    mpi_free( &( pt->Y ) );
-    mpi_free( &( pt->Z ) );
+    mbedtls_mpi_free( &( pt->X ) );
+    mbedtls_mpi_free( &( pt->Y ) );
+    mbedtls_mpi_free( &( pt->Z ) );
 }
 
 /*
  * Unallocate (the components of) a group
  */
-void ecp_group_free( ecp_group *grp )
+void mbedtls_ecp_group_free( mbedtls_ecp_group *grp )
 {
     size_t i;
 
@@ -337,46 +337,46 @@
 
     if( grp->h != 1 )
     {
-        mpi_free( &grp->P );
-        mpi_free( &grp->A );
-        mpi_free( &grp->B );
-        ecp_point_free( &grp->G );
-        mpi_free( &grp->N );
+        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++ )
-            ecp_point_free( &grp->T[i] );
-        polarssl_free( grp->T );
+            mbedtls_ecp_point_free( &grp->T[i] );
+        mbedtls_free( grp->T );
     }
 
-    polarssl_zeroize( grp, sizeof( ecp_group ) );
+    mbedtls_zeroize( grp, sizeof( mbedtls_ecp_group ) );
 }
 
 /*
  * Unallocate (the components of) a key pair
  */
-void ecp_keypair_free( ecp_keypair *key )
+void mbedtls_ecp_keypair_free( mbedtls_ecp_keypair *key )
 {
     if( key == NULL )
         return;
 
-    ecp_group_free( &key->grp );
-    mpi_free( &key->d );
-    ecp_point_free( &key->Q );
+    mbedtls_ecp_group_free( &key->grp );
+    mbedtls_mpi_free( &key->d );
+    mbedtls_ecp_point_free( &key->Q );
 }
 
 /*
  * Copy the contents of a point
  */
-int ecp_copy( ecp_point *P, const ecp_point *Q )
+int mbedtls_ecp_copy( mbedtls_ecp_point *P, const mbedtls_ecp_point *Q )
 {
     int ret;
 
-    MPI_CHK( mpi_copy( &P->X, &Q->X ) );
-    MPI_CHK( mpi_copy( &P->Y, &Q->Y ) );
-    MPI_CHK( mpi_copy( &P->Z, &Q->Z ) );
+    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 );
@@ -385,21 +385,21 @@
 /*
  * Copy the contents of a group object
  */
-int ecp_group_copy( ecp_group *dst, const ecp_group *src )
+int mbedtls_ecp_group_copy( mbedtls_ecp_group *dst, const mbedtls_ecp_group *src )
 {
-    return ecp_use_known_dp( dst, src->id );
+    return mbedtls_ecp_use_known_dp( dst, src->id );
 }
 
 /*
  * Set point to zero
  */
-int ecp_set_zero( ecp_point *pt )
+int mbedtls_ecp_set_zero( mbedtls_ecp_point *pt )
 {
     int ret;
 
-    MPI_CHK( mpi_lset( &pt->X , 1 ) );
-    MPI_CHK( mpi_lset( &pt->Y , 1 ) );
-    MPI_CHK( mpi_lset( &pt->Z , 0 ) );
+    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 );
@@ -408,22 +408,22 @@
 /*
  * Tell if a point is zero
  */
-int ecp_is_zero( ecp_point *pt )
+int mbedtls_ecp_is_zero( mbedtls_ecp_point *pt )
 {
-    return( mpi_cmp_int( &pt->Z, 0 ) == 0 );
+    return( mbedtls_mpi_cmp_int( &pt->Z, 0 ) == 0 );
 }
 
 /*
  * Import a non-zero point from ASCII strings
  */
-int ecp_point_read_string( ecp_point *P, int radix,
+int mbedtls_ecp_point_read_string( mbedtls_ecp_point *P, int radix,
                            const char *x, const char *y )
 {
     int ret;
 
-    MPI_CHK( mpi_read_string( &P->X, radix, x ) );
-    MPI_CHK( mpi_read_string( &P->Y, radix, y ) );
-    MPI_CHK( mpi_lset( &P->Z, 1 ) );
+    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 );
@@ -432,24 +432,24 @@
 /*
  * Export a point into unsigned binary data (SEC1 2.3.3)
  */
-int ecp_point_write_binary( const ecp_group *grp, const ecp_point *P,
+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 = 0;
     size_t plen;
 
-    if( format != POLARSSL_ECP_PF_UNCOMPRESSED &&
-        format != POLARSSL_ECP_PF_COMPRESSED )
-        return( POLARSSL_ERR_ECP_BAD_INPUT_DATA );
+    if( format != MBEDTLS_ECP_PF_UNCOMPRESSED &&
+        format != MBEDTLS_ECP_PF_COMPRESSED )
+        return( MBEDTLS_ERR_ECP_BAD_INPUT_DATA );
 
     /*
      * Common case: P == 0
      */
-    if( mpi_cmp_int( &P->Z, 0 ) == 0 )
+    if( mbedtls_mpi_cmp_int( &P->Z, 0 ) == 0 )
     {
         if( buflen < 1 )
-            return( POLARSSL_ERR_ECP_BUFFER_TOO_SMALL );
+            return( MBEDTLS_ERR_ECP_BUFFER_TOO_SMALL );
 
         buf[0] = 0x00;
         *olen = 1;
@@ -457,28 +457,28 @@
         return( 0 );
     }
 
-    plen = mpi_size( &grp->P );
+    plen = mbedtls_mpi_size( &grp->P );
 
-    if( format == POLARSSL_ECP_PF_UNCOMPRESSED )
+    if( format == MBEDTLS_ECP_PF_UNCOMPRESSED )
     {
         *olen = 2 * plen + 1;
 
         if( buflen < *olen )
-            return( POLARSSL_ERR_ECP_BUFFER_TOO_SMALL );
+            return( MBEDTLS_ERR_ECP_BUFFER_TOO_SMALL );
 
         buf[0] = 0x04;
-        MPI_CHK( mpi_write_binary( &P->X, buf + 1, plen ) );
-        MPI_CHK( mpi_write_binary( &P->Y, buf + 1 + plen, plen ) );
+        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 == POLARSSL_ECP_PF_COMPRESSED )
+    else if( format == MBEDTLS_ECP_PF_COMPRESSED )
     {
         *olen = plen + 1;
 
         if( buflen < *olen )
-            return( POLARSSL_ERR_ECP_BUFFER_TOO_SMALL );
+            return( MBEDTLS_ERR_ECP_BUFFER_TOO_SMALL );
 
-        buf[0] = 0x02 + mpi_get_bit( &P->Y, 0 );
-        MPI_CHK( mpi_write_binary( &P->X, buf + 1, plen ) );
+        buf[0] = 0x02 + mbedtls_mpi_get_bit( &P->Y, 0 );
+        MBEDTLS_MPI_CHK( mbedtls_mpi_write_binary( &P->X, buf + 1, plen ) );
     }
 
 cleanup:
@@ -488,34 +488,34 @@
 /*
  * Import a point from unsigned binary data (SEC1 2.3.4)
  */
-int ecp_point_read_binary( const ecp_group *grp, ecp_point *pt,
+int mbedtls_ecp_point_read_binary( const mbedtls_ecp_group *grp, mbedtls_ecp_point *pt,
                            const unsigned char *buf, size_t ilen )
 {
     int ret;
     size_t plen;
 
     if( ilen < 1 )
-        return( POLARSSL_ERR_ECP_BAD_INPUT_DATA );
+        return( MBEDTLS_ERR_ECP_BAD_INPUT_DATA );
 
     if( buf[0] == 0x00 )
     {
         if( ilen == 1 )
-            return( ecp_set_zero( pt ) );
+            return( mbedtls_ecp_set_zero( pt ) );
         else
-            return( POLARSSL_ERR_ECP_BAD_INPUT_DATA );
+            return( MBEDTLS_ERR_ECP_BAD_INPUT_DATA );
     }
 
-    plen = mpi_size( &grp->P );
+    plen = mbedtls_mpi_size( &grp->P );
 
     if( buf[0] != 0x04 )
-        return( POLARSSL_ERR_ECP_FEATURE_UNAVAILABLE );
+        return( MBEDTLS_ERR_ECP_FEATURE_UNAVAILABLE );
 
     if( ilen != 2 * plen + 1 )
-        return( POLARSSL_ERR_ECP_BAD_INPUT_DATA );
+        return( MBEDTLS_ERR_ECP_BAD_INPUT_DATA );
 
-    MPI_CHK( mpi_read_binary( &pt->X, buf + 1, plen ) );
-    MPI_CHK( mpi_read_binary( &pt->Y, buf + 1 + plen, plen ) );
-    MPI_CHK( mpi_lset( &pt->Z, 1 ) );
+    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 ) );
 
 cleanup:
     return( ret );
@@ -527,7 +527,7 @@
  *          opaque point <1..2^8-1>;
  *      } ECPoint;
  */
-int ecp_tls_read_point( const ecp_group *grp, ecp_point *pt,
+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;
@@ -537,11 +537,11 @@
      * We must have at least two bytes (1 for length, at least one for data)
      */
     if( buf_len < 2 )
-        return( POLARSSL_ERR_ECP_BAD_INPUT_DATA );
+        return( MBEDTLS_ERR_ECP_BAD_INPUT_DATA );
 
     data_len = *(*buf)++;
     if( data_len < 1 || data_len > buf_len - 1 )
-        return( POLARSSL_ERR_ECP_BAD_INPUT_DATA );
+        return( MBEDTLS_ERR_ECP_BAD_INPUT_DATA );
 
     /*
      * Save buffer start for read_binary and update buf
@@ -549,7 +549,7 @@
     buf_start = *buf;
     *buf += data_len;
 
-    return ecp_point_read_binary( grp, pt, buf_start, data_len );
+    return mbedtls_ecp_point_read_binary( grp, pt, buf_start, data_len );
 }
 
 /*
@@ -558,7 +558,7 @@
  *          opaque point <1..2^8-1>;
  *      } ECPoint;
  */
-int ecp_tls_write_point( const ecp_group *grp, const ecp_point *pt,
+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 )
 {
@@ -568,9 +568,9 @@
      * buffer length must be at least one, for our length byte
      */
     if( blen < 1 )
-        return( POLARSSL_ERR_ECP_BAD_INPUT_DATA );
+        return( MBEDTLS_ERR_ECP_BAD_INPUT_DATA );
 
-    if( ( ret = ecp_point_write_binary( grp, pt, format,
+    if( ( ret = mbedtls_ecp_point_write_binary( grp, pt, format,
                     olen, buf + 1, blen - 1) ) != 0 )
         return( ret );
 
@@ -586,23 +586,23 @@
 /*
  * Import an ECP group from ASCII strings, case A == -3
  */
-int ecp_group_read_string( ecp_group *grp, int radix,
+int mbedtls_ecp_group_read_string( mbedtls_ecp_group *grp, int radix,
                            const char *p, const char *b,
                            const char *gx, const char *gy, const char *n)
 {
     int ret;
 
-    MPI_CHK( mpi_read_string( &grp->P, radix, p ) );
-    MPI_CHK( mpi_read_string( &grp->B, radix, b ) );
-    MPI_CHK( ecp_point_read_string( &grp->G, radix, gx, gy ) );
-    MPI_CHK( mpi_read_string( &grp->N, radix, n ) );
+    MBEDTLS_MPI_CHK( mbedtls_mpi_read_string( &grp->P, radix, p ) );
+    MBEDTLS_MPI_CHK( mbedtls_mpi_read_string( &grp->B, radix, b ) );
+    MBEDTLS_MPI_CHK( mbedtls_ecp_point_read_string( &grp->G, radix, gx, gy ) );
+    MBEDTLS_MPI_CHK( mbedtls_mpi_read_string( &grp->N, radix, n ) );
 
-    grp->pbits = mpi_msb( &grp->P );
-    grp->nbits = mpi_msb( &grp->N );
+    grp->pbits = mbedtls_mpi_msb( &grp->P );
+    grp->nbits = mbedtls_mpi_msb( &grp->N );
 
 cleanup:
     if( ret != 0 )
-        ecp_group_free( grp );
+        mbedtls_ecp_group_free( grp );
 
     return( ret );
 }
@@ -610,22 +610,22 @@
 /*
  * Set a group from an ECParameters record (RFC 4492)
  */
-int ecp_tls_read_group( ecp_group *grp, const unsigned char **buf, size_t len )
+int mbedtls_ecp_tls_read_group( mbedtls_ecp_group *grp, const unsigned char **buf, size_t len )
 {
     uint16_t tls_id;
-    const ecp_curve_info *curve_info;
+    const mbedtls_ecp_curve_info *curve_info;
 
     /*
      * We expect at least three bytes (see below)
      */
     if( len < 3 )
-        return( POLARSSL_ERR_ECP_BAD_INPUT_DATA );
+        return( MBEDTLS_ERR_ECP_BAD_INPUT_DATA );
 
     /*
      * First byte is curve_type; only named_curve is handled
      */
-    if( *(*buf)++ != POLARSSL_ECP_TLS_NAMED_CURVE )
-        return( POLARSSL_ERR_ECP_BAD_INPUT_DATA );
+    if( *(*buf)++ != MBEDTLS_ECP_TLS_NAMED_CURVE )
+        return( MBEDTLS_ERR_ECP_BAD_INPUT_DATA );
 
