ECC support for curve y^2 = x^3 + a*x + b (`a` used to be fixed to -3)

23 files changed, 54 insertions, 41 deletions

diff --git a/src/ltc/headers/tomcrypt_pk.h b/src/ltc/headers/tomcrypt_pk.h
index c6540ca3..85804343 100644
--- a/src/ltc/headers/tomcrypt_pk.h
+++ b/src/ltc/headers/tomcrypt_pk.h
@@ -219,6 +219,9 @@ typedef struct {
    /** The prime that defines the field the curve is in (encoded in hex) */
    char *prime;
 
+   /** The fields A param (hex) */
+   char *A;
+
    /** The fields B param (hex) */
    char *B;
 
diff --git a/src/ltc/pk/ecc/ecc.c b/src/ltc/pk/ecc/ecc.c
index 56ed526e..218eda0a 100644
--- a/src/ltc/pk/ecc/ecc.c
+++ b/src/ltc/pk/ecc/ecc.c
@@ -9,7 +9,7 @@
  * Tom St Denis, tomstdenis@gmail.com, http://libtom.org
  */
 
-/* Implements ECC over Z/pZ for curve y^2 = x^3 - 3x + b
+/* Implements ECC over Z/pZ for curve y^2 = x^3 + a*x + b
  *
  * All curves taken from NIST recommendation paper of July 1999
  * Available at http://csrc.nist.gov/cryptval/dss.htm
@@ -30,6 +30,7 @@ const ltc_ecc_set_type ltc_ecc_sets[] = {
         14,
         "SECP112R1",
         "DB7C2ABF62E35E668076BEAD208B",
+        "DB7C2ABF62E35E668076BEAD2088",
         "659EF8BA043916EEDE8911702B22",
         "DB7C2ABF62E35E7628DFAC6561C5",
         "09487239995A5EE76B55F9C2F098",
@@ -41,6 +42,7 @@ const ltc_ecc_set_type ltc_ecc_sets[] = {
         16,
         "SECP128R1",
         "FFFFFFFDFFFFFFFFFFFFFFFFFFFFFFFF",
+        "FFFFFFFDFFFFFFFFFFFFFFFFFFFFFFFC",
         "E87579C11079F43DD824993C2CEE5ED3",
         "FFFFFFFE0000000075A30D1B9038A115",
         "161FF7528B899B2D0C28607CA52C5B86",
@@ -52,6 +54,7 @@ const ltc_ecc_set_type ltc_ecc_sets[] = {
         20,
         "SECP160R1",
         "FFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFF7FFFFFFF",
+        "FFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFF7FFFFFFC",
         "1C97BEFC54BD7A8B65ACF89F81D4D4ADC565FA45",
         "0100000000000000000001F4C8F927AED3CA752257",
         "4A96B5688EF573284664698968C38BB913CBFC82",
@@ -63,6 +66,7 @@ const ltc_ecc_set_type ltc_ecc_sets[] = {
         24,
         "ECC-192",
         "FFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFEFFFFFFFFFFFFFFFF",
+        "FFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFEFFFFFFFFFFFFFFFC",
         "64210519E59C80E70FA7E9AB72243049FEB8DEECC146B9B1",
         "FFFFFFFFFFFFFFFFFFFFFFFF99DEF836146BC9B1B4D22831",
         "188DA80EB03090F67CBF20EB43A18800F4FF0AFD82FF1012",
@@ -74,6 +78,7 @@ const ltc_ecc_set_type ltc_ecc_sets[] = {
         28,
         "ECC-224",
         "FFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFF000000000000000000000001",
+        "FFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFEFFFFFFFFFFFFFFFFFFFFFFFE",
         "B4050A850C04B3ABF54132565044B0B7D7BFD8BA270B39432355FFB4",
         "FFFFFFFFFFFFFFFFFFFFFFFFFFFF16A2E0B8F03E13DD29455C5C2A3D",
         "B70E0CBD6BB4BF7F321390B94A03C1D356C21122343280D6115C1D21",
@@ -85,6 +90,7 @@ const ltc_ecc_set_type ltc_ecc_sets[] = {
         32,
         "ECC-256",
         "FFFFFFFF00000001000000000000000000000000FFFFFFFFFFFFFFFFFFFFFFFF",
+        "FFFFFFFF00000001000000000000000000000000FFFFFFFFFFFFFFFFFFFFFFFC",
         "5AC635D8AA3A93E7B3EBBD55769886BC651D06B0CC53B0F63BCE3C3E27D2604B",
         "FFFFFFFF00000000FFFFFFFFFFFFFFFFBCE6FAADA7179E84F3B9CAC2FC632551",
         "6B17D1F2E12C4247F8BCE6E563A440F277037D812DEB33A0F4A13945D898C296",
@@ -96,6 +102,7 @@ const ltc_ecc_set_type ltc_ecc_sets[] = {
         48,
         "ECC-384",
         "FFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFEFFFFFFFF0000000000000000FFFFFFFF",
+        "FFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFEFFFFFFFF0000000000000000FFFFFFFC",
         "B3312FA7E23EE7E4988E056BE3F82D19181D9C6EFE8141120314088F5013875AC656398D8A2ED19D2A85C8EDD3EC2AEF",
         "FFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFC7634D81F4372DDF581A0DB248B0A77AECEC196ACCC52973",
         "AA87CA22BE8B05378EB1C71EF320AD746E1D3B628BA79B9859F741E082542A385502F25DBF55296C3A545E3872760AB7",
@@ -107,6 +114,7 @@ const ltc_ecc_set_type ltc_ecc_sets[] = {
         66,
         "ECC-521",
         "1FFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFF",
+        "1FFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFC",
         "51953EB9618E1C9A1F929A21A0B68540EEA2DA725B99B315F3B8B489918EF109E156193951EC7E937B1652C0BD3BB1BF073573DF883D2C34F1EF451FD46B503F00",
         "1FFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFA51868783BF2F966B7FCC0148F709A5D03BB5C9B8899C47AEBB6FB71E91386409",
         "C6858E06B70404E9CD9E3ECB662395B4429C648139053FB521F828AF606B4D3DBAA14B5E77EFE75928FE1DC127A2FFA8DE3348B3C1856A429BF97E7E31C2E5BD66",
diff --git a/src/ltc/pk/ecc/ecc_ansi_x963_export.c b/src/ltc/pk/ecc/ecc_ansi_x963_export.c
index 09dae070..a3ab2435 100644
--- a/src/ltc/pk/ecc/ecc_ansi_x963_export.c
+++ b/src/ltc/pk/ecc/ecc_ansi_x963_export.c
@@ -9,7 +9,7 @@
  * Tom St Denis, tomstdenis@gmail.com, http://libtom.org
  */
 
