diff --git a/library/CMakeLists.txt b/library/CMakeLists.txt
index 1a3e077..411c07d 100644
--- a/library/CMakeLists.txt
+++ b/library/CMakeLists.txt
@@ -17,6 +17,7 @@
      des.c
      dhm.c
      ecp.c
+     ecp_curves.c
      ecdh.c
      ecdsa.c
      entropy.c
diff --git a/library/Makefile b/library/Makefile
index 331c0a0..a9c86f8 100644
--- a/library/Makefile
+++ b/library/Makefile
@@ -40,7 +40,7 @@
 		certs.o		cipher.o	cipher_wrap.o	\
 		ctr_drbg.o	debug.o		des.o			\
 		dhm.o		ecdh.o		ecdsa.o			\
-		ecp.o									\
+		ecp.o		ecp_curves.o				\
 		entropy.o	entropy_poll.o				\
 		error.o		gcm.o		havege.o		\
 		md.o		md_wrap.o	md2.o			\
diff --git a/library/ecp.c b/library/ecp.c
index 969e11d..21e28c8 100644
--- a/library/ecp.c
+++ b/library/ecp.c
@@ -1,5 +1,5 @@
 /*
- *  Elliptic curves over GF(p)
+ *  Elliptic curves over GF(p): generic functions
  *
  *  Copyright (C) 2006-2013, Brainspark B.V.
  *
@@ -514,246 +514,6 @@
 }
 
 /*
- * Domain parameters for secp192r1
- */
-#define SECP192R1_P \
-    "FFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFEFFFFFFFFFFFFFFFF"
-#define SECP192R1_B \
-    "64210519E59C80E70FA7E9AB72243049FEB8DEECC146B9B1"
-#define SECP192R1_GX \
-    "188DA80EB03090F67CBF20EB43A18800F4FF0AFD82FF1012"
-#define SECP192R1_GY \
-    "07192B95FFC8DA78631011ED6B24CDD573F977A11E794811"
-#define SECP192R1_N \
-    "FFFFFFFFFFFFFFFFFFFFFFFF99DEF836146BC9B1B4D22831"
-
-/*
- * Domain parameters for secp224r1
- */
-#define SECP224R1_P \
-    "FFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFF000000000000000000000001"
-#define SECP224R1_B \
-    "B4050A850C04B3ABF54132565044B0B7D7BFD8BA270B39432355FFB4"
-#define SECP224R1_GX \
-    "B70E0CBD6BB4BF7F321390B94A03C1D356C21122343280D6115C1D21"
-#define SECP224R1_GY \
-    "BD376388B5F723FB4C22DFE6CD4375A05A07476444D5819985007E34"
-#define SECP224R1_N \
-    "FFFFFFFFFFFFFFFFFFFFFFFFFFFF16A2E0B8F03E13DD29455C5C2A3D"
-
-/*
- * Domain parameters for secp256r1
- */
-#define SECP256R1_P \
-    "FFFFFFFF00000001000000000000000000000000FFFFFFFFFFFFFFFFFFFFFFFF"
-#define SECP256R1_B \
-    "5AC635D8AA3A93E7B3EBBD55769886BC651D06B0CC53B0F63BCE3C3E27D2604B"
-#define SECP256R1_GX \
-    "6B17D1F2E12C4247F8BCE6E563A440F277037D812DEB33A0F4A13945D898C296"
-#define SECP256R1_GY \
-    "4FE342E2FE1A7F9B8EE7EB4A7C0F9E162BCE33576B315ECECBB6406837BF51F5"
-#define SECP256R1_N \
-    "FFFFFFFF00000000FFFFFFFFFFFFFFFFBCE6FAADA7179E84F3B9CAC2FC632551"
-
-/*
- * Domain parameters for secp384r1
- */
-#define SECP384R1_P \
-    "FFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFF" \
-    "FFFFFFFFFFFFFFFEFFFFFFFF0000000000000000FFFFFFFF"
-#define SECP384R1_B \
-    "B3312FA7E23EE7E4988E056BE3F82D19181D9C6EFE814112" \
-    "0314088F5013875AC656398D8A2ED19D2A85C8EDD3EC2AEF"
-#define SECP384R1_GX \
-    "AA87CA22BE8B05378EB1C71EF320AD746E1D3B628BA79B98" \
-    "59F741E082542A385502F25DBF55296C3A545E3872760AB7"
-#define SECP384R1_GY \
-    "3617DE4A96262C6F5D9E98BF9292DC29F8F41DBD289A147C" \
-    "E9DA3113B5F0B8C00A60B1CE1D7E819D7A431D7C90EA0E5F"
-#define SECP384R1_N \
-    "FFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFF" \
-    "C7634D81F4372DDF581A0DB248B0A77AECEC196ACCC52973"
-
-/*
- * Domain parameters for secp521r1
- */
-#define SECP521R1_P \
-    "000001FFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFF" \
-    "FFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFF" \
-    "FFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFF"
-#define SECP521R1_B \
-    "00000051953EB9618E1C9A1F929A21A0B68540EEA2DA725B" \
-    "99B315F3B8B489918EF109E156193951EC7E937B1652C0BD" \
-    "3BB1BF073573DF883D2C34F1EF451FD46B503F00"
-#define SECP521R1_GX \
-    "000000C6858E06B70404E9CD9E3ECB662395B4429C648139" \
-    "053FB521F828AF606B4D3DBAA14B5E77EFE75928FE1DC127" \
-    "A2FFA8DE3348B3C1856A429BF97E7E31C2E5BD66"
-#define SECP521R1_GY \
-    "0000011839296A789A3BC0045C8A5FB42C7D1BD998F54449" \
-    "579B446817AFBD17273E662C97EE72995EF42640C550B901" \
-    "3FAD0761353C7086A272C24088BE94769FD16650"
-#define SECP521R1_N \
-    "000001FFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFF" \
-    "FFFFFFFFFFFFFFFFFFFFFFFA51868783BF2F966B7FCC0148" \
-    "F709A5D03BB5C9B8899C47AEBB6FB71E91386409"
-
-/*
- * Domain parameters for brainpoolP256r1 (RFC 5639 3.4)
- */
-#define BP256R1_P \
-    "A9FB57DBA1EEA9BC3E660A909D838D726E3BF623D52620282013481D1F6E5377"
-#define BP256R1_A \
-    "7D5A0975FC2C3057EEF67530417AFFE7FB8055C126DC5C6CE94A4B44F330B5D9"
-#define BP256R1_B \
-    "26DC5C6CE94A4B44F330B5D9BBD77CBF958416295CF7E1CE6BCCDC18FF8C07B6"
-#define BP256R1_GX \
-    "8BD2AEB9CB7E57CB2C4B482FFC81B7AFB9DE27E1E3BD23C23A4453BD9ACE3262"
-#define BP256R1_GY \
-    "547EF835C3DAC4FD97F8461A14611DC9C27745132DED8E545C1D54C72F046997"
-#define BP256R1_N \
-    "A9FB57DBA1EEA9BC3E660A909D838D718C397AA3B561A6F7901E0E82974856A7"
-
-/*
- * Domain parameters for brainpoolP384r1 (RFC 5639 3.6)
- */
-#define BP384R1_P \
-    "8CB91E82A3386D280F5D6F7E50E641DF152F7109ED5456B412B1DA197FB711" \
-    "23ACD3A729901D1A71874700133107EC53"
-#define BP384R1_A \
-    "7BC382C63D8C150C3C72080ACE05AFA0C2BEA28E4FB22787139165EFBA91F9" \
-    "0F8AA5814A503AD4EB04A8C7DD22CE2826"
-#define BP384R1_B \
-    "04A8C7DD22CE28268B39B55416F0447C2FB77DE107DCD2A62E880EA53EEB62" \
-    "D57CB4390295DBC9943AB78696FA504C11"
-#define BP384R1_GX \
-    "1D1C64F068CF45FFA2A63A81B7C13F6B8847A3E77EF14FE3DB7FCAFE0CBD10" \
-    "E8E826E03436D646AAEF87B2E247D4AF1E"
-#define BP384R1_GY \
-    "8ABE1D7520F9C2A45CB1EB8E95CFD55262B70B29FEEC5864E19C054FF99129" \
-    "280E4646217791811142820341263C5315"
-#define BP384R1_N \
-    "8CB91E82A3386D280F5D6F7E50E641DF152F7109ED5456B31F166E6CAC0425" \