     /*
      * Next two bytes are the namedcurve value
@@ -634,34 +634,34 @@
     tls_id <<= 8;
     tls_id |= *(*buf)++;
 
-    if( ( curve_info = ecp_curve_info_from_tls_id( tls_id ) ) == NULL )
-        return( POLARSSL_ERR_ECP_FEATURE_UNAVAILABLE );
+    if( ( curve_info = mbedtls_ecp_curve_info_from_tls_id( tls_id ) ) == NULL )
+        return( MBEDTLS_ERR_ECP_FEATURE_UNAVAILABLE );
 
-    return ecp_use_known_dp( grp, curve_info->grp_id );
+    return mbedtls_ecp_use_known_dp( grp, curve_info->grp_id );
 }
 
 /*
  * Write the ECParameters record corresponding to a group (RFC 4492)
  */
-int ecp_tls_write_group( const ecp_group *grp, size_t *olen,
+int mbedtls_ecp_tls_write_group( const mbedtls_ecp_group *grp, size_t *olen,
                          unsigned char *buf, size_t blen )
 {
-    const ecp_curve_info *curve_info;
+    const mbedtls_ecp_curve_info *curve_info;
 
-    if( ( curve_info = ecp_curve_info_from_grp_id( grp->id ) ) == NULL )
-        return( POLARSSL_ERR_ECP_BAD_INPUT_DATA );
+    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( POLARSSL_ERR_ECP_BUFFER_TOO_SMALL );
+        return( MBEDTLS_ERR_ECP_BUFFER_TOO_SMALL );
 
     /*
      * First byte is curve_type, always named_curve
      */
-    *buf++ = POLARSSL_ECP_TLS_NAMED_CURVE;
+    *buf++ = MBEDTLS_ECP_TLS_NAMED_CURVE;
 
     /*
      * Next two bytes are the namedcurve value
@@ -673,34 +673,34 @@
 }
 
 /*
- * Wrapper around fast quasi-modp functions, with fall-back to mpi_mod_mpi.
- * See the documentation of struct ecp_group.
+ * 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 ecp_mul, so pay attention to perf.
+ * This function is in the critial loop for mbedtls_ecp_mul, so pay attention to perf.
  */
-static int ecp_modp( mpi *N, const ecp_group *grp )
+static int ecp_modp( mbedtls_mpi *N, const mbedtls_ecp_group *grp )
 {
     int ret;
 
     if( grp->modp == NULL )
-        return( mpi_mod_mpi( N, N, &grp->P ) );
+        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 && mpi_cmp_int( N, 0 ) != 0 ) ||
-        mpi_msb( N ) > 2 * grp->pbits )
+    if( ( N->s < 0 && mbedtls_mpi_cmp_int( N, 0 ) != 0 ) ||
+        mbedtls_mpi_msb( N ) > 2 * grp->pbits )
     {
-        return( POLARSSL_ERR_ECP_BAD_INPUT_DATA );
+        return( MBEDTLS_ERR_ECP_BAD_INPUT_DATA );
     }
 
-    MPI_CHK( grp->modp( N ) );
+    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 && mpi_cmp_int( N, 0 ) != 0 )
-        MPI_CHK( mpi_add_mpi( N, N, &grp->P ) );
+    while( N->s < 0 && mbedtls_mpi_cmp_int( N, 0 ) != 0 )
+        MBEDTLS_MPI_CHK( mbedtls_mpi_add_mpi( N, N, &grp->P ) );
 
-    while( mpi_cmp_mpi( N, &grp->P ) >= 0 )
+    while( mbedtls_mpi_cmp_mpi( N, &grp->P ) >= 0 )
         /* we known P, N and the result are positive */
-        MPI_CHK( mpi_sub_abs( N, N, &grp->P ) );
+        MBEDTLS_MPI_CHK( mbedtls_mpi_sub_abs( N, N, &grp->P ) );
 
 cleanup:
     return( ret );
@@ -710,42 +710,42 @@
  * 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
- * mpi_mul_mpi are in the 0..p range. So, after each operation we will
+ * 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 mpi mod p in-place, general case, to use after mpi_mul_mpi
+ * Reduce a mbedtls_mpi mod p in-place, general case, to use after mbedtls_mpi_mul_mpi
  */
-#if defined(POLARSSL_SELF_TEST)
+#if defined(MBEDTLS_SELF_TEST)
 #define INC_MUL_COUNT   mul_count++;
 #else
 #define INC_MUL_COUNT
 #endif
 
-#define MOD_MUL( N )    do { MPI_CHK( ecp_modp( &N, grp ) ); INC_MUL_COUNT } \
+#define MOD_MUL( N )    do { MBEDTLS_MPI_CHK( ecp_modp( &N, grp ) ); INC_MUL_COUNT } \
                         while( 0 )
 
 /*
- * Reduce a mpi mod p in-place, to use after mpi_sub_mpi
+ * 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 && mpi_cmp_int( &N, 0 ) != 0 )   \
-        MPI_CHK( mpi_add_mpi( &N, &N, &grp->P ) )
+    while( N.s < 0 && mbedtls_mpi_cmp_int( &N, 0 ) != 0 )   \
+        MBEDTLS_MPI_CHK( mbedtls_mpi_add_mpi( &N, &N, &grp->P ) )
 
 /*
- * Reduce a mpi mod p in-place, to use after mpi_add_mpi and mpi_mul_int.
+ * 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( mpi_cmp_mpi( &N, &grp->P ) >= 0 )        \
-        MPI_CHK( mpi_sub_abs( &N, &N, &grp->P ) )
+    while( mbedtls_mpi_cmp_mpi( &N, &grp->P ) >= 0 )        \
+        MBEDTLS_MPI_CHK( mbedtls_mpi_sub_abs( &N, &N, &grp->P ) )
 
-#if defined(POLARSSL_ECP_SHORT_WEIERSTRASS)
+#if defined(MBEDTLS_ECP_SHORT_WEIERSTRASS)
 /*
  * For curves in short Weierstrass form, we do all the internal operations in
  * Jacobian coordinates.
@@ -758,37 +758,37 @@
  * Normalize jacobian coordinates so that Z == 0 || Z == 1  (GECC 3.2.1)
  * Cost: 1N := 1I + 3M + 1S
  */
-static int ecp_normalize_jac( const ecp_group *grp, ecp_point *pt )
+static int ecp_normalize_jac( const mbedtls_ecp_group *grp, mbedtls_ecp_point *pt )
 {
     int ret;
-    mpi Zi, ZZi;
+    mbedtls_mpi Zi, ZZi;
 
-    if( mpi_cmp_int( &pt->Z, 0 ) == 0 )
+    if( mbedtls_mpi_cmp_int( &pt->Z, 0 ) == 0 )
         return( 0 );
 
-    mpi_init( &Zi ); mpi_init( &ZZi );
+    mbedtls_mpi_init( &Zi ); mbedtls_mpi_init( &ZZi );
 
     /*
      * X = X / Z^2  mod p
      */
-    MPI_CHK( mpi_inv_mod( &Zi,      &pt->Z,     &grp->P ) );
-    MPI_CHK( mpi_mul_mpi( &ZZi,     &Zi,        &Zi     ) ); MOD_MUL( ZZi );
-    MPI_CHK( mpi_mul_mpi( &pt->X,   &pt->X,     &ZZi    ) ); MOD_MUL( pt->X );
+    MBEDTLS_MPI_CHK( mbedtls_mpi_inv_mod( &Zi,      &pt->Z,     &grp->P ) );
+    MBEDTLS_MPI_CHK( mbedtls_mpi_mul_mpi( &ZZi,     &Zi,        &Zi     ) ); MOD_MUL( ZZi );
+    MBEDTLS_MPI_CHK( mbedtls_mpi_mul_mpi( &pt->X,   &pt->X,     &ZZi    ) ); MOD_MUL( pt->X );
 
     /*
      * Y = Y / Z^3  mod p
      */
-    MPI_CHK( mpi_mul_mpi( &pt->Y,   &pt->Y,     &ZZi    ) ); MOD_MUL( pt->Y );
-    MPI_CHK( mpi_mul_mpi( &pt->Y,   &pt->Y,     &Zi     ) ); MOD_MUL( pt->Y );
+    MBEDTLS_MPI_CHK( mbedtls_mpi_mul_mpi( &pt->Y,   &pt->Y,     &ZZi    ) ); MOD_MUL( pt->Y );
+    MBEDTLS_MPI_CHK( mbedtls_mpi_mul_mpi( &pt->Y,   &pt->Y,     &Zi     ) ); MOD_MUL( pt->Y );
 
     /*
      * Z = 1
      */
-    MPI_CHK( mpi_lset( &pt->Z, 1 ) );
+    MBEDTLS_MPI_CHK( mbedtls_mpi_lset( &pt->Z, 1 ) );
 
 cleanup:
 
-    mpi_free( &Zi ); mpi_free( &ZZi );
+    mbedtls_mpi_free( &Zi ); mbedtls_mpi_free( &ZZi );
 
     return( ret );
 }
@@ -804,37 +804,37 @@
  *
  * Cost: 1N(t) := 1I + (6t - 3)M + 1S
  */
-static int ecp_normalize_jac_many( const ecp_group *grp,
-                                   ecp_point *T[], size_t t_len )
+static int ecp_normalize_jac_many( const mbedtls_ecp_group *grp,
+                                   mbedtls_ecp_point *T[], size_t t_len )
 {
     int ret;
     size_t i;
-    mpi *c, u, Zi, ZZi;
+    mbedtls_mpi *c, u, Zi, ZZi;
 
     if( t_len < 2 )
         return( ecp_normalize_jac( grp, *T ) );
 
-    if( ( c = polarssl_malloc( t_len * sizeof( mpi ) ) ) == NULL )
-        return( POLARSSL_ERR_ECP_MALLOC_FAILED );
+    if( ( c = mbedtls_malloc( t_len * sizeof( mbedtls_mpi ) ) ) == NULL )
+        return( MBEDTLS_ERR_ECP_MALLOC_FAILED );
 
-    mpi_init( &u ); mpi_init( &Zi ); mpi_init( &ZZi );
+    mbedtls_mpi_init( &u ); mbedtls_mpi_init( &Zi ); mbedtls_mpi_init( &ZZi );
     for( i = 0; i < t_len; i++ )
-        mpi_init( &c[i] );
+        mbedtls_mpi_init( &c[i] );
 
     /*
      * c[i] = Z_0 * ... * Z_i
      */
-    MPI_CHK( mpi_copy( &c[0], &T[0]->Z ) );
+    MBEDTLS_MPI_CHK( mbedtls_mpi_copy( &c[0], &T[0]->Z ) );
     for( i = 1; i < t_len; i++ )
     {
-        MPI_CHK( mpi_mul_mpi( &c[i], &c[i-1], &T[i]->Z ) );
+        MBEDTLS_MPI_CHK( mbedtls_mpi_mul_mpi( &c[i], &c[i-1], &T[i]->Z ) );
         MOD_MUL( c[i] );
     }
 
     /*
      * u = 1 / (Z_0 * ... * Z_n) mod P
      */
-    MPI_CHK( mpi_inv_mod( &u, &c[t_len-1], &grp->P ) );
+    MBEDTLS_MPI_CHK( mbedtls_mpi_inv_mod( &u, &c[t_len-1], &grp->P ) );
 
     for( i = t_len - 1; ; i-- )
     {
@@ -843,21 +843,21 @@
          * u = 1 / (Z_0 * ... * Z_i) mod P
          */
         if( i == 0 ) {
-            MPI_CHK( mpi_copy( &Zi, &u ) );
+            MBEDTLS_MPI_CHK( mbedtls_mpi_copy( &Zi, &u ) );
         }
         else
         {
-            MPI_CHK( mpi_mul_mpi( &Zi, &u, &c[i-1]  ) ); MOD_MUL( Zi );
-            MPI_CHK( mpi_mul_mpi( &u,  &u, &T[i]->Z ) ); MOD_MUL( u );
+            MBEDTLS_MPI_CHK( mbedtls_mpi_mul_mpi( &Zi, &u, &c[i-1]  ) ); MOD_MUL( Zi );
+            MBEDTLS_MPI_CHK( mbedtls_mpi_mul_mpi( &u,  &u, &T[i]->Z ) ); MOD_MUL( u );
         }
 
         /*
          * proceed as in normalize()
          */
-        MPI_CHK( mpi_mul_mpi( &ZZi,     &Zi,      &Zi  ) ); MOD_MUL( ZZi );
-        MPI_CHK( mpi_mul_mpi( &T[i]->X, &T[i]->X, &ZZi ) ); MOD_MUL( T[i]->X );
-        MPI_CHK( mpi_mul_mpi( &T[i]->Y, &T[i]->Y, &ZZi ) ); MOD_MUL( T[i]->Y );
-        MPI_CHK( mpi_mul_mpi( &T[i]->Y, &T[i]->Y, &Zi  ) ); MOD_MUL( T[i]->Y );
+        MBEDTLS_MPI_CHK( mbedtls_mpi_mul_mpi( &ZZi,     &Zi,      &Zi  ) ); MOD_MUL( ZZi );
+        MBEDTLS_MPI_CHK( mbedtls_mpi_mul_mpi( &T[i]->X, &T[i]->X, &ZZi ) ); MOD_MUL( T[i]->X );
+        MBEDTLS_MPI_CHK( mbedtls_mpi_mul_mpi( &T[i]->Y, &T[i]->Y, &ZZi ) ); MOD_MUL( T[i]->Y );
+        MBEDTLS_MPI_CHK( mbedtls_mpi_mul_mpi( &T[i]->Y, &T[i]->Y, &Zi  ) ); MOD_MUL( T[i]->Y );
 