-/* Implements ECC over Z/pZ for curve y^2 = x^3 - 3x + b
+/* Implements ECC over Z/pZ for curve y^2 = x^3 + a*x + b
  *
  * All curves taken from NIST recommendation paper of July 1999
  * Available at http://csrc.nist.gov/cryptval/dss.htm
diff --git a/src/ltc/pk/ecc/ecc_ansi_x963_import.c b/src/ltc/pk/ecc/ecc_ansi_x963_import.c
index ec34245f..b16bae54 100644
--- a/src/ltc/pk/ecc/ecc_ansi_x963_import.c
+++ b/src/ltc/pk/ecc/ecc_ansi_x963_import.c
@@ -9,7 +9,7 @@
  * Tom St Denis, tomstdenis@gmail.com, http://libtom.org
  */
 
-/* Implements ECC over Z/pZ for curve y^2 = x^3 - 3x + b
+/* Implements ECC over Z/pZ for curve y^2 = x^3 + a*x + b
  *
  * All curves taken from NIST recommendation paper of July 1999
  * Available at http://csrc.nist.gov/cryptval/dss.htm
diff --git a/src/ltc/pk/ecc/ecc_decrypt_key.c b/src/ltc/pk/ecc/ecc_decrypt_key.c
index 6e09e616..fb5e041f 100644
--- a/src/ltc/pk/ecc/ecc_decrypt_key.c
+++ b/src/ltc/pk/ecc/ecc_decrypt_key.c
@@ -9,7 +9,7 @@
  * Tom St Denis, tomstdenis@gmail.com, http://libtom.org
  */
 
-/* Implements ECC over Z/pZ for curve y^2 = x^3 - 3x + b
+/* Implements ECC over Z/pZ for curve y^2 = x^3 + a*x + b
  *
  * All curves taken from NIST recommendation paper of July 1999
  * Available at http://csrc.nist.gov/cryptval/dss.htm
diff --git a/src/ltc/pk/ecc/ecc_encrypt_key.c b/src/ltc/pk/ecc/ecc_encrypt_key.c
index a74d50f2..4696faed 100644
--- a/src/ltc/pk/ecc/ecc_encrypt_key.c
+++ b/src/ltc/pk/ecc/ecc_encrypt_key.c
@@ -9,7 +9,7 @@
  * Tom St Denis, tomstdenis@gmail.com, http://libtom.org
  */
 