-    "A7CF3AB6AF6B7FC3103B883202E9046565"
-
-/*
- * Domain parameters for brainpoolP512r1 (RFC 5639 3.7)
- */
-#define BP512R1_P \
-    "AADD9DB8DBE9C48B3FD4E6AE33C9FC07CB308DB3B3C9D20ED6639CCA703308" \
-    "717D4D9B009BC66842AECDA12AE6A380E62881FF2F2D82C68528AA6056583A48F3"
-#define BP512R1_A \
-    "7830A3318B603B89E2327145AC234CC594CBDD8D3DF91610A83441CAEA9863" \
-    "BC2DED5D5AA8253AA10A2EF1C98B9AC8B57F1117A72BF2C7B9E7C1AC4D77FC94CA"
-#define BP512R1_B \
-    "3DF91610A83441CAEA9863BC2DED5D5AA8253AA10A2EF1C98B9AC8B57F1117" \
-    "A72BF2C7B9E7C1AC4D77FC94CADC083E67984050B75EBAE5DD2809BD638016F723"
-#define BP512R1_GX \
-    "81AEE4BDD82ED9645A21322E9C4C6A9385ED9F70B5D916C1B43B62EEF4D009" \
-    "8EFF3B1F78E2D0D48D50D1687B93B97D5F7C6D5047406A5E688B352209BCB9F822"
-#define BP512R1_GY \
-    "7DDE385D566332ECC0EABFA9CF7822FDF209F70024A57B1AA000C55B881F81" \
-    "11B2DCDE494A5F485E5BCA4BD88A2763AED1CA2B2FA8F0540678CD1E0F3AD80892"
-#define BP512R1_N \
-    "AADD9DB8DBE9C48B3FD4E6AE33C9FC07CB308DB3B3C9D20ED6639CCA703308" \
-    "70553E5C414CA92619418661197FAC10471DB1D381085DDADDB58796829CA90069"
-
-#if defined(POLARSSL_ECP_NIST_OPTIM)
-/* Forward declarations */
-static int ecp_mod_p192( mpi * );
-static int ecp_mod_p224( mpi * );
-static int ecp_mod_p256( mpi * );
-static int ecp_mod_p384( mpi * );
-static int ecp_mod_p521( mpi * );
-#endif
-
-/*
- * Set a group using well-known domain parameters
- */
-int ecp_use_known_dp( ecp_group *grp, ecp_group_id id )
-{
-    grp->id = id;
-
-    switch( id )
-    {
-#if defined(POLARSSL_ECP_DP_SECP192R1_ENABLED)
-        case POLARSSL_ECP_DP_SECP192R1:
-#if defined(POLARSSL_ECP_NIST_OPTIM)
-            grp->modp = ecp_mod_p192;
-#endif
-            return( ecp_group_read_string( grp, 16,
-                        SECP192R1_P, SECP192R1_B,
-                        SECP192R1_GX, SECP192R1_GY, SECP192R1_N ) );
-#endif /* POLARSSL_ECP_DP_SECP192R1_ENABLED */
-
-#if defined(POLARSSL_ECP_DP_SECP224R1_ENABLED)
-        case POLARSSL_ECP_DP_SECP224R1:
-#if defined(POLARSSL_ECP_NIST_OPTIM)
-            grp->modp = ecp_mod_p224;
-#endif
-            return( ecp_group_read_string( grp, 16,
-                        SECP224R1_P, SECP224R1_B,
-                        SECP224R1_GX, SECP224R1_GY, SECP224R1_N ) );
-#endif /* POLARSSL_ECP_DP_SECP224R1_ENABLED */
-
-#if defined(POLARSSL_ECP_DP_SECP256R1_ENABLED)
-        case POLARSSL_ECP_DP_SECP256R1:
-#if defined(POLARSSL_ECP_NIST_OPTIM)
-            grp->modp = ecp_mod_p256;
-#endif
-            return( ecp_group_read_string( grp, 16,
-                        SECP256R1_P, SECP256R1_B,
-                        SECP256R1_GX, SECP256R1_GY, SECP256R1_N ) );
-#endif /* POLARSSL_ECP_DP_SECP256R1_ENABLED */
-
-#if defined(POLARSSL_ECP_DP_SECP384R1_ENABLED)
-        case POLARSSL_ECP_DP_SECP384R1:
-#if defined(POLARSSL_ECP_NIST_OPTIM)
-            grp->modp = ecp_mod_p384;
-#endif
-            return( ecp_group_read_string( grp, 16,
-                        SECP384R1_P, SECP384R1_B,
-                        SECP384R1_GX, SECP384R1_GY, SECP384R1_N ) );
-#endif /* POLARSSL_ECP_DP_SECP384R1_ENABLED */
-
-#if defined(POLARSSL_ECP_DP_SECP521R1_ENABLED)
-        case POLARSSL_ECP_DP_SECP521R1:
-#if defined(POLARSSL_ECP_NIST_OPTIM)
-            grp->modp = ecp_mod_p521;
-#endif
-            return( ecp_group_read_string( grp, 16,
-                        SECP521R1_P, SECP521R1_B,
-                        SECP521R1_GX, SECP521R1_GY, SECP521R1_N ) );
-#endif /* POLARSSL_ECP_DP_SECP521R1_ENABLED */
-
-#if defined(POLARSSL_ECP_DP_BP256R1_ENABLED)
-        case POLARSSL_ECP_DP_BP256R1:
-            return( ecp_group_read_string_gen( grp, 16,
-                        BP256R1_P, BP256R1_A, BP256R1_B,
-                        BP256R1_GX, BP256R1_GY, BP256R1_N ) );
-#endif /* POLARSSL_ECP_DP_BP256R1_ENABLED */
-
-#if defined(POLARSSL_ECP_DP_BP384R1_ENABLED)
-        case POLARSSL_ECP_DP_BP384R1:
-            return( ecp_group_read_string_gen( grp, 16,
-                        BP384R1_P, BP384R1_A, BP384R1_B,
-                        BP384R1_GX, BP384R1_GY, BP384R1_N ) );
-#endif /* POLARSSL_ECP_DP_BP384R1_ENABLED */
-
-#if defined(POLARSSL_ECP_DP_BP512R1_ENABLED)
-        case POLARSSL_ECP_DP_BP512R1:
-            return( ecp_group_read_string_gen( grp, 16,
-                        BP512R1_P, BP512R1_A, BP512R1_B,
-                        BP512R1_GX, BP512R1_GY, BP512R1_N ) );
-#endif /* POLARSSL_ECP_DP_BP512R1_ENABLED */
-
-        default:
-            ecp_group_free( grp );
-            return( POLARSSL_ERR_ECP_FEATURE_UNAVAILABLE );
-    }
-}
-
-/*
  * Set a group from an ECParameters record (RFC 4492)
  */
 int ecp_tls_read_group( ecp_group *grp, const unsigned char **buf, size_t len )
@@ -1705,409 +1465,6 @@
     return( ecp_gen_keypair( &key->grp, &key->d, &key->Q, f_rng, p_rng ) );
 }
 
-#if defined(POLARSSL_ECP_NIST_OPTIM)
-/*
- * Fast reduction modulo the primes used by the NIST curves.
- *
- * These functions are: critical for speed, but not need for correct
- * operations. So, we make the choice to heavily rely on the internals of our
- * bignum library, which creates a tight coupling between these functions and
- * our MPI implementation.  However, the coupling between the ECP module and
- * MPI remains loose, since these functions can be deactivated at will.
- */
-
-#if defined(POLARSSL_ECP_DP_SECP192R1_ENABLED)
-/*
- * Compared to the way things are presented in FIPS 186-3 D.2,
- * we proceed in columns, from right (least significant chunk) to left,
- * adding chunks to N in place, and keeping a carry for the next chunk.
- * This avoids moving things around in memory, and uselessly adding zeros,
- * compared to the more straightforward, line-oriented approach.