         /*
          * Post-precessing: reclaim some memory by shrinking coordinates
@@ -865,9 +865,9 @@
          * - shrinking other coordinates, but still keeping the same number of
          *   limbs as P, as otherwise it will too likely be regrown too fast.
          */
-        MPI_CHK( mpi_shrink( &T[i]->X, grp->P.n ) );
-        MPI_CHK( mpi_shrink( &T[i]->Y, grp->P.n ) );
-        mpi_free( &T[i]->Z );
+        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;
@@ -875,10 +875,10 @@
 
 cleanup:
 
-    mpi_free( &u ); mpi_free( &Zi ); mpi_free( &ZZi );
+    mbedtls_mpi_free( &u ); mbedtls_mpi_free( &Zi ); mbedtls_mpi_free( &ZZi );
     for( i = 0; i < t_len; i++ )
-        mpi_free( &c[i] );
-    polarssl_free( c );
+        mbedtls_mpi_free( &c[i] );
+    mbedtls_free( c );
 
     return( ret );
 }
@@ -887,23 +887,23 @@
  * 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 ecp_group *grp,
-                            ecp_point *Q,
+static int ecp_safe_invert_jac( const mbedtls_ecp_group *grp,
+                            mbedtls_ecp_point *Q,
                             unsigned char inv )
 {
     int ret;
     unsigned char nonzero;
-    mpi mQY;
+    mbedtls_mpi mQY;
 
-    mpi_init( &mQY );
+    mbedtls_mpi_init( &mQY );
 
     /* Use the fact that -Q.Y mod P = P - Q.Y unless Q.Y == 0 */
-    MPI_CHK( mpi_sub_mpi( &mQY, &grp->P, &Q->Y ) );
-    nonzero = mpi_cmp_int( &Q->Y, 0 ) != 0;
-    MPI_CHK( mpi_safe_cond_assign( &Q->Y, &mQY, inv & nonzero ) );
+    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:
-    mpi_free( &mQY );
+    mbedtls_mpi_free( &mQY );
 
     return( ret );
 }
@@ -918,63 +918,63 @@
  *
  * Cost: 1D := 2M + 8S
  */
-static int ecp_double_jac( const ecp_group *grp, ecp_point *R,
-                           const ecp_point *P )
+static int ecp_double_jac( const mbedtls_ecp_group *grp, mbedtls_ecp_point *R,
+                           const mbedtls_ecp_point *P )
 {
     int ret;
-    mpi T1, T2, T3, X3, Y3, Z3;
+    mbedtls_mpi T1, T2, T3, X3, Y3, Z3;
 
-#if defined(POLARSSL_SELF_TEST)
+#if defined(MBEDTLS_SELF_TEST)
     dbl_count++;
 #endif
 
-    mpi_init( &T1 ); mpi_init( &T2 ); mpi_init( &T3 );
-    mpi_init( &X3 ); mpi_init( &Y3 ); mpi_init( &Z3 );
+    mbedtls_mpi_init( &T1 ); mbedtls_mpi_init( &T2 ); mbedtls_mpi_init( &T3 );
+    mbedtls_mpi_init( &X3 ); mbedtls_mpi_init( &Y3 ); mbedtls_mpi_init( &Z3 );
 
-    MPI_CHK( mpi_mul_mpi( &T3,  &P->X,  &P->X   ) ); MOD_MUL( T3 );
-    MPI_CHK( mpi_mul_mpi( &T2,  &P->Y,  &P->Y   ) ); MOD_MUL( T2 );
-    MPI_CHK( mpi_mul_mpi( &Y3,  &T2,    &T2     ) ); MOD_MUL( Y3 );
-    MPI_CHK( mpi_add_mpi( &X3,  &P->X,  &T2     ) ); MOD_ADD( X3 );
-    MPI_CHK( mpi_mul_mpi( &X3,  &X3,    &X3     ) ); MOD_MUL( X3 );
-    MPI_CHK( mpi_sub_mpi( &X3,  &X3,    &Y3     ) ); MOD_SUB( X3 );
-    MPI_CHK( mpi_sub_mpi( &X3,  &X3,    &T3     ) ); MOD_SUB( X3 );
-    MPI_CHK( mpi_mul_int( &T1,  &X3,    2       ) ); MOD_ADD( T1 );
-    MPI_CHK( mpi_mul_mpi( &Z3,  &P->Z,  &P->Z   ) ); MOD_MUL( Z3 );
-    MPI_CHK( mpi_mul_mpi( &X3,  &Z3,    &Z3     ) ); MOD_MUL( X3 );
-    MPI_CHK( mpi_mul_int( &T3,  &T3,    3       ) ); MOD_ADD( T3 );
+    MBEDTLS_MPI_CHK( mbedtls_mpi_mul_mpi( &T3,  &P->X,  &P->X   ) ); MOD_MUL( T3 );
+    MBEDTLS_MPI_CHK( mbedtls_mpi_mul_mpi( &T2,  &P->Y,  &P->Y   ) ); MOD_MUL( T2 );
+    MBEDTLS_MPI_CHK( mbedtls_mpi_mul_mpi( &Y3,  &T2,    &T2     ) ); MOD_MUL( Y3 );
+    MBEDTLS_MPI_CHK( mbedtls_mpi_add_mpi( &X3,  &P->X,  &T2     ) ); MOD_ADD( X3 );
+    MBEDTLS_MPI_CHK( mbedtls_mpi_mul_mpi( &X3,  &X3,    &X3     ) ); MOD_MUL( X3 );
+    MBEDTLS_MPI_CHK( mbedtls_mpi_sub_mpi( &X3,  &X3,    &Y3     ) ); MOD_SUB( X3 );
+    MBEDTLS_MPI_CHK( mbedtls_mpi_sub_mpi( &X3,  &X3,    &T3     ) ); MOD_SUB( X3 );
+    MBEDTLS_MPI_CHK( mbedtls_mpi_mul_int( &T1,  &X3,    2       ) ); MOD_ADD( T1 );
+    MBEDTLS_MPI_CHK( mbedtls_mpi_mul_mpi( &Z3,  &P->Z,  &P->Z   ) ); MOD_MUL( Z3 );
+    MBEDTLS_MPI_CHK( mbedtls_mpi_mul_mpi( &X3,  &Z3,    &Z3     ) ); MOD_MUL( X3 );
+    MBEDTLS_MPI_CHK( mbedtls_mpi_mul_int( &T3,  &T3,    3       ) ); MOD_ADD( T3 );
 
     /* Special case for A = -3 */
     if( grp->A.p == NULL )
     {
-        MPI_CHK( mpi_mul_int( &X3, &X3, 3 ) );
-        X3.s = -1; /* mpi_mul_int doesn't handle negative numbers */
+        MBEDTLS_MPI_CHK( mbedtls_mpi_mul_int( &X3, &X3, 3 ) );
+        X3.s = -1; /* mbedtls_mpi_mul_int doesn't handle negative numbers */
         MOD_SUB( X3 );
     }
     else
     {
-        MPI_CHK( mpi_mul_mpi( &X3,  &X3,    &grp->A ) ); MOD_MUL( X3 );
+        MBEDTLS_MPI_CHK( mbedtls_mpi_mul_mpi( &X3,  &X3,    &grp->A ) ); MOD_MUL( X3 );
     }
 
-    MPI_CHK( mpi_add_mpi( &T3,  &T3,    &X3     ) ); MOD_ADD( T3 );
-    MPI_CHK( mpi_mul_mpi( &X3,  &T3,    &T3     ) ); MOD_MUL( X3 );
-    MPI_CHK( mpi_sub_mpi( &X3,  &X3,    &T1     ) ); MOD_SUB( X3 );
-    MPI_CHK( mpi_sub_mpi( &X3,  &X3,    &T1     ) ); MOD_SUB( X3 );
-    MPI_CHK( mpi_sub_mpi( &T1,  &T1,    &X3     ) ); MOD_SUB( T1 );
-    MPI_CHK( mpi_mul_mpi( &T1,  &T3,    &T1     ) ); MOD_MUL( T1 );
-    MPI_CHK( mpi_mul_int( &T3,  &Y3,    8       ) ); MOD_ADD( T3 );
-    MPI_CHK( mpi_sub_mpi( &Y3,  &T1,    &T3     ) ); MOD_SUB( Y3 );
-    MPI_CHK( mpi_add_mpi( &T1,  &P->Y,  &P->Z   ) ); MOD_ADD( T1 );
-    MPI_CHK( mpi_mul_mpi( &T1,  &T1,    &T1     ) ); MOD_MUL( T1 );
-    MPI_CHK( mpi_sub_mpi( &T1,  &T1,    &T2     ) ); MOD_SUB( T1 );
-    MPI_CHK( mpi_sub_mpi( &Z3,  &T1,    &Z3     ) ); MOD_SUB( Z3 );
+    MBEDTLS_MPI_CHK( mbedtls_mpi_add_mpi( &T3,  &T3,    &X3     ) ); MOD_ADD( T3 );
+    MBEDTLS_MPI_CHK( mbedtls_mpi_mul_mpi( &X3,  &T3,    &T3     ) ); MOD_MUL( X3 );
+    MBEDTLS_MPI_CHK( mbedtls_mpi_sub_mpi( &X3,  &X3,    &T1     ) ); MOD_SUB( X3 );
+    MBEDTLS_MPI_CHK( mbedtls_mpi_sub_mpi( &X3,  &X3,    &T1     ) ); MOD_SUB( X3 );
+    MBEDTLS_MPI_CHK( mbedtls_mpi_sub_mpi( &T1,  &T1,    &X3     ) ); MOD_SUB( T1 );
+    MBEDTLS_MPI_CHK( mbedtls_mpi_mul_mpi( &T1,  &T3,    &T1     ) ); MOD_MUL( T1 );
+    MBEDTLS_MPI_CHK( mbedtls_mpi_mul_int( &T3,  &Y3,    8       ) ); MOD_ADD( T3 );
+    MBEDTLS_MPI_CHK( mbedtls_mpi_sub_mpi( &Y3,  &T1,    &T3     ) ); MOD_SUB( Y3 );
+    MBEDTLS_MPI_CHK( mbedtls_mpi_add_mpi( &T1,  &P->Y,  &P->Z   ) ); MOD_ADD( T1 );
+    MBEDTLS_MPI_CHK( mbedtls_mpi_mul_mpi( &T1,  &T1,    &T1     ) ); MOD_MUL( T1 );
+    MBEDTLS_MPI_CHK( mbedtls_mpi_sub_mpi( &T1,  &T1,    &T2     ) ); MOD_SUB( T1 );
+    MBEDTLS_MPI_CHK( mbedtls_mpi_sub_mpi( &Z3,  &T1,    &Z3     ) ); MOD_SUB( Z3 );
 
-    MPI_CHK( mpi_copy( &R->X, &X3 ) );
-    MPI_CHK( mpi_copy( &R->Y, &Y3 ) );
-    MPI_CHK( mpi_copy( &R->Z, &Z3 ) );
+    MBEDTLS_MPI_CHK( mbedtls_mpi_copy( &R->X, &X3 ) );
+    MBEDTLS_MPI_CHK( mbedtls_mpi_copy( &R->Y, &Y3 ) );
+    MBEDTLS_MPI_CHK( mbedtls_mpi_copy( &R->Z, &Z3 ) );
 
 cleanup:
-    mpi_free( &T1 ); mpi_free( &T2 ); mpi_free( &T3 );
-    mpi_free( &X3 ); mpi_free( &Y3 ); mpi_free( &Z3 );
+    mbedtls_mpi_free( &T1 ); mbedtls_mpi_free( &T2 ); mbedtls_mpi_free( &T3 );
+    mbedtls_mpi_free( &X3 ); mbedtls_mpi_free( &Y3 ); mbedtls_mpi_free( &Z3 );
 
     return( ret );
 }
@@ -997,77 +997,77 @@
  *
  * Cost: 1A := 8M + 3S
  */
-static int ecp_add_mixed( const ecp_group *grp, ecp_point *R,
-                          const ecp_point *P, const ecp_point *Q )
+static int ecp_add_mixed( const mbedtls_ecp_group *grp, mbedtls_ecp_point *R,
+                          const mbedtls_ecp_point *P, const mbedtls_ecp_point *Q )
 {
     int ret;
-    mpi T1, T2, T3, T4, X, Y, Z;
+    mbedtls_mpi T1, T2, T3, T4, X, Y, Z;
 
-#if defined(POLARSSL_SELF_TEST)
+#if defined(MBEDTLS_SELF_TEST)
     add_count++;
 #endif
 