-/* Implements ECC over Z/pZ for curve y^2 = x^3 - 3x + b
+/* Implements ECC over Z/pZ for curve y^2 = x^3 + a*x + b
  *
  * All curves taken from NIST recommendation paper of July 1999
  * Available at http://csrc.nist.gov/cryptval/dss.htm
diff --git a/src/ltc/pk/ecc/ecc_export.c b/src/ltc/pk/ecc/ecc_export.c
index b6c34853..7ea029b4 100644
--- a/src/ltc/pk/ecc/ecc_export.c
+++ b/src/ltc/pk/ecc/ecc_export.c
@@ -9,7 +9,7 @@
  * Tom St Denis, tomstdenis@gmail.com, http://libtom.org
  */
 
-/* Implements ECC over Z/pZ for curve y^2 = x^3 - 3x + b
+/* Implements ECC over Z/pZ for curve y^2 = x^3 + a*x + b
  *
  * All curves taken from NIST recommendation paper of July 1999
  * Available at http://csrc.nist.gov/cryptval/dss.htm
diff --git a/src/ltc/pk/ecc/ecc_free.c b/src/ltc/pk/ecc/ecc_free.c
index c9e5d6cd..f1cc5691 100644
--- a/src/ltc/pk/ecc/ecc_free.c
+++ b/src/ltc/pk/ecc/ecc_free.c
@@ -9,7 +9,7 @@
  * Tom St Denis, tomstdenis@gmail.com, http://libtom.org
  */
 
-/* Implements ECC over Z/pZ for curve y^2 = x^3 - 3x + b
+/* Implements ECC over Z/pZ for curve y^2 = x^3 + a*x + b
  *
  * All curves taken from NIST recommendation paper of July 1999
  * Available at http://csrc.nist.gov/cryptval/dss.htm
diff --git a/src/ltc/pk/ecc/ecc_get_size.c b/src/ltc/pk/ecc/ecc_get_size.c
index a824aa49..15263926 100644
--- a/src/ltc/pk/ecc/ecc_get_size.c
+++ b/src/ltc/pk/ecc/ecc_get_size.c
@@ -9,7 +9,7 @@
  * Tom St Denis, tomstdenis@gmail.com, http://libtom.org
  */
 
-/* Implements ECC over Z/pZ for curve y^2 = x^3 - 3x + b
+/* Implements ECC over Z/pZ for curve y^2 = x^3 + a*x + b
  *
  * All curves taken from NIST recommendation paper of July 1999
  * Available at http://csrc.nist.gov/cryptval/dss.htm
diff --git a/src/ltc/pk/ecc/ecc_import.c b/src/ltc/pk/ecc/ecc_import.c
index efb1d706..a8babf59 100644
--- a/src/ltc/pk/ecc/ecc_import.c
+++ b/src/ltc/pk/ecc/ecc_import.c
@@ -9,7 +9,7 @@
  * Tom St Denis, tomstdenis@gmail.com, http://libtom.org
  */
 
-/* Implements ECC over Z/pZ for curve y^2 = x^3 - 3x + b
+/* Implements ECC over Z/pZ for curve y^2 = x^3 + a*x + b
  *
  * All curves taken from NIST recommendation paper of July 1999
  * Available at http://csrc.nist.gov/cryptval/dss.htm
@@ -19,53 +19,55 @@
 /**
   @file ecc_import.c
   ECC Crypto, Tom St Denis
-*/  
+*/
 