- *
- * For this prime we need to handle data in chunks of 64 bits.
- * Since this is always a multiple of our basic t_uint, we can
- * use a t_uint * to designate such a chunk, and small loops to handle it.
- */
-
-/* Add 64-bit chunks (dst += src) and update carry */
-static inline void add64( t_uint *dst, t_uint *src, t_uint *carry )
-{
-    unsigned char i;
-    t_uint c = 0;
-    for( i = 0; i < 8 / sizeof( t_uint ); i++, dst++, src++ )
-    {
-        *dst += c;      c  = ( *dst < c );
-        *dst += *src;   c += ( *dst < *src );
-    }
-    *carry += c;
-}
-
-/* Add carry to a 64-bit chunk and update carry */
-static inline void carry64( t_uint *dst, t_uint *carry )
-{
-    unsigned char i;
-    for( i = 0; i < 8 / sizeof( t_uint ); i++, dst++ )
-    {
-        *dst += *carry;
-        *carry  = ( *dst < *carry );
-    }
-}
-
-#define WIDTH       8 / sizeof( t_uint )
-#define A( i )      N->p + i * WIDTH
-#define ADD( i )    add64( p, A( i ), &c )
-#define NEXT        p += WIDTH; carry64( p, &c )
-#define LAST        p += WIDTH; *p = c; while( ++p < end ) *p = 0
-
-/*
- * Fast quasi-reduction modulo p192 (FIPS 186-3 D.2.1)
- */
-static int ecp_mod_p192( mpi *N )
-{
-    int ret;
-    t_uint c = 0;
-    t_uint *p, *end;
-
-    /* Make sure we have enough blocks so that A(5) is legal */
-    MPI_CHK( mpi_grow( N, 6 * WIDTH ) );
-
-    p = N->p;
-    end = p + N->n;
-
-    ADD( 3 ); ADD( 5 );             NEXT; // A0 += A3 + A5
-    ADD( 3 ); ADD( 4 ); ADD( 5 );   NEXT; // A1 += A3 + A4 + A5
-    ADD( 4 ); ADD( 5 );             LAST; // A2 += A4 + A5
-
-cleanup:
-    return( ret );
-}
-
-#undef WIDTH
-#undef A
-#undef ADD
-#undef NEXT
-#undef LAST
-#endif /* POLARSSL_ECP_DP_SECP192R1_ENABLED */
-
-#if defined(POLARSSL_ECP_DP_SECP224R1_ENABLED) ||   \
-    defined(POLARSSL_ECP_DP_SECP256R1_ENABLED) ||   \
-    defined(POLARSSL_ECP_DP_SECP384R1_ENABLED)
-/*
- * The reader is advised to first understand ecp_mod_p192() since the same
- * general structure is used here, but with additional complications:
- * (1) chunks of 32 bits, and (2) subtractions.
- */
-
-/*
- * For these primes, we need to handle data in chunks of 32 bits.
- * This makes it more complicated if we use 64 bits limbs in MPI,
- * which prevents us from using a uniform access method as for p192.
- *
- * So, we define a mini abstraction layer to access 32 bit chunks,
- * load them in 'cur' for work, and store them back from 'cur' when done.
- *
- * While at it, also define the size of N in terms of 32-bit chunks.
- */
-#define LOAD32      cur = A( i );
-
-#if defined(POLARSSL_HAVE_INT8)     /* 8 bit */
-
-#define MAX32       N->n / 4
-#define A( j )      (uint32_t)( N->p[4*j+0]       ) |  \
-                              ( N->p[4*j+1] << 8  ) |  \
-                              ( N->p[4*j+2] << 16 ) |  \
-                              ( N->p[4*j+3] << 24 )
-#define STORE32     N->p[4*i+0] = (t_uint)( cur       );   \
-                    N->p[4*i+1] = (t_uint)( cur >> 8  );   \
-                    N->p[4*i+2] = (t_uint)( cur >> 16 );   \
-                    N->p[4*i+3] = (t_uint)( cur >> 24 );
-
-#elif defined(POLARSSL_HAVE_INT16)  /* 16 bit */
-
-#define MAX32       N->n / 2
-#define A( j )      (uint32_t)( N->p[2*j] ) | ( N->p[2*j+1] << 16 )
-#define STORE32     N->p[2*i+0] = (t_uint)( cur       );  \
-                    N->p[2*i+1] = (t_uint)( cur >> 16 );
-
-#elif defined(POLARSSL_HAVE_INT32)  /* 32 bit */
-
-#define MAX32       N->n
-#define A( j )      N->p[j]
-#define STORE32     N->p[i] = cur;
-
-#else                               /* 64-bit */
-
-#define MAX32       N->n * 2
-#define A( j ) j % 2 ? (uint32_t)( N->p[j/2] >> 32 ) : (uint32_t)( N->p[j/2] )
-#define STORE32                                   \
-    if( i % 2 ) {                                 \
-        N->p[i/2] &= 0x00000000FFFFFFFF;          \
-        N->p[i/2] |= ((t_uint) cur) << 32;        \
-    } else {                                      \
-        N->p[i/2] &= 0xFFFFFFFF00000000;          \
-        N->p[i/2] |= (t_uint) cur;                \
-    }
-
-#endif /* sizeof( t_uint ) */
-
-/*
- * Helpers for addition and subtraction of chunks, with signed carry.
- */
-static inline void add32( uint32_t *dst, uint32_t src, signed char *carry )
-{
-    *dst += src;
-    *carry += ( *dst < src );
-}
-
-static inline void sub32( uint32_t *dst, uint32_t src, signed char *carry )
-{
-    *carry -= ( *dst < src );
-    *dst -= src;
-}
-
-#define ADD( j )    add32( &cur, A( j ), &c );
-#define SUB( j )    sub32( &cur, A( j ), &c );
-
-/*
- * Helpers for the main 'loop'
- * (see fix_negative for the motivation of C)
- */
-#define INIT( b )                                           \
-    int ret;                                                \
-    signed char c = 0, cc;                                  \
-    uint32_t cur;                                           \
-    size_t i = 0, bits = b;                                 \
-    mpi C;                                                  \
-    t_uint Cp[ b / 8 / sizeof( t_uint) + 1 ];               \
-                                                            \
-    C.s = 1;                                                \
-    C.n = b / 8 / sizeof( t_uint) + 1;                      \
-    C.p = Cp;                                               \
-    memset( Cp, 0, C.n * sizeof( t_uint ) );                \
-                                                            \
-    MPI_CHK( mpi_grow( N, b * 2 / 8 / sizeof( t_uint ) ) ); \
-    LOAD32;
-
-#define NEXT                    \
-    STORE32; i++; LOAD32;       \
-    cc = c; c = 0;              \
-    if( cc < 0 )                \
-        sub32( &cur, -cc, &c ); \
-    else                        \
-        add32( &cur, cc, &c );  \
-
-#define LAST                                    \
-    STORE32; i++;                               \
-    cur = c > 0 ? c : 0; STORE32;               \
-    cur = 0; while( ++i < MAX32 ) { STORE32; }  \
-    if( c < 0 ) fix_negative( N, c, &C, bits );
-
-/*
- * If the result is negative, we get it in the form
- * c * 2^(bits + 32) + N, with c negative and N positive shorter than 'bits'
- */
-static inline int fix_negative( mpi *N, signed char c, mpi *C, size_t bits )