     /*
      * Trivial cases: P == 0 or Q == 0 (case 1)
      */
-    if( mpi_cmp_int( &P->Z, 0 ) == 0 )
-        return( ecp_copy( R, Q ) );
+    if( mbedtls_mpi_cmp_int( &P->Z, 0 ) == 0 )
+        return( mbedtls_ecp_copy( R, Q ) );
 
-    if( Q->Z.p != NULL && mpi_cmp_int( &Q->Z, 0 ) == 0 )
-        return( ecp_copy( R, P ) );
+    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 && mpi_cmp_int( &Q->Z, 1 ) != 0 )
-        return( POLARSSL_ERR_ECP_BAD_INPUT_DATA );
+    if( Q->Z.p != NULL && mbedtls_mpi_cmp_int( &Q->Z, 1 ) != 0 )
+        return( MBEDTLS_ERR_ECP_BAD_INPUT_DATA );
 
-    mpi_init( &T1 ); mpi_init( &T2 ); mpi_init( &T3 ); mpi_init( &T4 );
-    mpi_init( &X ); mpi_init( &Y ); mpi_init( &Z );
+    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 );
 
-    MPI_CHK( mpi_mul_mpi( &T1,  &P->Z,  &P->Z ) );  MOD_MUL( T1 );
-    MPI_CHK( mpi_mul_mpi( &T2,  &T1,    &P->Z ) );  MOD_MUL( T2 );
-    MPI_CHK( mpi_mul_mpi( &T1,  &T1,    &Q->X ) );  MOD_MUL( T1 );
-    MPI_CHK( mpi_mul_mpi( &T2,  &T2,    &Q->Y ) );  MOD_MUL( T2 );
-    MPI_CHK( mpi_sub_mpi( &T1,  &T1,    &P->X ) );  MOD_SUB( T1 );
-    MPI_CHK( mpi_sub_mpi( &T2,  &T2,    &P->Y ) );  MOD_SUB( T2 );
+    MBEDTLS_MPI_CHK( mbedtls_mpi_mul_mpi( &T1,  &P->Z,  &P->Z ) );  MOD_MUL( T1 );
+    MBEDTLS_MPI_CHK( mbedtls_mpi_mul_mpi( &T2,  &T1,    &P->Z ) );  MOD_MUL( T2 );
+    MBEDTLS_MPI_CHK( mbedtls_mpi_mul_mpi( &T1,  &T1,    &Q->X ) );  MOD_MUL( T1 );
+    MBEDTLS_MPI_CHK( mbedtls_mpi_mul_mpi( &T2,  &T2,    &Q->Y ) );  MOD_MUL( T2 );
+    MBEDTLS_MPI_CHK( mbedtls_mpi_sub_mpi( &T1,  &T1,    &P->X ) );  MOD_SUB( T1 );
+    MBEDTLS_MPI_CHK( mbedtls_mpi_sub_mpi( &T2,  &T2,    &P->Y ) );  MOD_SUB( T2 );
 
     /* Special cases (2) and (3) */
-    if( mpi_cmp_int( &T1, 0 ) == 0 )
+    if( mbedtls_mpi_cmp_int( &T1, 0 ) == 0 )
     {
-        if( mpi_cmp_int( &T2, 0 ) == 0 )
+        if( mbedtls_mpi_cmp_int( &T2, 0 ) == 0 )
         {
             ret = ecp_double_jac( grp, R, P );
             goto cleanup;
         }
         else
         {
-            ret = ecp_set_zero( R );
+            ret = mbedtls_ecp_set_zero( R );
             goto cleanup;
         }
     }
 
-    MPI_CHK( mpi_mul_mpi( &Z,   &P->Z,  &T1   ) );  MOD_MUL( Z  );
-    MPI_CHK( mpi_mul_mpi( &T3,  &T1,    &T1   ) );  MOD_MUL( T3 );
-    MPI_CHK( mpi_mul_mpi( &T4,  &T3,    &T1   ) );  MOD_MUL( T4 );
-    MPI_CHK( mpi_mul_mpi( &T3,  &T3,    &P->X ) );  MOD_MUL( T3 );
-    MPI_CHK( mpi_mul_int( &T1,  &T3,    2     ) );  MOD_ADD( T1 );
-    MPI_CHK( mpi_mul_mpi( &X,   &T2,    &T2   ) );  MOD_MUL( X  );
-    MPI_CHK( mpi_sub_mpi( &X,   &X,     &T1   ) );  MOD_SUB( X  );
-    MPI_CHK( mpi_sub_mpi( &X,   &X,     &T4   ) );  MOD_SUB( X  );
-    MPI_CHK( mpi_sub_mpi( &T3,  &T3,    &X    ) );  MOD_SUB( T3 );
-    MPI_CHK( mpi_mul_mpi( &T3,  &T3,    &T2   ) );  MOD_MUL( T3 );
-    MPI_CHK( mpi_mul_mpi( &T4,  &T4,    &P->Y ) );  MOD_MUL( T4 );
-    MPI_CHK( mpi_sub_mpi( &Y,   &T3,    &T4   ) );  MOD_SUB( Y  );
+    MBEDTLS_MPI_CHK( mbedtls_mpi_mul_mpi( &Z,   &P->Z,  &T1   ) );  MOD_MUL( Z  );
+    MBEDTLS_MPI_CHK( mbedtls_mpi_mul_mpi( &T3,  &T1,    &T1   ) );  MOD_MUL( T3 );
+    MBEDTLS_MPI_CHK( mbedtls_mpi_mul_mpi( &T4,  &T3,    &T1   ) );  MOD_MUL( T4 );
+    MBEDTLS_MPI_CHK( mbedtls_mpi_mul_mpi( &T3,  &T3,    &P->X ) );  MOD_MUL( T3 );
+    MBEDTLS_MPI_CHK( mbedtls_mpi_mul_int( &T1,  &T3,    2     ) );  MOD_ADD( T1 );
+    MBEDTLS_MPI_CHK( mbedtls_mpi_mul_mpi( &X,   &T2,    &T2   ) );  MOD_MUL( X  );
+    MBEDTLS_MPI_CHK( mbedtls_mpi_sub_mpi( &X,   &X,     &T1   ) );  MOD_SUB( X  );
+    MBEDTLS_MPI_CHK( mbedtls_mpi_sub_mpi( &X,   &X,     &T4   ) );  MOD_SUB( X  );
+    MBEDTLS_MPI_CHK( mbedtls_mpi_sub_mpi( &T3,  &T3,    &X    ) );  MOD_SUB( T3 );
+    MBEDTLS_MPI_CHK( mbedtls_mpi_mul_mpi( &T3,  &T3,    &T2   ) );  MOD_MUL( T3 );
+    MBEDTLS_MPI_CHK( mbedtls_mpi_mul_mpi( &T4,  &T4,    &P->Y ) );  MOD_MUL( T4 );
+    MBEDTLS_MPI_CHK( mbedtls_mpi_sub_mpi( &Y,   &T3,    &T4   ) );  MOD_SUB( Y  );
 
-    MPI_CHK( mpi_copy( &R->X, &X ) );
-    MPI_CHK( mpi_copy( &R->Y, &Y ) );
-    MPI_CHK( mpi_copy( &R->Z, &Z ) );
+    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:
 
-    mpi_free( &T1 ); mpi_free( &T2 ); mpi_free( &T3 ); mpi_free( &T4 );
-    mpi_free( &X ); mpi_free( &Y ); mpi_free( &Z );
+    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 );
 }
@@ -1075,16 +1075,16 @@
 /*
  * Addition: R = P + Q, result's coordinates normalized
  */
-int ecp_add( const ecp_group *grp, ecp_point *R,
-             const ecp_point *P, const ecp_point *Q )
+int mbedtls_ecp_add( const mbedtls_ecp_group *grp, mbedtls_ecp_point *R,
+             const mbedtls_ecp_point *P, const mbedtls_ecp_point *Q )
 {
     int ret;
 
-    if( ecp_get_type( grp ) != POLARSSL_ECP_TYPE_SHORT_WEIERSTRASS )
-        return( POLARSSL_ERR_ECP_FEATURE_UNAVAILABLE );
+    if( ecp_get_type( grp ) != MBEDTLS_ECP_TYPE_SHORT_WEIERSTRASS )
+        return( MBEDTLS_ERR_ECP_FEATURE_UNAVAILABLE );
 
-    MPI_CHK( ecp_add_mixed( grp, R, P, Q ) );
-    MPI_CHK( ecp_normalize_jac( grp, R ) );
+    MBEDTLS_MPI_CHK( ecp_add_mixed( grp, R, P, Q ) );
+    MBEDTLS_MPI_CHK( ecp_normalize_jac( grp, R ) );
 
 cleanup:
     return( ret );
@@ -1093,27 +1093,27 @@
 /*
  * Subtraction: R = P - Q, result's coordinates normalized
  */
-int ecp_sub( const ecp_group *grp, ecp_point *R,
-             const ecp_point *P, const ecp_point *Q )
+int mbedtls_ecp_sub( const mbedtls_ecp_group *grp, mbedtls_ecp_point *R,
+             const mbedtls_ecp_point *P, const mbedtls_ecp_point *Q )
 {
     int ret;
-    ecp_point mQ;
+    mbedtls_ecp_point mQ;
 
-    ecp_point_init( &mQ );
+    mbedtls_ecp_point_init( &mQ );
 
-    if( ecp_get_type( grp ) != POLARSSL_ECP_TYPE_SHORT_WEIERSTRASS )
-        return( POLARSSL_ERR_ECP_FEATURE_UNAVAILABLE );
+    if( ecp_get_type( grp ) != MBEDTLS_ECP_TYPE_SHORT_WEIERSTRASS )
+        return( MBEDTLS_ERR_ECP_FEATURE_UNAVAILABLE );
 
     /* mQ = - Q */
-    MPI_CHK( ecp_copy( &mQ, Q ) );
-    if( mpi_cmp_int( &mQ.Y, 0 ) != 0 )
-        MPI_CHK( mpi_sub_mpi( &mQ.Y, &grp->P, &mQ.Y ) );
+    MBEDTLS_MPI_CHK( mbedtls_ecp_copy( &mQ, Q ) );
+    if( mbedtls_mpi_cmp_int( &mQ.Y, 0 ) != 0 )
+        MBEDTLS_MPI_CHK( mbedtls_mpi_sub_mpi( &mQ.Y, &grp->P, &mQ.Y ) );
 
-    MPI_CHK( ecp_add_mixed( grp, R, P, &mQ ) );
-    MPI_CHK( ecp_normalize_jac( grp, R ) );
+    MBEDTLS_MPI_CHK( ecp_add_mixed( grp, R, P, &mQ ) );
+    MBEDTLS_MPI_CHK( ecp_normalize_jac( grp, R ) );
 
 cleanup:
-    ecp_point_free( &mQ );
+    mbedtls_ecp_point_free( &mQ );
 
     return( ret );
 }
@@ -1125,42 +1125,42 @@
  *
  * This countermeasure was first suggested in [2].
  */
-static int ecp_randomize_jac( const ecp_group *grp, ecp_point *pt,
+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 )
 {
     int ret;
-    mpi l, ll;
+    mbedtls_mpi l, ll;
     size_t p_size = ( grp->pbits + 7 ) / 8;
     int count = 0;
 
-    mpi_init( &l ); mpi_init( &ll );
+    mbedtls_mpi_init( &l ); mbedtls_mpi_init( &ll );
 
     /* Generate l such that 1 < l < p */
     do
     {
-        mpi_fill_random( &l, p_size, f_rng, p_rng );
+        mbedtls_mpi_fill_random( &l, p_size, f_rng, p_rng );
 
-        while( mpi_cmp_mpi( &l, &grp->P ) >= 0 )
-            MPI_CHK( mpi_shift_r( &l, 1 ) );
+        while( mbedtls_mpi_cmp_mpi( &l, &grp->P ) >= 0 )
+            MBEDTLS_MPI_CHK( mbedtls_mpi_shift_r( &l, 1 ) );
 
         if( count++ > 10 )
-            return( POLARSSL_ERR_ECP_RANDOM_FAILED );
+            return( MBEDTLS_ERR_ECP_RANDOM_FAILED );
     }
-    while( mpi_cmp_int( &l, 1 ) <= 0 );
+    while( mbedtls_mpi_cmp_int( &l, 1 ) <= 0 );
 
     /* Z = l * Z */
-    MPI_CHK( mpi_mul_mpi( &pt->Z,   &pt->Z,     &l  ) ); MOD_MUL( pt->Z );
+    MBEDTLS_MPI_CHK( mbedtls_mpi_mul_mpi( &pt->Z,   &pt->Z,     &l  ) ); MOD_MUL( pt->Z );
 
     /* X = l^2 * X */
-    MPI_CHK( mpi_mul_mpi( &ll,      &l,         &l  ) ); MOD_MUL( ll );
-    MPI_CHK( mpi_mul_mpi( &pt->X,   &pt->X,     &ll ) ); MOD_MUL( pt->X );
+    MBEDTLS_MPI_CHK( mbedtls_mpi_mul_mpi( &ll,      &l,         &l  ) ); MOD_MUL( ll );
+    MBEDTLS_MPI_CHK( mbedtls_mpi_mul_mpi( &pt->X,   &pt->X,     &ll ) ); MOD_MUL( pt->X );
 