-{
-    int ret;
-
-    /* C = - c * 2^(bits + 32) */
-#if !defined(POLARSSL_HAVE_INT64)
-    ((void) bits);
-#else
-    if( bits == 224 )
-        C->p[ C->n - 1 ] = ((t_uint) -c) << 32;
-    else
-#endif
-        C->p[ C->n - 1 ] = (t_uint) -c;
-
-    /* N = - ( C - N ) */
-    MPI_CHK( mpi_sub_abs( N, C, N ) );
-    N->s = -1;
-
-cleanup:
-
-    return( ret );
-}
-
-#if defined(POLARSSL_ECP_DP_SECP224R1_ENABLED)
-/*
- * Fast quasi-reduction modulo p224 (FIPS 186-3 D.2.2)
- */
-static int ecp_mod_p224( mpi *N )
-{
-    INIT( 224 );
-
-    SUB(  7 ); SUB( 11 );               NEXT; // A0 += -A7 - A11
-    SUB(  8 ); SUB( 12 );               NEXT; // A1 += -A8 - A12
-    SUB(  9 ); SUB( 13 );               NEXT; // A2 += -A9 - A13
-    SUB( 10 ); ADD(  7 ); ADD( 11 );    NEXT; // A3 += -A10 + A7 + A11
-    SUB( 11 ); ADD(  8 ); ADD( 12 );    NEXT; // A4 += -A11 + A8 + A12
-    SUB( 12 ); ADD(  9 ); ADD( 13 );    NEXT; // A5 += -A12 + A9 + A13
-    SUB( 13 ); ADD( 10 );               LAST; // A6 += -A13 + A10
-
-cleanup:
-    return( ret );
-}
-#endif /* POLARSSL_ECP_DP_SECP224R1_ENABLED */
-
-#if defined(POLARSSL_ECP_DP_SECP256R1_ENABLED)
-/*
- * Fast quasi-reduction modulo p256 (FIPS 186-3 D.2.3)
- */
-static int ecp_mod_p256( mpi *N )
-{
-    INIT( 256 );
-
-    ADD(  8 ); ADD(  9 );
-    SUB( 11 ); SUB( 12 ); SUB( 13 ); SUB( 14 );             NEXT; // A0
-
-    ADD(  9 ); ADD( 10 );
-    SUB( 12 ); SUB( 13 ); SUB( 14 ); SUB( 15 );             NEXT; // A1
-
-    ADD( 10 ); ADD( 11 );
-    SUB( 13 ); SUB( 14 ); SUB( 15 );                        NEXT; // A2
-
-    ADD( 11 ); ADD( 11 ); ADD( 12 ); ADD( 12 ); ADD( 13 );
-    SUB( 15 ); SUB(  8 ); SUB(  9 );                        NEXT; // A3
-
-    ADD( 12 ); ADD( 12 ); ADD( 13 ); ADD( 13 ); ADD( 14 );
-    SUB(  9 ); SUB( 10 );                                   NEXT; // A4
-
-    ADD( 13 ); ADD( 13 ); ADD( 14 ); ADD( 14 ); ADD( 15 );
-    SUB( 10 ); SUB( 11 );                                   NEXT; // A5
-
-    ADD( 14 ); ADD( 14 ); ADD( 15 ); ADD( 15 ); ADD( 14 ); ADD( 13 );
-    SUB(  8 ); SUB(  9 );                                   NEXT; // A6
-
-    ADD( 15 ); ADD( 15 ); ADD( 15 ); ADD( 8 );
-    SUB( 10 ); SUB( 11 ); SUB( 12 ); SUB( 13 );             LAST; // A7
-
-cleanup:
-    return( ret );
-}
-#endif /* POLARSSL_ECP_DP_SECP256R1_ENABLED */
-
-#if defined(POLARSSL_ECP_DP_SECP384R1_ENABLED)
-/*
- * Fast quasi-reduction modulo p384 (FIPS 186-3 D.2.4)
- */
-static int ecp_mod_p384( mpi *N )
-{
-    INIT( 384 );
-
-    ADD( 12 ); ADD( 21 ); ADD( 20 );
-    SUB( 23 );                                              NEXT; // A0
-
-    ADD( 13 ); ADD( 22 ); ADD( 23 );
-    SUB( 12 ); SUB( 20 );                                   NEXT; // A2
-
-    ADD( 14 ); ADD( 23 );
-    SUB( 13 ); SUB( 21 );                                   NEXT; // A2
-
-    ADD( 15 ); ADD( 12 ); ADD( 20 ); ADD( 21 );
-    SUB( 14 ); SUB( 22 ); SUB( 23 );                        NEXT; // A3
-
-    ADD( 21 ); ADD( 21 ); ADD( 16 ); ADD( 13 ); ADD( 12 ); ADD( 20 ); ADD( 22 );
-    SUB( 15 ); SUB( 23 ); SUB( 23 );                        NEXT; // A4
-
-    ADD( 22 ); ADD( 22 ); ADD( 17 ); ADD( 14 ); ADD( 13 ); ADD( 21 ); ADD( 23 );
-    SUB( 16 );                                              NEXT; // A5
-
-    ADD( 23 ); ADD( 23 ); ADD( 18 ); ADD( 15 ); ADD( 14 ); ADD( 22 );
-    SUB( 17 );                                              NEXT; // A6
-
-    ADD( 19 ); ADD( 16 ); ADD( 15 ); ADD( 23 );
-    SUB( 18 );                                              NEXT; // A7
-
-    ADD( 20 ); ADD( 17 ); ADD( 16 );
-    SUB( 19 );                                              NEXT; // A8
-
-    ADD( 21 ); ADD( 18 ); ADD( 17 );
-    SUB( 20 );                                              NEXT; // A9
-
-    ADD( 22 ); ADD( 19 ); ADD( 18 );
-    SUB( 21 );                                              NEXT; // A10
-
-    ADD( 23 ); ADD( 20 ); ADD( 19 );
-    SUB( 22 );                                              LAST; // A11
-
-cleanup:
-    return( ret );
-}
-#endif /* POLARSSL_ECP_DP_SECP384R1_ENABLED */
-
-#undef A
-#undef LOAD32
-#undef STORE32
-#undef MAX32
-#undef INIT
-#undef NEXT
-#undef LAST
-
-#endif /* POLARSSL_ECP_DP_SECP224R1_ENABLED ||
-          POLARSSL_ECP_DP_SECP256R1_ENABLED ||
-          POLARSSL_ECP_DP_SECP384R1_ENABLED */
-
-#if defined(POLARSSL_ECP_DP_SECP521R1_ENABLED)
-/*
- * Here we have an actual Mersenne prime, so things are more straightforward.
- * However, chunks are aligned on a 'weird' boundary (521 bits).
- */
-
-/* Size of p521 in terms of t_uint */
-#define P521_WIDTH      ( 521 / 8 / sizeof( t_uint ) + 1 )
-
-/* Bits to keep in the most significant t_uint */
-#if defined(POLARSSL_HAVE_INT8)
-#define P521_MASK       0x01
-#else
-#define P521_MASK       0x01FF
-#endif
-
-/*
- * Fast quasi-reduction modulo p521 (FIPS 186-3 D.2.5)
- * Write N as A1 + 2^521 A0, return A0 + A1
- */
-static int ecp_mod_p521( mpi *N )
-{
-    int ret;
-    size_t i;
-    mpi M;
-    t_uint Mp[P521_WIDTH + 1];
-    /* Worst case for the size of M is when t_uint is 16 bits:
-     * we need to hold bits 513 to 1056, which is 34 limbs, that is
-     * P521_WIDTH + 1. Otherwise P521_WIDTH is enough. */
-
-    if( N->n < P521_WIDTH )
-        return( 0 );
-
-    /* M = A1 */
-    M.s = 1;
-    M.n = N->n - ( P521_WIDTH - 1 );
-    if( M.n > P521_WIDTH + 1 )
-        M.n = P521_WIDTH + 1;
-    M.p = Mp;
-    memcpy( Mp, N->p + P521_WIDTH - 1, M.n * sizeof( t_uint ) );
-    MPI_CHK( mpi_shift_r( &M, 521 % ( 8 * sizeof( t_uint ) ) ) );
-
-    /* N = A0 */
-    N->p[P521_WIDTH - 1] &= P521_MASK;
-    for( i = P521_WIDTH; i < N->n; i++ )
-        N->p[i] = 0;
-
-    /* N = A0 + A1 */
-    MPI_CHK( mpi_add_abs( N, N, &M ) );
-
-cleanup:
-    return( ret );
-}
-
-#undef P521_WIDTH
-#undef P521_MASK
-#endif /* POLARSSL_ECP_DP_SECP521R1_ENABLED */
-
-#endif /* POLARSSL_ECP_NIST_OPTIM */
-
 #if defined(POLARSSL_SELF_TEST)
 
 /*
diff --git a/library/ecp_curves.c b/library/ecp_curves.c
new file mode 100644
index 0000000..a7b7bc7
--- /dev/null
+++ b/library/ecp_curves.c
@@ -0,0 +1,700 @@
+/*
+ *  Elliptic curves over GF(p): curve-specific data and functions
+ *
+ *  Copyright (C) 2006-2013, Brainspark B.V.
+ *
+ *  This file is part of PolarSSL (http://www.polarssl.org)
+ *  Lead Maintainer: Paul Bakker <polarssl_maintainer at polarssl.org>
+ *
+ *  All rights reserved.
+ *
+ *  This program is free software; you can redistribute it and/or modify
+ *  it under the terms of the GNU General Public License as published by
+ *  the Free Software Foundation; either version 2 of the License, or
+ *  (at your option) any later version.
+ *
+ *  This program is distributed in the hope that it will be useful,
+ *  but WITHOUT ANY WARRANTY; without even the implied warranty of
+ *  MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE.  See the
+ *  GNU General Public License for more details.
+ *
+ *  You should have received a copy of the GNU General Public License along
+ *  with this program; if not, write to the Free Software Foundation, Inc.,
+ *  51 Franklin Street, Fifth Floor, Boston, MA 02110-1301 USA.
+ */
+
+#include "polarssl/config.h"
+
+#if defined(POLARSSL_ECP_C)
+
+#include "polarssl/ecp.h"
+
+/*
+ * Domain parameters for secp192r1
+ */
+#define SECP192R1_P \
+    "FFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFEFFFFFFFFFFFFFFFF"
+#define SECP192R1_B \
+    "64210519E59C80E70FA7E9AB72243049FEB8DEECC146B9B1"
+#define SECP192R1_GX \
+    "188DA80EB03090F67CBF20EB43A18800F4FF0AFD82FF1012"
+#define SECP192R1_GY \
+    "07192B95FFC8DA78631011ED6B24CDD573F977A11E794811"
+#define SECP192R1_N \
+    "FFFFFFFFFFFFFFFFFFFFFFFF99DEF836146BC9B1B4D22831"
+
+/*
+ * Domain parameters for secp224r1
+ */
+#define SECP224R1_P \
+    "FFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFF000000000000000000000001"
+#define SECP224R1_B \
+    "B4050A850C04B3ABF54132565044B0B7D7BFD8BA270B39432355FFB4"
+#define SECP224R1_GX \
+    "B70E0CBD6BB4BF7F321390B94A03C1D356C21122343280D6115C1D21"
+#define SECP224R1_GY \
+    "BD376388B5F723FB4C22DFE6CD4375A05A07476444D5819985007E34"
+#define SECP224R1_N \
+    "FFFFFFFFFFFFFFFFFFFFFFFFFFFF16A2E0B8F03E13DD29455C5C2A3D"
+
+/*
+ * Domain parameters for secp256r1
+ */
+#define SECP256R1_P \
+    "FFFFFFFF00000001000000000000000000000000FFFFFFFFFFFFFFFFFFFFFFFF"
+#define SECP256R1_B \
+    "5AC635D8AA3A93E7B3EBBD55769886BC651D06B0CC53B0F63BCE3C3E27D2604B"
+#define SECP256R1_GX \
+    "6B17D1F2E12C4247F8BCE6E563A440F277037D812DEB33A0F4A13945D898C296"
+#define SECP256R1_GY \
+    "4FE342E2FE1A7F9B8EE7EB4A7C0F9E162BCE33576B315ECECBB6406837BF51F5"
+#define SECP256R1_N \
+    "FFFFFFFF00000000FFFFFFFFFFFFFFFFBCE6FAADA7179E84F3B9CAC2FC632551"
+
+/*
+ * Domain parameters for secp384r1
+ */
+#define SECP384R1_P \
+    "FFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFF" \
+    "FFFFFFFFFFFFFFFEFFFFFFFF0000000000000000FFFFFFFF"
+#define SECP384R1_B \
+    "B3312FA7E23EE7E4988E056BE3F82D19181D9C6EFE814112" \
+    "0314088F5013875AC656398D8A2ED19D2A85C8EDD3EC2AEF"
+#define SECP384R1_GX \
+    "AA87CA22BE8B05378EB1C71EF320AD746E1D3B628BA79B98" \
+    "59F741E082542A385502F25DBF55296C3A545E3872760AB7"
+#define SECP384R1_GY \
+    "3617DE4A96262C6F5D9E98BF9292DC29F8F41DBD289A147C" \
+    "E9DA3113B5F0B8C00A60B1CE1D7E819D7A431D7C90EA0E5F"
+#define SECP384R1_N \
+    "FFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFF" \
+    "C7634D81F4372DDF581A0DB248B0A77AECEC196ACCC52973"
+
+/*
+ * Domain parameters for secp521r1
+ */
+#define SECP521R1_P \
+    "000001FFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFF" \
+    "FFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFF" \
+    "FFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFF"
+#define SECP521R1_B \
+    "00000051953EB9618E1C9A1F929A21A0B68540EEA2DA725B" \
+    "99B315F3B8B489918EF109E156193951EC7E937B1652C0BD" \
+    "3BB1BF073573DF883D2C34F1EF451FD46B503F00"
+#define SECP521R1_GX \
+    "000000C6858E06B70404E9CD9E3ECB662395B4429C648139" \
+    "053FB521F828AF606B4D3DBAA14B5E77EFE75928FE1DC127" \
+    "A2FFA8DE3348B3C1856A429BF97E7E31C2E5BD66"
+#define SECP521R1_GY \
+    "0000011839296A789A3BC0045C8A5FB42C7D1BD998F54449" \
+    "579B446817AFBD17273E662C97EE72995EF42640C550B901" \
+    "3FAD0761353C7086A272C24088BE94769FD16650"
+#define SECP521R1_N \
+    "000001FFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFF" \
+    "FFFFFFFFFFFFFFFFFFFFFFFA51868783BF2F966B7FCC0148" \
+    "F709A5D03BB5C9B8899C47AEBB6FB71E91386409"
+
+/*
+ * Domain parameters for brainpoolP256r1 (RFC 5639 3.4)
+ */
+#define BP256R1_P \
+    "A9FB57DBA1EEA9BC3E660A909D838D726E3BF623D52620282013481D1F6E5377"
+#define BP256R1_A \
+    "7D5A0975FC2C3057EEF67530417AFFE7FB8055C126DC5C6CE94A4B44F330B5D9"
+#define BP256R1_B \
+    "26DC5C6CE94A4B44F330B5D9BBD77CBF958416295CF7E1CE6BCCDC18FF8C07B6"
+#define BP256R1_GX \
+    "8BD2AEB9CB7E57CB2C4B482FFC81B7AFB9DE27E1E3BD23C23A4453BD9ACE3262"
+#define BP256R1_GY \
+    "547EF835C3DAC4FD97F8461A14611DC9C27745132DED8E545C1D54C72F046997"
+#define BP256R1_N \
+    "A9FB57DBA1EEA9BC3E660A909D838D718C397AA3B561A6F7901E0E82974856A7"
+
+/*
+ * Domain parameters for brainpoolP384r1 (RFC 5639 3.6)
+ */
+#define BP384R1_P \
+    "8CB91E82A3386D280F5D6F7E50E641DF152F7109ED5456B412B1DA197FB711" \
+    "23ACD3A729901D1A71874700133107EC53"
+#define BP384R1_A \
+    "7BC382C63D8C150C3C72080ACE05AFA0C2BEA28E4FB22787139165EFBA91F9" \
+    "0F8AA5814A503AD4EB04A8C7DD22CE2826"
+#define BP384R1_B \
+    "04A8C7DD22CE28268B39B55416F0447C2FB77DE107DCD2A62E880EA53EEB62" \
+    "D57CB4390295DBC9943AB78696FA504C11"
+#define BP384R1_GX \
+    "1D1C64F068CF45FFA2A63A81B7C13F6B8847A3E77EF14FE3DB7FCAFE0CBD10" \
+    "E8E826E03436D646AAEF87B2E247D4AF1E"
+#define BP384R1_GY \
+    "8ABE1D7520F9C2A45CB1EB8E95CFD55262B70B29FEEC5864E19C054FF99129" \
+    "280E4646217791811142820341263C5315"
+#define BP384R1_N \
+    "8CB91E82A3386D280F5D6F7E50E641DF152F7109ED5456B31F166E6CAC0425" \