     /* Y = l^3 * Y */
-    MPI_CHK( mpi_mul_mpi( &ll,      &ll,        &l  ) ); MOD_MUL( ll );
-    MPI_CHK( mpi_mul_mpi( &pt->Y,   &pt->Y,     &ll ) ); MOD_MUL( pt->Y );
+    MBEDTLS_MPI_CHK( mbedtls_mpi_mul_mpi( &ll,      &ll,        &l  ) ); MOD_MUL( ll );
+    MBEDTLS_MPI_CHK( mbedtls_mpi_mul_mpi( &pt->Y,   &pt->Y,     &ll ) ); MOD_MUL( pt->Y );
 
 cleanup:
-    mpi_free( &l ); mpi_free( &ll );
+    mbedtls_mpi_free( &l ); mbedtls_mpi_free( &ll );
 
     return( ret );
 }
@@ -1168,15 +1168,15 @@
 /*
  * Check and define parameters used by the comb method (see below for details)
  */
-#if POLARSSL_ECP_WINDOW_SIZE < 2 || POLARSSL_ECP_WINDOW_SIZE > 7
-#error "POLARSSL_ECP_WINDOW_SIZE out of bounds"
+#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      ( POLARSSL_ECP_MAX_BITS + 1 ) / 2
+#define COMB_MAX_D      ( MBEDTLS_ECP_MAX_BITS + 1 ) / 2
 
 /* number of precomputed points */
-#define COMB_MAX_PRE    ( 1 << ( POLARSSL_ECP_WINDOW_SIZE - 1 ) )
+#define COMB_MAX_PRE    ( 1 << ( MBEDTLS_ECP_WINDOW_SIZE - 1 ) )
 
 /*
  * Compute the representation of m that will be used with our comb method.
@@ -1194,12 +1194,12 @@
  * 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 POLARSSL_ECP_WINDOW_SIZE)
+ *   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_fixed( unsigned char x[], size_t d,
-                            unsigned char w, const mpi *m )
+                            unsigned char w, const mbedtls_mpi *m )
 {
     size_t i, j;
     unsigned char c, cc, adjust;
@@ -1209,7 +1209,7 @@
     /* 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] |= mpi_get_bit( m, i + d * j ) << j;
+            x[i] |= mbedtls_mpi_get_bit( m, i + d * j ) << j;
 
     /* Now make sure x_1 .. x_d are odd */
     c = 0;
@@ -1238,33 +1238,33 @@
  *
  * Cost: d(w-1) D + (2^{w-1} - 1) A + 1 N(w-1) + 1 N(2^{w-1} - 1)
  */
-static int ecp_precompute_comb( const ecp_group *grp,
-                                ecp_point T[], const ecp_point *P,
+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 )
 {
     int ret;
     unsigned char i, k;
     size_t j;
-    ecp_point *cur, *TT[COMB_MAX_PRE - 1];
+    mbedtls_ecp_point *cur, *TT[COMB_MAX_PRE - 1];
 
     /*
      * Set T[0] = P and
      * T[2^{l-1}] = 2^{dl} P for l = 1 .. w-1 (this is not the final value)
      */
-    MPI_CHK( ecp_copy( &T[0], P ) );
+    MBEDTLS_MPI_CHK( mbedtls_ecp_copy( &T[0], P ) );
 
     k = 0;
     for( i = 1; i < ( 1U << ( w - 1 ) ); i <<= 1 )
     {
         cur = T + i;
-        MPI_CHK( ecp_copy( cur, T + ( i >> 1 ) ) );
+        MBEDTLS_MPI_CHK( mbedtls_ecp_copy( cur, T + ( i >> 1 ) ) );
         for( j = 0; j < d; j++ )
-            MPI_CHK( ecp_double_jac( grp, cur, cur ) );
+            MBEDTLS_MPI_CHK( ecp_double_jac( grp, cur, cur ) );
 
         TT[k++] = cur;
     }
 
-    MPI_CHK( ecp_normalize_jac_many( grp, TT, k ) );
+    MBEDTLS_MPI_CHK( ecp_normalize_jac_many( grp, TT, k ) );
 
     /*
      * Compute the remaining ones using the minimal number of additions
@@ -1276,12 +1276,12 @@
         j = i;
         while( j-- )
         {
-            MPI_CHK( ecp_add_mixed( grp, &T[i + j], &T[j], &T[i] ) );
+            MBEDTLS_MPI_CHK( ecp_add_mixed( grp, &T[i + j], &T[j], &T[i] ) );
             TT[k++] = &T[i + j];
         }
     }
 
-    MPI_CHK( ecp_normalize_jac_many( grp, TT, k ) );
+    MBEDTLS_MPI_CHK( ecp_normalize_jac_many( grp, TT, k ) );
 
 cleanup:
     return( ret );
@@ -1290,8 +1290,8 @@
 /*
  * Select precomputed point: R = sign(i) * T[ abs(i) / 2 ]
  */
-static int ecp_select_comb( const ecp_group *grp, ecp_point *R,
-                            const ecp_point T[], unsigned char t_len,
+static int ecp_select_comb( const mbedtls_ecp_group *grp, mbedtls_ecp_point *R,
+                            const mbedtls_ecp_point T[], unsigned char t_len,
                             unsigned char i )
 {
     int ret;
@@ -1303,12 +1303,12 @@
     /* Read the whole table to thwart cache-based timing attacks */
     for( j = 0; j < t_len; j++ )
     {
-        MPI_CHK( mpi_safe_cond_assign( &R->X, &T[j].X, j == ii ) );
-        MPI_CHK( mpi_safe_cond_assign( &R->Y, &T[j].Y, j == ii ) );
+        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" */
-    MPI_CHK( ecp_safe_invert_jac( grp, R, i >> 7 ) );
+    MBEDTLS_MPI_CHK( ecp_safe_invert_jac( grp, R, i >> 7 ) );
 
 cleanup:
     return( ret );
@@ -1320,34 +1320,34 @@
  *
  * Cost: d A + d D + 1 R
  */
-static int ecp_mul_comb_core( const ecp_group *grp, ecp_point *R,
-                              const ecp_point T[], unsigned char t_len,
+static int ecp_mul_comb_core( const mbedtls_ecp_group *grp, mbedtls_ecp_point *R,
+                              const mbedtls_ecp_point T[], unsigned char t_len,
                               const unsigned char x[], size_t d,
                               int (*f_rng)(void *, unsigned char *, size_t),
                               void *p_rng )
 {
     int ret;
-    ecp_point Txi;
+    mbedtls_ecp_point Txi;
     size_t i;
 
-    ecp_point_init( &Txi );
+    mbedtls_ecp_point_init( &Txi );
 
     /* Start with a non-zero point and randomize its coordinates */
     i = d;
-    MPI_CHK( ecp_select_comb( grp, R, T, t_len, x[i] ) );
-    MPI_CHK( mpi_lset( &R->Z, 1 ) );
+    MBEDTLS_MPI_CHK( ecp_select_comb( grp, R, T, t_len, x[i] ) );
+    MBEDTLS_MPI_CHK( mbedtls_mpi_lset( &R->Z, 1 ) );
     if( f_rng != 0 )
-        MPI_CHK( ecp_randomize_jac( grp, R, f_rng, p_rng ) );
+        MBEDTLS_MPI_CHK( ecp_randomize_jac( grp, R, f_rng, p_rng ) );
 
     while( i-- != 0 )
     {
-        MPI_CHK( ecp_double_jac( grp, R, R ) );
-        MPI_CHK( ecp_select_comb( grp, &Txi, T, t_len, x[i] ) );
-        MPI_CHK( ecp_add_mixed( grp, R, R, &Txi ) );
+        MBEDTLS_MPI_CHK( ecp_double_jac( grp, R, R ) );
+        MBEDTLS_MPI_CHK( ecp_select_comb( grp, &Txi, T, t_len, x[i] ) );
+        MBEDTLS_MPI_CHK( ecp_add_mixed( grp, R, R, &Txi ) );
     }
 
 cleanup:
-    ecp_point_free( &Txi );
+    mbedtls_ecp_point_free( &Txi );
 
     return( ret );
 }
@@ -1356,8 +1356,8 @@
  * Multiplication using the comb method,
  * for curves in short Weierstrass form
  */
-static int ecp_mul_comb( ecp_group *grp, ecp_point *R,
-                         const mpi *m, const ecp_point *P,
+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 )
 {
@@ -1365,15 +1365,15 @@
     unsigned char w, m_is_odd, p_eq_g, pre_len, i;
     size_t d;
     unsigned char k[COMB_MAX_D + 1];
-    ecp_point *T;
-    mpi M, mm;
+    mbedtls_ecp_point *T;
+    mbedtls_mpi M, mm;
 
-    mpi_init( &M );
-    mpi_init( &mm );
+    mbedtls_mpi_init( &M );
+    mbedtls_mpi_init( &mm );
 
     /* we need N to be odd to trnaform m in an odd number, check now */
-    if( mpi_get_bit( &grp->N, 0 ) != 1 )
-        return( POLARSSL_ERR_ECP_BAD_INPUT_DATA );
+    if( mbedtls_mpi_get_bit( &grp->N, 0 ) != 1 )
+        return( MBEDTLS_ERR_ECP_BAD_INPUT_DATA );
 
     /*
      * Minimize the number of multiplications, that is minimize
@@ -1387,9 +1387,9 @@
      * Just adding one avoids upping the cost of the first mul too much,
      * and the memory cost too.
      */
-#if POLARSSL_ECP_FIXED_POINT_OPTIM == 1
-    p_eq_g = ( mpi_cmp_mpi( &P->Y, &grp->G.Y ) == 0 &&
-               mpi_cmp_mpi( &P->X, &grp->G.X ) == 0 );
+#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 );
     if( p_eq_g )
         w++;
 #else
@@ -1400,8 +1400,8 @@
      * Make sure w is within bounds.
      * (The last test is useful only for very small curves in the test suite.)
      */
-    if( w > POLARSSL_ECP_WINDOW_SIZE )
-        w = POLARSSL_ECP_WINDOW_SIZE;
+    if( w > MBEDTLS_ECP_WINDOW_SIZE )
+        w = MBEDTLS_ECP_WINDOW_SIZE;
     if( w >= grp->nbits )
         w = 2;
 
@@ -1417,17 +1417,17 @@
 
     if( T == NULL )
     {
-        T = polarssl_malloc( pre_len * sizeof( ecp_point ) );
+        T = mbedtls_malloc( pre_len * sizeof( mbedtls_ecp_point ) );
         if( T == NULL )
         {
-            ret = POLARSSL_ERR_ECP_MALLOC_FAILED;
+            ret = MBEDTLS_ERR_ECP_MALLOC_FAILED;
             goto cleanup;
         }
 
         for( i = 0; i < pre_len; i++ )
-            ecp_point_init( &T[i] );
+            mbedtls_ecp_point_init( &T[i] );
 
-        MPI_CHK( ecp_precompute_comb( grp, T, P, w, d ) );
+        MBEDTLS_MPI_CHK( ecp_precompute_comb( grp, T, P, w, d ) );
 
         if( p_eq_g )
         {
@@ -1440,44 +1440,44 @@
      * Make sure M is odd (M = m or M = N - m, since N is odd)
      * using the fact that m * P = - (N - m) * P
      */
-    m_is_odd = ( mpi_get_bit( m, 0 ) == 1 );
-    MPI_CHK( mpi_copy( &M, m ) );
-    MPI_CHK( mpi_sub_mpi( &mm, &grp->N, m ) );
-    MPI_CHK( mpi_safe_cond_assign( &M, &mm, ! m_is_odd ) );
+    m_is_odd = ( mbedtls_mpi_get_bit( m, 0 ) == 1 );
+    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, ! m_is_odd ) );
 
     /*
      * Go for comb multiplication, R = M * P
      */
     ecp_comb_fixed( k, d, w, &M );
-    MPI_CHK( ecp_mul_comb_core( grp, R, T, pre_len, k, d, f_rng, p_rng ) );
+    MBEDTLS_MPI_CHK( ecp_mul_comb_core( grp, R, T, pre_len, k, d, f_rng, p_rng ) );
 
     /*
      * Now get m * P from M * P and normalize it
      */
-    MPI_CHK( ecp_safe_invert_jac( grp, R, ! m_is_odd ) );
-    MPI_CHK( ecp_normalize_jac( grp, R ) );
+    MBEDTLS_MPI_CHK( ecp_safe_invert_jac( grp, R, ! m_is_odd ) );
+    MBEDTLS_MPI_CHK( ecp_normalize_jac( grp, R ) );
 
 cleanup:
 
     if( T != NULL && ! p_eq_g )
     {
         for( i = 0; i < pre_len; i++ )
-            ecp_point_free( &T[i] );
-        polarssl_free( T );
+            mbedtls_ecp_point_free( &T[i] );
+        mbedtls_free( T );
     }
 
-    mpi_free( &M );
-    mpi_free( &mm );
+    mbedtls_mpi_free( &M );
+    mbedtls_mpi_free( &mm );
 
     if( ret != 0 )
-        ecp_point_free( R );
+        mbedtls_ecp_point_free( R );
 
     return( ret );
 }
 
-#endif /* POLARSSL_ECP_SHORT_WEIERSTRASS */
+#endif /* MBEDTLS_ECP_SHORT_WEIERSTRASS */
 
-#if defined(POLARSSL_ECP_MONTGOMERY)
+#if defined(MBEDTLS_ECP_MONTGOMERY)
 /*
  * For Montgomery curves, we do all the internal arithmetic in projective
  * coordinates. Import/export of points uses only the x coordinates, which is
@@ -1490,13 +1490,13 @@
  * Normalize Montgomery x/z coordinates: X = X/Z, Z = 1
  * Cost: 1M + 1I
  */
-static int ecp_normalize_mxz( const ecp_group *grp, ecp_point *P )
+static int ecp_normalize_mxz( const mbedtls_ecp_group *grp, mbedtls_ecp_point *P )
 {
     int ret;
 
-    MPI_CHK( mpi_inv_mod( &P->Z, &P->Z, &grp->P ) );
-    MPI_CHK( mpi_mul_mpi( &P->X, &P->X, &P->Z ) ); MOD_MUL( P->X );
-    MPI_CHK( mpi_lset( &P->Z, 1 ) );
+    MBEDTLS_MPI_CHK( mbedtls_mpi_inv_mod( &P->Z, &P->Z, &grp->P ) );
+    MBEDTLS_MPI_CHK( mbedtls_mpi_mul_mpi( &P->X, &P->X, &P->Z ) ); MOD_MUL( P->X );
+    MBEDTLS_MPI_CHK( mbedtls_mpi_lset( &P->Z, 1 ) );
 
 cleanup:
     return( ret );
@@ -1510,34 +1510,34 @@
  * This countermeasure was first suggested in [2].
  * Cost: 2M
  */
-static int ecp_randomize_mxz( const ecp_group *grp, ecp_point *P,
+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 )
 {
     int ret;
-    mpi l;
+    mbedtls_mpi l;
     size_t p_size = ( grp->pbits + 7 ) / 8;
     int count = 0;
 
-    mpi_init( &l );
+    mbedtls_mpi_init( &l );
 
     /* Generate l such that 1 < l < p */
     do
     {
-        mpi_fill_random( &l, p_size, f_rng, p_rng );
+        mbedtls_mpi_fill_random( &l, p_size, f_rng, p_rng );
 
-        while( mpi_cmp_mpi( &l, &grp->P ) >= 0 )
-            MPI_CHK( mpi_shift_r( &l, 1 ) );
+        while( mbedtls_mpi_cmp_mpi( &l, &grp->P ) >= 0 )
+            MBEDTLS_MPI_CHK( mbedtls_mpi_shift_r( &l, 1 ) );
 
         if( count++ > 10 )
-            return( POLARSSL_ERR_ECP_RANDOM_FAILED );
+            return( MBEDTLS_ERR_ECP_RANDOM_FAILED );
     }
-    while( mpi_cmp_int( &l, 1 ) <= 0 );
+    while( mbedtls_mpi_cmp_int( &l, 1 ) <= 0 );
 
-    MPI_CHK( mpi_mul_mpi( &P->X, &P->X, &l ) ); MOD_MUL( P->X );
-    MPI_CHK( mpi_mul_mpi( &P->Z, &P->Z, &l ) ); MOD_MUL( P->Z );
+    MBEDTLS_MPI_CHK( mbedtls_mpi_mul_mpi( &P->X, &P->X, &l ) ); MOD_MUL( P->X );
+    MBEDTLS_MPI_CHK( mbedtls_mpi_mul_mpi( &P->Z, &P->Z, &l ) ); MOD_MUL( P->Z );
 
 cleanup:
-    mpi_free( &l );
+    mbedtls_mpi_free( &l );
 
     return( ret );
 }
@@ -1557,41 +1557,41 @@
  *
  * Cost: 5M + 4S
  */
-static int ecp_double_add_mxz( const ecp_group *grp,
-                               ecp_point *R, ecp_point *S,
-                               const ecp_point *P, const ecp_point *Q,
-                               const mpi *d )
+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 )
 {
     int ret;
-    mpi A, AA, B, BB, E, C, D, DA, CB;
+    mbedtls_mpi A, AA, B, BB, E, C, D, DA, CB;
 
-    mpi_init( &A ); mpi_init( &AA ); mpi_init( &B );
-    mpi_init( &BB ); mpi_init( &E ); mpi_init( &C );
-    mpi_init( &D ); mpi_init( &DA ); mpi_init( &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 );
 
-    MPI_CHK( mpi_add_mpi( &A,    &P->X,   &P->Z ) ); MOD_ADD( A    );
-    MPI_CHK( mpi_mul_mpi( &AA,   &A,      &A    ) ); MOD_MUL( AA   );
-    MPI_CHK( mpi_sub_mpi( &B,    &P->X,   &P->Z ) ); MOD_SUB( B    );
-    MPI_CHK( mpi_mul_mpi( &BB,   &B,      &B    ) ); MOD_MUL( BB   );
-    MPI_CHK( mpi_sub_mpi( &E,    &AA,     &BB   ) ); MOD_SUB( E    );
-    MPI_CHK( mpi_add_mpi( &C,    &Q->X,   &Q->Z ) ); MOD_ADD( C    );
-    MPI_CHK( mpi_sub_mpi( &D,    &Q->X,   &Q->Z ) ); MOD_SUB( D    );
-    MPI_CHK( mpi_mul_mpi( &DA,   &D,      &A    ) ); MOD_MUL( DA   );
-    MPI_CHK( mpi_mul_mpi( &CB,   &C,      &B    ) ); MOD_MUL( CB   );
-    MPI_CHK( mpi_add_mpi( &S->X, &DA,     &CB   ) ); MOD_MUL( S->X );
-    MPI_CHK( mpi_mul_mpi( &S->X, &S->X,   &S->X ) ); MOD_MUL( S->X );
-    MPI_CHK( mpi_sub_mpi( &S->Z, &DA,     &CB   ) ); MOD_SUB( S->Z );
-    MPI_CHK( mpi_mul_mpi( &S->Z, &S->Z,   &S->Z ) ); MOD_MUL( S->Z );
-    MPI_CHK( mpi_mul_mpi( &S->Z, d,       &S->Z ) ); MOD_MUL( S->Z );
-    MPI_CHK( mpi_mul_mpi( &R->X, &AA,     &BB   ) ); MOD_MUL( R->X );
-    MPI_CHK( mpi_mul_mpi( &R->Z, &grp->A, &E    ) ); MOD_MUL( R->Z );
-    MPI_CHK( mpi_add_mpi( &R->Z, &BB,     &R->Z ) ); MOD_ADD( R->Z );
-    MPI_CHK( mpi_mul_mpi( &R->Z, &E,      &R->Z ) ); MOD_MUL( R->Z );
+    MBEDTLS_MPI_CHK( mbedtls_mpi_add_mpi( &A,    &P->X,   &P->Z ) ); MOD_ADD( A    );
+    MBEDTLS_MPI_CHK( mbedtls_mpi_mul_mpi( &AA,   &A,      &A    ) ); MOD_MUL( AA   );
+    MBEDTLS_MPI_CHK( mbedtls_mpi_sub_mpi( &B,    &P->X,   &P->Z ) ); MOD_SUB( B    );
+    MBEDTLS_MPI_CHK( mbedtls_mpi_mul_mpi( &BB,   &B,      &B    ) ); MOD_MUL( BB   );
+    MBEDTLS_MPI_CHK( mbedtls_mpi_sub_mpi( &E,    &AA,     &BB   ) ); MOD_SUB( E    );
+    MBEDTLS_MPI_CHK( mbedtls_mpi_add_mpi( &C,    &Q->X,   &Q->Z ) ); MOD_ADD( C    );
+    MBEDTLS_MPI_CHK( mbedtls_mpi_sub_mpi( &D,    &Q->X,   &Q->Z ) ); MOD_SUB( D    );
+    MBEDTLS_MPI_CHK( mbedtls_mpi_mul_mpi( &DA,   &D,      &A    ) ); MOD_MUL( DA   );
+    MBEDTLS_MPI_CHK( mbedtls_mpi_mul_mpi( &CB,   &C,      &B    ) ); MOD_MUL( CB   );
+    MBEDTLS_MPI_CHK( mbedtls_mpi_add_mpi( &S->X, &DA,     &CB   ) ); MOD_MUL( S->X );
+    MBEDTLS_MPI_CHK( mbedtls_mpi_mul_mpi( &S->X, &S->X,   &S->X ) ); MOD_MUL( S->X );
+    MBEDTLS_MPI_CHK( mbedtls_mpi_sub_mpi( &S->Z, &DA,     &CB   ) ); MOD_SUB( S->Z );
+    MBEDTLS_MPI_CHK( mbedtls_mpi_mul_mpi( &S->Z, &S->Z,   &S->Z ) ); MOD_MUL( S->Z );
+    MBEDTLS_MPI_CHK( mbedtls_mpi_mul_mpi( &S->Z, d,       &S->Z ) ); MOD_MUL( S->Z );
+    MBEDTLS_MPI_CHK( mbedtls_mpi_mul_mpi( &R->X, &AA,     &BB   ) ); MOD_MUL( R->X );
+    MBEDTLS_MPI_CHK( mbedtls_mpi_mul_mpi( &R->Z, &grp->A, &E    ) ); MOD_MUL( R->Z );
+    MBEDTLS_MPI_CHK( mbedtls_mpi_add_mpi( &R->Z, &BB,     &R->Z ) ); MOD_ADD( R->Z );
+    MBEDTLS_MPI_CHK( mbedtls_mpi_mul_mpi( &R->Z, &E,      &R->Z ) ); MOD_MUL( R->Z );
 
 cleanup:
-    mpi_free( &A ); mpi_free( &AA ); mpi_free( &B );
-    mpi_free( &BB ); mpi_free( &E ); mpi_free( &C );
-    mpi_free( &D ); mpi_free( &DA ); mpi_free( &CB );
+    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 );
 }
@@ -1600,40 +1600,40 @@
  * Multiplication with Montgomery ladder in x/z coordinates,
  * for curves in Montgomery form
  */
-static int ecp_mul_mxz( ecp_group *grp, ecp_point *R,
-                        const mpi *m, const ecp_point *P,
+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;
     size_t i;
     unsigned char b;
-    ecp_point RP;
-    mpi PX;
+    mbedtls_ecp_point RP;
+    mbedtls_mpi PX;
 
-    ecp_point_init( &RP ); mpi_init( &PX );
+    mbedtls_ecp_point_init( &RP ); mbedtls_mpi_init( &PX );
 
     /* Save PX and read from P before writing to R, in case P == R */
-    MPI_CHK( mpi_copy( &PX, &P->X ) );
-    MPI_CHK( ecp_copy( &RP, P ) );
+    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 */
-    MPI_CHK( mpi_lset( &R->X, 1 ) );
-    MPI_CHK( mpi_lset( &R->Z, 0 ) );
-    mpi_free( &R->Y );
+    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( f_rng != NULL )
-        MPI_CHK( ecp_randomize_mxz( grp, &RP, f_rng, p_rng ) );
+        MBEDTLS_MPI_CHK( ecp_randomize_mxz( grp, &RP, f_rng, p_rng ) );
 
     /* Loop invariant: R = result so far, RP = R + P */
-    i = mpi_msb( m ); /* one past the (zero-based) most significant bit */
+    i = mbedtls_mpi_msb( m ); /* one past the (zero-based) most significant bit */
     while( i-- > 0 )
     {
-        b = mpi_get_bit( m, i );
+        b = mbedtls_mpi_get_bit( m, i );
         /*
          *  if (b) R = 2R + P else R = 2R,
          * which is:
@@ -1641,207 +1641,207 @@
          *  else   double_add( R, RP, R, RP )
          * but using safe conditional swaps to avoid leaks
          */
-        MPI_CHK( mpi_safe_cond_swap( &R->X, &RP.X, b ) );
-        MPI_CHK( mpi_safe_cond_swap( &R->Z, &RP.Z, b ) );
-        MPI_CHK( ecp_double_add_mxz( grp, R, &RP, R, &RP, &PX ) );
-        MPI_CHK( mpi_safe_cond_swap( &R->X, &RP.X, b ) );
-        MPI_CHK( mpi_safe_cond_swap( &R->Z, &RP.Z, b ) );
+        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 ) );
     }
 
-    MPI_CHK( ecp_normalize_mxz( grp, R ) );
+    MBEDTLS_MPI_CHK( ecp_normalize_mxz( grp, R ) );
 
 cleanup:
-    ecp_point_free( &RP ); mpi_free( &PX );
+    mbedtls_ecp_point_free( &RP ); mbedtls_mpi_free( &PX );
 
     return( ret );
 }
 
-#endif /* POLARSSL_ECP_MONTGOMERY */
+#endif /* MBEDTLS_ECP_MONTGOMERY */
 
 /*
  * Multiplication R = m * P
  */
-int ecp_mul( ecp_group *grp, ecp_point *R,
-             const mpi *m, const ecp_point *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 )
 {
     int ret;
 