+    "A7CF3AB6AF6B7FC3103B883202E9046565"
+
+/*
+ * Domain parameters for brainpoolP512r1 (RFC 5639 3.7)
+ */
+#define BP512R1_P \
+    "AADD9DB8DBE9C48B3FD4E6AE33C9FC07CB308DB3B3C9D20ED6639CCA703308" \
+    "717D4D9B009BC66842AECDA12AE6A380E62881FF2F2D82C68528AA6056583A48F3"
+#define BP512R1_A \
+    "7830A3318B603B89E2327145AC234CC594CBDD8D3DF91610A83441CAEA9863" \
+    "BC2DED5D5AA8253AA10A2EF1C98B9AC8B57F1117A72BF2C7B9E7C1AC4D77FC94CA"
+#define BP512R1_B \
+    "3DF91610A83441CAEA9863BC2DED5D5AA8253AA10A2EF1C98B9AC8B57F1117" \
+    "A72BF2C7B9E7C1AC4D77FC94CADC083E67984050B75EBAE5DD2809BD638016F723"
+#define BP512R1_GX \
+    "81AEE4BDD82ED9645A21322E9C4C6A9385ED9F70B5D916C1B43B62EEF4D009" \
+    "8EFF3B1F78E2D0D48D50D1687B93B97D5F7C6D5047406A5E688B352209BCB9F822"
+#define BP512R1_GY \
+    "7DDE385D566332ECC0EABFA9CF7822FDF209F70024A57B1AA000C55B881F81" \
+    "11B2DCDE494A5F485E5BCA4BD88A2763AED1CA2B2FA8F0540678CD1E0F3AD80892"
+#define BP512R1_N \
+    "AADD9DB8DBE9C48B3FD4E6AE33C9FC07CB308DB3B3C9D20ED6639CCA703308" \
+    "70553E5C414CA92619418661197FAC10471DB1D381085DDADDB58796829CA90069"
+
+/*
+ * Import an ECP group from ASCII strings, general case (A used)
+ */
+static int ecp_group_read_string_gen( ecp_group *grp, int radix,
+                           const char *p, const char *a, 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->A, radix, a ) );
+    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 ) );
+
+    grp->pbits = mpi_msb( &grp->P );
+    grp->nbits = mpi_msb( &grp->N );
+
+cleanup:
+    if( ret != 0 )
+        ecp_group_free( grp );
+
+    return( ret );
+}
+
+#if defined(POLARSSL_ECP_NIST_OPTIM)
+/* Forward declarations */
+int ecp_mod_p192( mpi * );
+int ecp_mod_p224( mpi * );
+int ecp_mod_p256( mpi * );
+int ecp_mod_p384( mpi * );
+int ecp_mod_p521( mpi * );
+#endif
+
+/*
+ * Set a group using well-known domain parameters
+ */
+int ecp_use_known_dp( ecp_group *grp, ecp_group_id id )
+{
+    grp->id = id;
+
+    switch( id )
+    {
+#if defined(POLARSSL_ECP_DP_SECP192R1_ENABLED)
+        case POLARSSL_ECP_DP_SECP192R1:
+#if defined(POLARSSL_ECP_NIST_OPTIM)
+            grp->modp = ecp_mod_p192;
+#endif
+            return( ecp_group_read_string( grp, 16,
+                        SECP192R1_P, SECP192R1_B,
+                        SECP192R1_GX, SECP192R1_GY, SECP192R1_N ) );
+#endif /* POLARSSL_ECP_DP_SECP192R1_ENABLED */
+
+#if defined(POLARSSL_ECP_DP_SECP224R1_ENABLED)
+        case POLARSSL_ECP_DP_SECP224R1:
+#if defined(POLARSSL_ECP_NIST_OPTIM)
+            grp->modp = ecp_mod_p224;
+#endif
+            return( ecp_group_read_string( grp, 16,
+                        SECP224R1_P, SECP224R1_B,
+                        SECP224R1_GX, SECP224R1_GY, SECP224R1_N ) );
+#endif /* POLARSSL_ECP_DP_SECP224R1_ENABLED */
+
+#if defined(POLARSSL_ECP_DP_SECP256R1_ENABLED)
+        case POLARSSL_ECP_DP_SECP256R1:
+#if defined(POLARSSL_ECP_NIST_OPTIM)
+            grp->modp = ecp_mod_p256;
+#endif
+            return( ecp_group_read_string( grp, 16,
+                        SECP256R1_P, SECP256R1_B,
+                        SECP256R1_GX, SECP256R1_GY, SECP256R1_N ) );
+#endif /* POLARSSL_ECP_DP_SECP256R1_ENABLED */
+
+#if defined(POLARSSL_ECP_DP_SECP384R1_ENABLED)
+        case POLARSSL_ECP_DP_SECP384R1:
+#if defined(POLARSSL_ECP_NIST_OPTIM)
+            grp->modp = ecp_mod_p384;
+#endif
+            return( ecp_group_read_string( grp, 16,
+                        SECP384R1_P, SECP384R1_B,
+                        SECP384R1_GX, SECP384R1_GY, SECP384R1_N ) );
+#endif /* POLARSSL_ECP_DP_SECP384R1_ENABLED */
+
+#if defined(POLARSSL_ECP_DP_SECP521R1_ENABLED)
+        case POLARSSL_ECP_DP_SECP521R1:
+#if defined(POLARSSL_ECP_NIST_OPTIM)
+            grp->modp = ecp_mod_p521;
+#endif
+            return( ecp_group_read_string( grp, 16,
+                        SECP521R1_P, SECP521R1_B,
+                        SECP521R1_GX, SECP521R1_GY, SECP521R1_N ) );
+#endif /* POLARSSL_ECP_DP_SECP521R1_ENABLED */
+
+#if defined(POLARSSL_ECP_DP_BP256R1_ENABLED)
+        case POLARSSL_ECP_DP_BP256R1:
+            return( ecp_group_read_string_gen( grp, 16,
+                        BP256R1_P, BP256R1_A, BP256R1_B,
+                        BP256R1_GX, BP256R1_GY, BP256R1_N ) );
+#endif /* POLARSSL_ECP_DP_BP256R1_ENABLED */
+
+#if defined(POLARSSL_ECP_DP_BP384R1_ENABLED)
+        case POLARSSL_ECP_DP_BP384R1:
+            return( ecp_group_read_string_gen( grp, 16,
+                        BP384R1_P, BP384R1_A, BP384R1_B,
+                        BP384R1_GX, BP384R1_GY, BP384R1_N ) );
+#endif /* POLARSSL_ECP_DP_BP384R1_ENABLED */
+
+#if defined(POLARSSL_ECP_DP_BP512R1_ENABLED)
+        case POLARSSL_ECP_DP_BP512R1:
+            return( ecp_group_read_string_gen( grp, 16,
+                        BP512R1_P, BP512R1_A, BP512R1_B,
+                        BP512R1_GX, BP512R1_GY, BP512R1_N ) );
+#endif /* POLARSSL_ECP_DP_BP512R1_ENABLED */
+
+        default:
+            ecp_group_free( grp );
+            return( POLARSSL_ERR_ECP_FEATURE_UNAVAILABLE );
+    }
+}
+
+#if defined(POLARSSL_ECP_NIST_OPTIM)
+/*
+ * Fast reduction modulo the primes used by the NIST curves.
+ *
+ * These functions are critical for speed, but not needed for correct
+ * operations. So, we make the choice to heavily rely on the internals of our
+ * bignum library, which creates a tight coupling between these functions and
+ * our MPI implementation.  However, the coupling between the ECP module and
+ * MPI remains loose, since these functions can be deactivated at will.
+ */
+
+#if defined(POLARSSL_ECP_DP_SECP192R1_ENABLED)
+/*
+ * Compared to the way things are presented in FIPS 186-3 D.2,
+ * we proceed in columns, from right (least significant chunk) to left,
+ * adding chunks to N in place, and keeping a carry for the next chunk.
+ * This avoids moving things around in memory, and uselessly adding zeros,
+ * compared to the more straightforward, line-oriented approach.
+ *
+ * For this prime we need to handle data in chunks of 64 bits.
+ * Since this is always a multiple of our basic t_uint, we can
+ * use a t_uint * to designate such a chunk, and small loops to handle it.
+ */
+
+/* Add 64-bit chunks (dst += src) and update carry */
+static inline void add64( t_uint *dst, t_uint *src, t_uint *carry )
+{
+    unsigned char i;
+    t_uint c = 0;
+    for( i = 0; i < 8 / sizeof( t_uint ); i++, dst++, src++ )
+    {
+        *dst += c;      c  = ( *dst < c );
+        *dst += *src;   c += ( *dst < *src );
+    }
+    *carry += c;
+}
+
+/* Add carry to a 64-bit chunk and update carry */
+static inline void carry64( t_uint *dst, t_uint *carry )
+{
+    unsigned char i;
+    for( i = 0; i < 8 / sizeof( t_uint ); i++, dst++ )
+    {
+        *dst += *carry;
+        *carry  = ( *dst < *carry );
+    }
+}
+
+#define WIDTH       8 / sizeof( t_uint )
+#define A( i )      N->p + i * WIDTH
+#define ADD( i )    add64( p, A( i ), &c )
+#define NEXT        p += WIDTH; carry64( p, &c )
+#define LAST        p += WIDTH; *p = c; while( ++p < end ) *p = 0
+
+/*
+ * Fast quasi-reduction modulo p192 (FIPS 186-3 D.2.1)
+ */
+int ecp_mod_p192( mpi *N )
+{
+    int ret;
+    t_uint c = 0;
+    t_uint *p, *end;
+
+    /* Make sure we have enough blocks so that A(5) is legal */
+    MPI_CHK( mpi_grow( N, 6 * WIDTH ) );
+
+    p = N->p;
+    end = p + N->n;
+
+    ADD( 3 ); ADD( 5 );             NEXT; // A0 += A3 + A5
+    ADD( 3 ); ADD( 4 ); ADD( 5 );   NEXT; // A1 += A3 + A4 + A5
+    ADD( 4 ); ADD( 5 );             LAST; // A2 += A4 + A5
+
+cleanup:
+    return( ret );
+}
+
+#undef WIDTH
+#undef A
+#undef ADD
+#undef NEXT
+#undef LAST
+#endif /* POLARSSL_ECP_DP_SECP192R1_ENABLED */
+
+#if defined(POLARSSL_ECP_DP_SECP224R1_ENABLED) ||   \
+    defined(POLARSSL_ECP_DP_SECP256R1_ENABLED) ||   \
+    defined(POLARSSL_ECP_DP_SECP384R1_ENABLED)
+/*
+ * The reader is advised to first understand ecp_mod_p192() since the same
+ * general structure is used here, but with additional complications:
+ * (1) chunks of 32 bits, and (2) subtractions.
+ */
+
+/*
+ * For these primes, we need to handle data in chunks of 32 bits.
+ * This makes it more complicated if we use 64 bits limbs in MPI,
+ * which prevents us from using a uniform access method as for p192.
+ *
+ * So, we define a mini abstraction layer to access 32 bit chunks,
+ * load them in 'cur' for work, and store them back from 'cur' when done.
+ *
+ * While at it, also define the size of N in terms of 32-bit chunks.
+ */
+#define LOAD32      cur = A( i );
+
+#if defined(POLARSSL_HAVE_INT8)     /* 8 bit */
+
+#define MAX32       N->n / 4
+#define A( j )      (uint32_t)( N->p[4*j+0]       ) |  \
+                              ( N->p[4*j+1] << 8  ) |  \
+                              ( N->p[4*j+2] << 16 ) |  \
+                              ( N->p[4*j+3] << 24 )
+#define STORE32     N->p[4*i+0] = (t_uint)( cur       );   \
+                    N->p[4*i+1] = (t_uint)( cur >> 8  );   \
+                    N->p[4*i+2] = (t_uint)( cur >> 16 );   \
+                    N->p[4*i+3] = (t_uint)( cur >> 24 );
+
+#elif defined(POLARSSL_HAVE_INT16)  /* 16 bit */
+
+#define MAX32       N->n / 2
+#define A( j )      (uint32_t)( N->p[2*j] ) | ( N->p[2*j+1] << 16 )
+#define STORE32     N->p[2*i+0] = (t_uint)( cur       );  \
+                    N->p[2*i+1] = (t_uint)( cur >> 16 );
+
+#elif defined(POLARSSL_HAVE_INT32)  /* 32 bit */
+
+#define MAX32       N->n
+#define A( j )      N->p[j]
+#define STORE32     N->p[i] = cur;
+
+#else                               /* 64-bit */
+
+#define MAX32       N->n * 2
+#define A( j ) j % 2 ? (uint32_t)( N->p[j/2] >> 32 ) : (uint32_t)( N->p[j/2] )
+#define STORE32                                   \
+    if( i % 2 ) {                                 \
+        N->p[i/2] &= 0x00000000FFFFFFFF;          \
+        N->p[i/2] |= ((t_uint) cur) << 32;        \
+    } else {                                      \
+        N->p[i/2] &= 0xFFFFFFFF00000000;          \
+        N->p[i/2] |= (t_uint) cur;                \
+    }
+
+#endif /* sizeof( t_uint ) */
+
+/*
+ * Helpers for addition and subtraction of chunks, with signed carry.
+ */
+static inline void add32( uint32_t *dst, uint32_t src, signed char *carry )
+{
+    *dst += src;
+    *carry += ( *dst < src );
+}
+
+static inline void sub32( uint32_t *dst, uint32_t src, signed char *carry )
+{
+    *carry -= ( *dst < src );
+    *dst -= src;
+}
+
+#define ADD( j )    add32( &cur, A( j ), &c );
+#define SUB( j )    sub32( &cur, A( j ), &c );
+
+/*
+ * Helpers for the main 'loop'
+ * (see fix_negative for the motivation of C)
+ */
+#define INIT( b )                                           \
+    int ret;                                                \
+    signed char c = 0, cc;                                  \
+    uint32_t cur;                                           \
+    size_t i = 0, bits = b;                                 \
+    mpi C;                                                  \
+    t_uint Cp[ b / 8 / sizeof( t_uint) + 1 ];               \
+                                                            \
+    C.s = 1;                                                \
+    C.n = b / 8 / sizeof( t_uint) + 1;                      \
+    C.p = Cp;                                               \
+    memset( Cp, 0, C.n * sizeof( t_uint ) );                \
+                                                            \
+    MPI_CHK( mpi_grow( N, b * 2 / 8 / sizeof( t_uint ) ) ); \
+    LOAD32;
+
+#define NEXT                    \
+    STORE32; i++; LOAD32;       \
+    cc = c; c = 0;              \
+    if( cc < 0 )                \
+        sub32( &cur, -cc, &c ); \
+    else                        \
+        add32( &cur, cc, &c );  \
+
+#define LAST                                    \
+    STORE32; i++;                               \
+    cur = c > 0 ? c : 0; STORE32;               \
+    cur = 0; while( ++i < MAX32 ) { STORE32; }  \