     /* Common sanity checks */
-    if( mpi_cmp_int( &P->Z, 1 ) != 0 )
-        return( POLARSSL_ERR_ECP_BAD_INPUT_DATA );
+    if( mbedtls_mpi_cmp_int( &P->Z, 1 ) != 0 )
+        return( MBEDTLS_ERR_ECP_BAD_INPUT_DATA );
 
-    if( ( ret = ecp_check_privkey( grp, m ) ) != 0 ||
-        ( ret = ecp_check_pubkey( grp, P ) ) != 0 )
+    if( ( ret = mbedtls_ecp_check_privkey( grp, m ) ) != 0 ||
+        ( ret = mbedtls_ecp_check_pubkey( grp, P ) ) != 0 )
         return( ret );
 
-#if defined(POLARSSL_ECP_MONTGOMERY)
-    if( ecp_get_type( grp ) == POLARSSL_ECP_TYPE_MONTGOMERY )
+#if defined(MBEDTLS_ECP_MONTGOMERY)
+    if( ecp_get_type( grp ) == MBEDTLS_ECP_TYPE_MONTGOMERY )
         return( ecp_mul_mxz( grp, R, m, P, f_rng, p_rng ) );
 #endif
-#if defined(POLARSSL_ECP_SHORT_WEIERSTRASS)
-    if( ecp_get_type( grp ) == POLARSSL_ECP_TYPE_SHORT_WEIERSTRASS )
+#if defined(MBEDTLS_ECP_SHORT_WEIERSTRASS)
+    if( ecp_get_type( grp ) == MBEDTLS_ECP_TYPE_SHORT_WEIERSTRASS )
         return( ecp_mul_comb( grp, R, m, P, f_rng, p_rng ) );
 #endif
-    return( POLARSSL_ERR_ECP_BAD_INPUT_DATA );
+    return( MBEDTLS_ERR_ECP_BAD_INPUT_DATA );
 }
 
-#if defined(POLARSSL_ECP_SHORT_WEIERSTRASS)
+#if defined(MBEDTLS_ECP_SHORT_WEIERSTRASS)
 /*
  * 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 ecp_group *grp, const ecp_point *pt )
+static int ecp_check_pubkey_sw( const mbedtls_ecp_group *grp, const mbedtls_ecp_point *pt )
 {
     int ret;
-    mpi YY, RHS;
+    mbedtls_mpi YY, RHS;
 
     /* pt coordinates must be normalized for our checks */
-    if( mpi_cmp_int( &pt->X, 0 ) < 0 ||
-        mpi_cmp_int( &pt->Y, 0 ) < 0 ||
-        mpi_cmp_mpi( &pt->X, &grp->P ) >= 0 ||
-        mpi_cmp_mpi( &pt->Y, &grp->P ) >= 0 )
-        return( POLARSSL_ERR_ECP_INVALID_KEY );
+    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 );
 
-    mpi_init( &YY ); mpi_init( &RHS );
+    mbedtls_mpi_init( &YY ); mbedtls_mpi_init( &RHS );
 
     /*
      * YY = Y^2
      * RHS = X (X^2 + A) + B = X^3 + A X + B
      */
-    MPI_CHK( mpi_mul_mpi( &YY,  &pt->Y,   &pt->Y  ) );  MOD_MUL( YY  );
-    MPI_CHK( mpi_mul_mpi( &RHS, &pt->X,   &pt->X  ) );  MOD_MUL( RHS );
+    MBEDTLS_MPI_CHK( mbedtls_mpi_mul_mpi( &YY,  &pt->Y,   &pt->Y  ) );  MOD_MUL( YY  );
+    MBEDTLS_MPI_CHK( mbedtls_mpi_mul_mpi( &RHS, &pt->X,   &pt->X  ) );  MOD_MUL( RHS );
 
     /* Special case for A = -3 */
     if( grp->A.p == NULL )
     {
-        MPI_CHK( mpi_sub_int( &RHS, &RHS, 3       ) );  MOD_SUB( RHS );
+        MBEDTLS_MPI_CHK( mbedtls_mpi_sub_int( &RHS, &RHS, 3       ) );  MOD_SUB( RHS );
     }
     else
     {
-        MPI_CHK( mpi_add_mpi( &RHS, &RHS, &grp->A ) );  MOD_ADD( RHS );
+        MBEDTLS_MPI_CHK( mbedtls_mpi_add_mpi( &RHS, &RHS, &grp->A ) );  MOD_ADD( RHS );
     }
 
-    MPI_CHK( mpi_mul_mpi( &RHS, &RHS,     &pt->X  ) );  MOD_MUL( RHS );
-    MPI_CHK( mpi_add_mpi( &RHS, &RHS,     &grp->B ) );  MOD_ADD( RHS );
+    MBEDTLS_MPI_CHK( mbedtls_mpi_mul_mpi( &RHS, &RHS,     &pt->X  ) );  MOD_MUL( RHS );
+    MBEDTLS_MPI_CHK( mbedtls_mpi_add_mpi( &RHS, &RHS,     &grp->B ) );  MOD_ADD( RHS );
 
-    if( mpi_cmp_mpi( &YY, &RHS ) != 0 )
-        ret = POLARSSL_ERR_ECP_INVALID_KEY;
+    if( mbedtls_mpi_cmp_mpi( &YY, &RHS ) != 0 )
+        ret = MBEDTLS_ERR_ECP_INVALID_KEY;
 
 cleanup:
 
-    mpi_free( &YY ); mpi_free( &RHS );
+    mbedtls_mpi_free( &YY ); mbedtls_mpi_free( &RHS );
 
     return( ret );
 }
-#endif /* POLARSSL_ECP_SHORT_WEIERSTRASS */
+#endif /* MBEDTLS_ECP_SHORT_WEIERSTRASS */
 
 
-#if defined(POLARSSL_ECP_MONTGOMERY)
+#if defined(MBEDTLS_ECP_MONTGOMERY)
 /*
  * Check validity of a public key for Montgomery curves with x-only schemes
  */
-static int ecp_check_pubkey_mx( const ecp_group *grp, const ecp_point *pt )
+static int ecp_check_pubkey_mx( const mbedtls_ecp_group *grp, const mbedtls_ecp_point *pt )
 {
     /* [M255 p. 5] Just check X is the correct number of bytes */
-    if( mpi_size( &pt->X ) > ( grp->nbits + 7 ) / 8 )
-        return( POLARSSL_ERR_ECP_INVALID_KEY );
+    if( mbedtls_mpi_size( &pt->X ) > ( grp->nbits + 7 ) / 8 )
+        return( MBEDTLS_ERR_ECP_INVALID_KEY );
 
     return( 0 );
 }
-#endif /* POLARSSL_ECP_MONTGOMERY */
+#endif /* MBEDTLS_ECP_MONTGOMERY */
 
 /*
  * Check that a point is valid as a public key
  */
-int ecp_check_pubkey( const ecp_group *grp, const ecp_point *pt )
+int mbedtls_ecp_check_pubkey( const mbedtls_ecp_group *grp, const mbedtls_ecp_point *pt )
 {
     /* Must use affine coordinates */
-    if( mpi_cmp_int( &pt->Z, 1 ) != 0 )
-        return( POLARSSL_ERR_ECP_INVALID_KEY );
+    if( mbedtls_mpi_cmp_int( &pt->Z, 1 ) != 0 )
+        return( MBEDTLS_ERR_ECP_INVALID_KEY );
 
-#if defined(POLARSSL_ECP_MONTGOMERY)
-    if( ecp_get_type( grp ) == POLARSSL_ECP_TYPE_MONTGOMERY )
+#if defined(MBEDTLS_ECP_MONTGOMERY)
+    if( ecp_get_type( grp ) == MBEDTLS_ECP_TYPE_MONTGOMERY )
         return( ecp_check_pubkey_mx( grp, pt ) );
 #endif
-#if defined(POLARSSL_ECP_SHORT_WEIERSTRASS)
-    if( ecp_get_type( grp ) == POLARSSL_ECP_TYPE_SHORT_WEIERSTRASS )
+#if defined(MBEDTLS_ECP_SHORT_WEIERSTRASS)
+    if( ecp_get_type( grp ) == MBEDTLS_ECP_TYPE_SHORT_WEIERSTRASS )
         return( ecp_check_pubkey_sw( grp, pt ) );
 #endif
-    return( POLARSSL_ERR_ECP_BAD_INPUT_DATA );
+    return( MBEDTLS_ERR_ECP_BAD_INPUT_DATA );
 }
 
 /*
- * Check that an mpi is valid as a private key
+ * Check that an mbedtls_mpi is valid as a private key
  */
-int ecp_check_privkey( const ecp_group *grp, const mpi *d )
+int mbedtls_ecp_check_privkey( const mbedtls_ecp_group *grp, const mbedtls_mpi *d )
 {
-#if defined(POLARSSL_ECP_MONTGOMERY)
-    if( ecp_get_type( grp ) == POLARSSL_ECP_TYPE_MONTGOMERY )
+#if defined(MBEDTLS_ECP_MONTGOMERY)
+    if( ecp_get_type( grp ) == MBEDTLS_ECP_TYPE_MONTGOMERY )
     {
         /* see [M255] page 5 */
-        if( mpi_get_bit( d, 0 ) != 0 ||
-            mpi_get_bit( d, 1 ) != 0 ||
-            mpi_get_bit( d, 2 ) != 0 ||
-            mpi_msb( d ) - 1 != grp->nbits ) /* mpi_msb is one-based! */
-            return( POLARSSL_ERR_ECP_INVALID_KEY );
+        if( mbedtls_mpi_get_bit( d, 0 ) != 0 ||
+            mbedtls_mpi_get_bit( d, 1 ) != 0 ||
+            mbedtls_mpi_get_bit( d, 2 ) != 0 ||
+            mbedtls_mpi_msb( d ) - 1 != grp->nbits ) /* mbedtls_mpi_msb is one-based! */
+            return( MBEDTLS_ERR_ECP_INVALID_KEY );
         else
             return( 0 );
     }
-#endif /* POLARSSL_ECP_MONTGOMERY */
-#if defined(POLARSSL_ECP_SHORT_WEIERSTRASS)
-    if( ecp_get_type( grp ) == POLARSSL_ECP_TYPE_SHORT_WEIERSTRASS )
+#endif /* MBEDTLS_ECP_MONTGOMERY */
+#if defined(MBEDTLS_ECP_SHORT_WEIERSTRASS)
+    if( ecp_get_type( grp ) == MBEDTLS_ECP_TYPE_SHORT_WEIERSTRASS )
     {
         /* see SEC1 3.2 */
-        if( mpi_cmp_int( d, 1 ) < 0 ||
-            mpi_cmp_mpi( d, &grp->N ) >= 0 )
-            return( POLARSSL_ERR_ECP_INVALID_KEY );
+        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 /* POLARSSL_ECP_SHORT_WEIERSTRASS */
+#endif /* MBEDTLS_ECP_SHORT_WEIERSTRASS */
 
-    return( POLARSSL_ERR_ECP_BAD_INPUT_DATA );
+    return( MBEDTLS_ERR_ECP_BAD_INPUT_DATA );
 }
 
 /*
  * Generate a keypair
  */
-int ecp_gen_keypair( ecp_group *grp, mpi *d, ecp_point *Q,
+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 )
 {
     int ret;
     size_t n_size = ( grp->nbits + 7 ) / 8;
 
-#if defined(POLARSSL_ECP_MONTGOMERY)
-    if( ecp_get_type( grp ) == POLARSSL_ECP_TYPE_MONTGOMERY )
+#if defined(MBEDTLS_ECP_MONTGOMERY)
+    if( ecp_get_type( grp ) == MBEDTLS_ECP_TYPE_MONTGOMERY )
     {
         /* [M225] page 5 */
         size_t b;
 
-        MPI_CHK( mpi_fill_random( d, n_size, f_rng, p_rng ) );
+        MBEDTLS_MPI_CHK( mbedtls_mpi_fill_random( d, n_size, f_rng, p_rng ) );
 
         /* Make sure the most significant bit is nbits */
-        b = mpi_msb( d ) - 1; /* mpi_msb is one-based */
+        b = mbedtls_mpi_msb( d ) - 1; /* mbedtls_mpi_msb is one-based */
         if( b > grp->nbits )
-            MPI_CHK( mpi_shift_r( d, b - grp->nbits ) );
+            MBEDTLS_MPI_CHK( mbedtls_mpi_shift_r( d, b - grp->nbits ) );
         else
-            MPI_CHK( mpi_set_bit( d, grp->nbits, 1 ) );
+            MBEDTLS_MPI_CHK( mbedtls_mpi_set_bit( d, grp->nbits, 1 ) );
 