+    if( c < 0 ) fix_negative( N, c, &C, bits );
+
+/*
+ * If the result is negative, we get it in the form
+ * c * 2^(bits + 32) + N, with c negative and N positive shorter than 'bits'
+ */
+static inline int fix_negative( mpi *N, signed char c, mpi *C, size_t bits )
+{
+    int ret;
+
+    /* C = - c * 2^(bits + 32) */
+#if !defined(POLARSSL_HAVE_INT64)
+    ((void) bits);
+#else
+    if( bits == 224 )
+        C->p[ C->n - 1 ] = ((t_uint) -c) << 32;
+    else
+#endif
+        C->p[ C->n - 1 ] = (t_uint) -c;
+
+    /* N = - ( C - N ) */
+    MPI_CHK( mpi_sub_abs( N, C, N ) );
+    N->s = -1;
+
+cleanup:
+
+    return( ret );
+}
+
+#if defined(POLARSSL_ECP_DP_SECP224R1_ENABLED)
+/*
+ * Fast quasi-reduction modulo p224 (FIPS 186-3 D.2.2)
+ */
+int ecp_mod_p224( mpi *N )
+{
+    INIT( 224 );
+
+    SUB(  7 ); SUB( 11 );               NEXT; // A0 += -A7 - A11
+    SUB(  8 ); SUB( 12 );               NEXT; // A1 += -A8 - A12
+    SUB(  9 ); SUB( 13 );               NEXT; // A2 += -A9 - A13
+    SUB( 10 ); ADD(  7 ); ADD( 11 );    NEXT; // A3 += -A10 + A7 + A11
+    SUB( 11 ); ADD(  8 ); ADD( 12 );    NEXT; // A4 += -A11 + A8 + A12
+    SUB( 12 ); ADD(  9 ); ADD( 13 );    NEXT; // A5 += -A12 + A9 + A13
+    SUB( 13 ); ADD( 10 );               LAST; // A6 += -A13 + A10
+
+cleanup:
+    return( ret );
+}
+#endif /* POLARSSL_ECP_DP_SECP224R1_ENABLED */
+
+#if defined(POLARSSL_ECP_DP_SECP256R1_ENABLED)
+/*
+ * Fast quasi-reduction modulo p256 (FIPS 186-3 D.2.3)
+ */
+int ecp_mod_p256( mpi *N )
+{
+    INIT( 256 );
+
+    ADD(  8 ); ADD(  9 );
+    SUB( 11 ); SUB( 12 ); SUB( 13 ); SUB( 14 );             NEXT; // A0
+
+    ADD(  9 ); ADD( 10 );
+    SUB( 12 ); SUB( 13 ); SUB( 14 ); SUB( 15 );             NEXT; // A1
+
+    ADD( 10 ); ADD( 11 );
+    SUB( 13 ); SUB( 14 ); SUB( 15 );                        NEXT; // A2
+
+    ADD( 11 ); ADD( 11 ); ADD( 12 ); ADD( 12 ); ADD( 13 );
+    SUB( 15 ); SUB(  8 ); SUB(  9 );                        NEXT; // A3
+
+    ADD( 12 ); ADD( 12 ); ADD( 13 ); ADD( 13 ); ADD( 14 );
+    SUB(  9 ); SUB( 10 );                                   NEXT; // A4
+
+    ADD( 13 ); ADD( 13 ); ADD( 14 ); ADD( 14 ); ADD( 15 );
+    SUB( 10 ); SUB( 11 );                                   NEXT; // A5
+
+    ADD( 14 ); ADD( 14 ); ADD( 15 ); ADD( 15 ); ADD( 14 ); ADD( 13 );
+    SUB(  8 ); SUB(  9 );                                   NEXT; // A6
+
+    ADD( 15 ); ADD( 15 ); ADD( 15 ); ADD( 8 );
+    SUB( 10 ); SUB( 11 ); SUB( 12 ); SUB( 13 );             LAST; // A7
+
+cleanup:
+    return( ret );
+}
+#endif /* POLARSSL_ECP_DP_SECP256R1_ENABLED */
+
+#if defined(POLARSSL_ECP_DP_SECP384R1_ENABLED)
+/*
+ * Fast quasi-reduction modulo p384 (FIPS 186-3 D.2.4)
+ */
+int ecp_mod_p384( mpi *N )
+{
+    INIT( 384 );
+
+    ADD( 12 ); ADD( 21 ); ADD( 20 );
+    SUB( 23 );                                              NEXT; // A0
+
+    ADD( 13 ); ADD( 22 ); ADD( 23 );
+    SUB( 12 ); SUB( 20 );                                   NEXT; // A2
+
+    ADD( 14 ); ADD( 23 );
+    SUB( 13 ); SUB( 21 );                                   NEXT; // A2
+
+    ADD( 15 ); ADD( 12 ); ADD( 20 ); ADD( 21 );
+    SUB( 14 ); SUB( 22 ); SUB( 23 );                        NEXT; // A3
+
+    ADD( 21 ); ADD( 21 ); ADD( 16 ); ADD( 13 ); ADD( 12 ); ADD( 20 ); ADD( 22 );
+    SUB( 15 ); SUB( 23 ); SUB( 23 );                        NEXT; // A4
+
+    ADD( 22 ); ADD( 22 ); ADD( 17 ); ADD( 14 ); ADD( 13 ); ADD( 21 ); ADD( 23 );
+    SUB( 16 );                                              NEXT; // A5
+
+    ADD( 23 ); ADD( 23 ); ADD( 18 ); ADD( 15 ); ADD( 14 ); ADD( 22 );
+    SUB( 17 );                                              NEXT; // A6
+
+    ADD( 19 ); ADD( 16 ); ADD( 15 ); ADD( 23 );
+    SUB( 18 );                                              NEXT; // A7
+
+    ADD( 20 ); ADD( 17 ); ADD( 16 );
+    SUB( 19 );                                              NEXT; // A8
+
+    ADD( 21 ); ADD( 18 ); ADD( 17 );
+    SUB( 20 );                                              NEXT; // A9
+
+    ADD( 22 ); ADD( 19 ); ADD( 18 );
+    SUB( 21 );                                              NEXT; // A10
+
+    ADD( 23 ); ADD( 20 ); ADD( 19 );
+    SUB( 22 );                                              LAST; // A11
+
+cleanup:
+    return( ret );
+}
+#endif /* POLARSSL_ECP_DP_SECP384R1_ENABLED */
+
+#undef A
+#undef LOAD32
+#undef STORE32
+#undef MAX32
+#undef INIT
+#undef NEXT
+#undef LAST
+
+#endif /* POLARSSL_ECP_DP_SECP224R1_ENABLED ||
+          POLARSSL_ECP_DP_SECP256R1_ENABLED ||
+          POLARSSL_ECP_DP_SECP384R1_ENABLED */
+
+#if defined(POLARSSL_ECP_DP_SECP521R1_ENABLED)
+/*
+ * Here we have an actual Mersenne prime, so things are more straightforward.
+ * However, chunks are aligned on a 'weird' boundary (521 bits).
+ */
+
+/* Size of p521 in terms of t_uint */
+#define P521_WIDTH      ( 521 / 8 / sizeof( t_uint ) + 1 )
+
+/* Bits to keep in the most significant t_uint */
+#if defined(POLARSSL_HAVE_INT8)
+#define P521_MASK       0x01
+#else
+#define P521_MASK       0x01FF
+#endif
+
+/*
+ * Fast quasi-reduction modulo p521 (FIPS 186-3 D.2.5)
+ * Write N as A1 + 2^521 A0, return A0 + A1
+ */
+int ecp_mod_p521( mpi *N )
+{
+    int ret;
+    size_t i;
+    mpi M;
+    t_uint Mp[P521_WIDTH + 1];
+    /* Worst case for the size of M is when t_uint is 16 bits:
+     * we need to hold bits 513 to 1056, which is 34 limbs, that is
+     * P521_WIDTH + 1. Otherwise P521_WIDTH is enough. */
+
+    if( N->n < P521_WIDTH )
+        return( 0 );
+
+    /* M = A1 */
+    M.s = 1;
+    M.n = N->n - ( P521_WIDTH - 1 );
+    if( M.n > P521_WIDTH + 1 )
+        M.n = P521_WIDTH + 1;
+    M.p = Mp;
+    memcpy( Mp, N->p + P521_WIDTH - 1, M.n * sizeof( t_uint ) );
+    MPI_CHK( mpi_shift_r( &M, 521 % ( 8 * sizeof( t_uint ) ) ) );
+
+    /* N = A0 */
+    N->p[P521_WIDTH - 1] &= P521_MASK;
+    for( i = P521_WIDTH; i < N->n; i++ )
+        N->p[i] = 0;
+
+    /* N = A0 + A1 */
+    MPI_CHK( mpi_add_abs( N, N, &M ) );
+
+cleanup:
+    return( ret );
+}
+
+#undef P521_WIDTH
+#undef P521_MASK
+#endif /* POLARSSL_ECP_DP_SECP521R1_ENABLED */
+
+#endif /* POLARSSL_ECP_NIST_OPTIM */
+
+#endif