         /* Make sure the last three bits are unset */
-        MPI_CHK( mpi_set_bit( d, 0, 0 ) );
-        MPI_CHK( mpi_set_bit( d, 1, 0 ) );
-        MPI_CHK( mpi_set_bit( d, 2, 0 ) );
+        MBEDTLS_MPI_CHK( mbedtls_mpi_set_bit( d, 0, 0 ) );
+        MBEDTLS_MPI_CHK( mbedtls_mpi_set_bit( d, 1, 0 ) );
+        MBEDTLS_MPI_CHK( mbedtls_mpi_set_bit( d, 2, 0 ) );
     }
     else
-#endif /* POLARSSL_ECP_MONTGOMERY */
-#if defined(POLARSSL_ECP_SHORT_WEIERSTRASS)
-    if( ecp_get_type( grp ) == POLARSSL_ECP_TYPE_SHORT_WEIERSTRASS )
+#endif /* MBEDTLS_ECP_MONTGOMERY */
+#if defined(MBEDTLS_ECP_SHORT_WEIERSTRASS)
+    if( ecp_get_type( grp ) == MBEDTLS_ECP_TYPE_SHORT_WEIERSTRASS )
     {
         /* SEC1 3.2.1: Generate d such that 1 <= n < N */
         int count = 0;
-        unsigned char rnd[POLARSSL_ECP_MAX_BYTES];
+        unsigned char rnd[MBEDTLS_ECP_MAX_BYTES];
 
         /*
          * Match the procedure given in RFC 6979 (deterministic ECDSA):
@@ -1852,9 +1852,9 @@
          */
         do
         {
-            MPI_CHK( f_rng( p_rng, rnd, n_size ) );
-            MPI_CHK( mpi_read_binary( d, rnd, n_size ) );
-            MPI_CHK( mpi_shift_r( d, 8 * n_size - grp->nbits ) );
+            MBEDTLS_MPI_CHK( f_rng( p_rng, rnd, n_size ) );
+            MBEDTLS_MPI_CHK( mbedtls_mpi_read_binary( d, rnd, n_size ) );
+            MBEDTLS_MPI_CHK( mbedtls_mpi_shift_r( d, 8 * n_size - grp->nbits ) );
 
             /*
              * Each try has at worst a probability 1/2 of failing (the msb has
@@ -1866,90 +1866,90 @@
              * such as secp224k1 are actually very close to the worst case.
              */
             if( ++count > 30 )
-                return( POLARSSL_ERR_ECP_RANDOM_FAILED );
+                return( MBEDTLS_ERR_ECP_RANDOM_FAILED );
         }
-        while( mpi_cmp_int( d, 1 ) < 0 ||
-               mpi_cmp_mpi( d, &grp->N ) >= 0 );
+        while( mbedtls_mpi_cmp_int( d, 1 ) < 0 ||
+               mbedtls_mpi_cmp_mpi( d, &grp->N ) >= 0 );
     }
     else
-#endif /* POLARSSL_ECP_SHORT_WEIERSTRASS */
-        return( POLARSSL_ERR_ECP_BAD_INPUT_DATA );
+#endif /* MBEDTLS_ECP_SHORT_WEIERSTRASS */
+        return( MBEDTLS_ERR_ECP_BAD_INPUT_DATA );
 
 cleanup:
     if( ret != 0 )
         return( ret );
 
-    return( ecp_mul( grp, Q, d, &grp->G, f_rng, p_rng ) );
+    return( mbedtls_ecp_mul( grp, Q, d, &grp->G, f_rng, p_rng ) );
 }
 
 /*
  * Generate a keypair, prettier wrapper
  */
-int ecp_gen_key( ecp_group_id grp_id, ecp_keypair *key,
+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;
 
-    if( ( ret = ecp_use_known_dp( &key->grp, grp_id ) ) != 0 )
+    if( ( ret = mbedtls_ecp_use_known_dp( &key->grp, grp_id ) ) != 0 )
         return( ret );
 
-    return( ecp_gen_keypair( &key->grp, &key->d, &key->Q, f_rng, p_rng ) );
+    return( mbedtls_ecp_gen_keypair( &key->grp, &key->d, &key->Q, f_rng, p_rng ) );
 }
 
 /*
  * Check a public-private key pair
  */
-int ecp_check_pub_priv( const ecp_keypair *pub, const ecp_keypair *prv )
+int mbedtls_ecp_check_pub_priv( const mbedtls_ecp_keypair *pub, const mbedtls_ecp_keypair *prv )
 {
     int ret;
-    ecp_point Q;
-    ecp_group grp;
+    mbedtls_ecp_point Q;
+    mbedtls_ecp_group grp;
 
-    if( pub->grp.id == POLARSSL_ECP_DP_NONE ||
+    if( pub->grp.id == MBEDTLS_ECP_DP_NONE ||
         pub->grp.id != prv->grp.id ||
-        mpi_cmp_mpi( &pub->Q.X, &prv->Q.X ) ||
-        mpi_cmp_mpi( &pub->Q.Y, &prv->Q.Y ) ||
-        mpi_cmp_mpi( &pub->Q.Z, &prv->Q.Z ) )
+        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( POLARSSL_ERR_ECP_BAD_INPUT_DATA );
+        return( MBEDTLS_ERR_ECP_BAD_INPUT_DATA );
     }
 
-    ecp_point_init( &Q );
-    ecp_group_init( &grp );
+    mbedtls_ecp_point_init( &Q );
+    mbedtls_ecp_group_init( &grp );
 
-    /* ecp_mul() needs a non-const group... */
-    ecp_group_copy( &grp, &prv->grp );
+    /* mbedtls_ecp_mul() needs a non-const group... */
+    mbedtls_ecp_group_copy( &grp, &prv->grp );
 
     /* Also checks d is valid */
-    MPI_CHK( ecp_mul( &grp, &Q, &prv->d, &prv->grp.G, NULL, NULL ) );
+    MBEDTLS_MPI_CHK( mbedtls_ecp_mul( &grp, &Q, &prv->d, &prv->grp.G, NULL, NULL ) );
 
-    if( mpi_cmp_mpi( &Q.X, &prv->Q.X ) ||
-        mpi_cmp_mpi( &Q.Y, &prv->Q.Y ) ||
-        mpi_cmp_mpi( &Q.Z, &prv->Q.Z ) )
+    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 = POLARSSL_ERR_ECP_BAD_INPUT_DATA;
+        ret = MBEDTLS_ERR_ECP_BAD_INPUT_DATA;
         goto cleanup;
     }
 
 cleanup:
-    ecp_point_free( &Q );
-    ecp_group_free( &grp );
+    mbedtls_ecp_point_free( &Q );
+    mbedtls_ecp_group_free( &grp );
 
     return( ret );
 }
 
-#if defined(POLARSSL_SELF_TEST)
+#if defined(MBEDTLS_SELF_TEST)
 
 /*
  * Checkup routine
  */
-int ecp_self_test( int verbose )
+int mbedtls_ecp_self_test( int verbose )
 {
     int ret;
     size_t i;
-    ecp_group grp;
-    ecp_point R, P;
-    mpi m;
+    mbedtls_ecp_group grp;
+    mbedtls_ecp_point R, P;
+    mbedtls_mpi m;
     unsigned long add_c_prev, dbl_c_prev, mul_c_prev;
     /* exponents especially adapted for secp192r1 */
     const char *exponents[] =
@@ -1962,30 +1962,30 @@
         "555555555555555555555555555555555555555555555555", /* 101010... */
     };
 
-    ecp_group_init( &grp );
-    ecp_point_init( &R );
-    ecp_point_init( &P );
-    mpi_init( &m );
+    mbedtls_ecp_group_init( &grp );
+    mbedtls_ecp_point_init( &R );
+    mbedtls_ecp_point_init( &P );
+    mbedtls_mpi_init( &m );
 
     /* Use secp192r1 if available, or any available curve */
-#if defined(POLARSSL_ECP_DP_SECP192R1_ENABLED)
-    MPI_CHK( ecp_use_known_dp( &grp, POLARSSL_ECP_DP_SECP192R1 ) );
+#if defined(MBEDTLS_ECP_DP_SECP192R1_ENABLED)
+    MBEDTLS_MPI_CHK( mbedtls_ecp_use_known_dp( &grp, MBEDTLS_ECP_DP_SECP192R1 ) );
 #else
-    MPI_CHK( ecp_use_known_dp( &grp, ecp_curve_list()->grp_id ) );
+    MBEDTLS_MPI_CHK( mbedtls_ecp_use_known_dp( &grp, mbedtls_ecp_curve_list()->grp_id ) );
 #endif
 
     if( verbose != 0 )
-        polarssl_printf( "  ECP test #1 (constant op_count, base point G): " );
+        mbedtls_printf( "  ECP test #1 (constant op_count, base point G): " );
 
     /* Do a dummy multiplication first to trigger precomputation */
-    MPI_CHK( mpi_lset( &m, 2 ) );
-    MPI_CHK( ecp_mul( &grp, &P, &m, &grp.G, NULL, NULL ) );
+    MBEDTLS_MPI_CHK( mbedtls_mpi_lset( &m, 2 ) );
+    MBEDTLS_MPI_CHK( mbedtls_ecp_mul( &grp, &P, &m, &grp.G, NULL, NULL ) );
 
     add_count = 0;
     dbl_count = 0;
     mul_count = 0;
-    MPI_CHK( mpi_read_string( &m, 16, exponents[0] ) );
-    MPI_CHK( ecp_mul( &grp, &R, &m, &grp.G, NULL, NULL ) );
+    MBEDTLS_MPI_CHK( mbedtls_mpi_read_string( &m, 16, exponents[0] ) );
+    MBEDTLS_MPI_CHK( mbedtls_ecp_mul( &grp, &R, &m, &grp.G, NULL, NULL ) );
 
     for( i = 1; i < sizeof( exponents ) / sizeof( exponents[0] ); i++ )
     {
@@ -1996,15 +1996,15 @@
         dbl_count = 0;
         mul_count = 0;
 
-        MPI_CHK( mpi_read_string( &m, 16, exponents[i] ) );
-        MPI_CHK( ecp_mul( &grp, &R, &m, &grp.G, NULL, NULL ) );
+        MBEDTLS_MPI_CHK( mbedtls_mpi_read_string( &m, 16, exponents[i] ) );
+        MBEDTLS_MPI_CHK( mbedtls_ecp_mul( &grp, &R, &m, &grp.G, NULL, NULL ) );
 
         if( add_count != add_c_prev ||
             dbl_count != dbl_c_prev ||
             mul_count != mul_c_prev )
         {
             if( verbose != 0 )
-                polarssl_printf( "failed (%u)\n", (unsigned int) i );
+                mbedtls_printf( "failed (%u)\n", (unsigned int) i );
 
             ret = 1;
             goto cleanup;
@@ -2012,17 +2012,17 @@
     }
 
     if( verbose != 0 )
-        polarssl_printf( "passed\n" );
+        mbedtls_printf( "passed\n" );
 
     if( verbose != 0 )
-        polarssl_printf( "  ECP test #2 (constant op_count, other point): " );
+        mbedtls_printf( "  ECP test #2 (constant op_count, other point): " );
     /* We computed P = 2G last time, use it */
 
     add_count = 0;
     dbl_count = 0;
     mul_count = 0;
-    MPI_CHK( mpi_read_string( &m, 16, exponents[0] ) );
-    MPI_CHK( ecp_mul( &grp, &R, &m, &P, NULL, NULL ) );
+    MBEDTLS_MPI_CHK( mbedtls_mpi_read_string( &m, 16, exponents[0] ) );
+    MBEDTLS_MPI_CHK( mbedtls_ecp_mul( &grp, &R, &m, &P, NULL, NULL ) );
 
     for( i = 1; i < sizeof( exponents ) / sizeof( exponents[0] ); i++ )
     {
@@ -2033,15 +2033,15 @@
         dbl_count = 0;
         mul_count = 0;
 
-        MPI_CHK( mpi_read_string( &m, 16, exponents[i] ) );
-        MPI_CHK( ecp_mul( &grp, &R, &m, &P, NULL, NULL ) );
+        MBEDTLS_MPI_CHK( mbedtls_mpi_read_string( &m, 16, exponents[i] ) );
+        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 )
         {
             if( verbose != 0 )
-                polarssl_printf( "failed (%u)\n", (unsigned int) i );
+                mbedtls_printf( "failed (%u)\n", (unsigned int) i );
 
             ret = 1;
             goto cleanup;
@@ -2049,24 +2049,24 @@
     }
 
     if( verbose != 0 )
-        polarssl_printf( "passed\n" );
+        mbedtls_printf( "passed\n" );
 
 cleanup:
 
     if( ret < 0 && verbose != 0 )
-        polarssl_printf( "Unexpected error, return code = %08X\n", ret );
+        mbedtls_printf( "Unexpected error, return code = %08X\n", ret );
 
-    ecp_group_free( &grp );
-    ecp_point_free( &R );
-    ecp_point_free( &P );
-    mpi_free( &m );
+    mbedtls_ecp_group_free( &grp );
+    mbedtls_ecp_point_free( &R );
+    mbedtls_ecp_point_free( &P );
+    mbedtls_mpi_free( &m );
 
     if( verbose != 0 )
-        polarssl_printf( "\n" );
+        mbedtls_printf( "\n" );
 
     return( ret );
 }
 
-#endif /* POLARSSL_SELF_TEST */
+#endif /* MBEDTLS_SELF_TEST */
 
-#endif /* POLARSSL_ECP_C */
+#endif /* MBEDTLS_ECP_C */