 #ifdef LTC_MECC
 
 static int is_point(ecc_key *key)
 {
-   void *prime, *b, *t1, *t2;
+   void *prime, *a, *b, *t1, *t2;
    int err;
-   
-   if ((err = mp_init_multi(&prime, &b, &t1, &t2, NULL)) != CRYPT_OK) {
+
+   if ((err = mp_init_multi(&prime, &a, &b, &t1, &t2, NULL)) != CRYPT_OK) {
       return err;
    }
-   
-   /* load prime and b */
+
+   /* load prime, a and b */
    if ((err = mp_read_radix(prime, key->dp->prime, 16)) != CRYPT_OK)                          { goto error; }
    if ((err = mp_read_radix(b, key->dp->B, 16)) != CRYPT_OK)                                  { goto error; }
-   
+   if ((err = mp_read_radix(a, key->dp->A, 16)) != CRYPT_OK)                                  { goto error; }
+
    /* compute y^2 */
    if ((err = mp_sqr(key->pubkey.y, t1)) != CRYPT_OK)                                         { goto error; }
-   
+
    /* compute x^3 */
    if ((err = mp_sqr(key->pubkey.x, t2)) != CRYPT_OK)                                         { goto error; }
    if ((err = mp_mod(t2, prime, t2)) != CRYPT_OK)                                             { goto error; }
    if ((err = mp_mul(key->pubkey.x, t2, t2)) != CRYPT_OK)                                     { goto error; }
-   
+
    /* compute y^2 - x^3 */
    if ((err = mp_sub(t1, t2, t1)) != CRYPT_OK)                                                { goto error; }
-   
-   /* compute y^2 - x^3 + 3x */
-   if ((err = mp_add(t1, key->pubkey.x, t1)) != CRYPT_OK)                                     { goto error; }
-   if ((err = mp_add(t1, key->pubkey.x, t1)) != CRYPT_OK)                                     { goto error; }
-   if ((err = mp_add(t1, key->pubkey.x, t1)) != CRYPT_OK)                                     { goto error; }
-   if ((err = mp_mod(t1, prime, t1)) != CRYPT_OK)                                             { goto error; }
+
+   /* compute y^2 - x^3 - a*x */
+   if ((err = mp_submod(prime, a, prime, t2)) != CRYPT_OK)                                    { goto error; }
+   if ((err = mp_mulmod(t2, key->pubkey.x, prime, t2)) != CRYPT_OK)                           { goto error; }
+   if ((err = mp_addmod(t1, t2, prime, t1)) != CRYPT_OK)                                      { goto error; }
+
+   /* adjust range (0, prime) */
    while (mp_cmp_d(t1, 0) == LTC_MP_LT) {
       if ((err = mp_add(t1, prime, t1)) != CRYPT_OK)                                          { goto error; }
    }
    while (mp_cmp(t1, prime) != LTC_MP_LT) {
       if ((err = mp_sub(t1, prime, t1)) != CRYPT_OK)                                          { goto error; }
    }
-   
+
    /* compare to b */
    if (mp_cmp(t1, b) != LTC_MP_EQ) {
       err = CRYPT_INVALID_PACKET;
    } else {
       err = CRYPT_OK;
    }
-   
+
 error:
    mp_clear_multi(prime, b, t1, t2, NULL);
    return err;
@@ -107,7 +109,7 @@ int ecc_import_ex(const unsigned char *in, unsigned long inlen, ecc_key *key, co
    }
 
    /* find out what type of key it is */
-   if ((err = der_decode_sequence_multi(in, inlen, 
+   if ((err = der_decode_sequence_multi(in, inlen,
                                   LTC_ASN1_BIT_STRING, 1UL, &flags,
                                   LTC_ASN1_EOL,        0UL, NULL)) != CRYPT_OK) {
       goto done;
@@ -153,7 +155,7 @@ int ecc_import_ex(const unsigned char *in, unsigned long inlen, ecc_key *key, co
    }
    /* set z */
    if ((err = mp_set(key->pubkey.z, 1)) != CRYPT_OK) { goto done; }
-   
+
    /* is it a point on the curve?  */
    if ((err = is_point(key)) != CRYPT_OK) {
       goto done;
diff --git a/src/ltc/pk/ecc/ecc_make_key.c b/src/ltc/pk/ecc/ecc_make_key.c
index 9bbeb44d..6674bb66 100644
--- a/src/ltc/pk/ecc/ecc_make_key.c
+++ b/src/ltc/pk/ecc/ecc_make_key.c
@@ -9,7 +9,7 @@
  * Tom St Denis, tomstdenis@gmail.com, http://libtom.org
  */
 
-/* Implements ECC over Z/pZ for curve y^2 = x^3 - 3x + b
+/* Implements ECC over Z/pZ for curve y^2 = x^3 + a*x + b
  *
  * All curves taken from NIST recommendation paper of July 1999
  * Available at http://csrc.nist.gov/cryptval/dss.htm
diff --git a/src/ltc/pk/ecc/ecc_shared_secret.c b/src/ltc/pk/ecc/ecc_shared_secret.c
index 5aece5e3..dbb1e8f2 100644
--- a/src/ltc/pk/ecc/ecc_shared_secret.c
+++ b/src/ltc/pk/ecc/ecc_shared_secret.c
@@ -9,7 +9,7 @@
  * Tom St Denis, tomstdenis@gmail.com, http://libtom.org
  */
 
-/* Implements ECC over Z/pZ for curve y^2 = x^3 - 3x + b
+/* Implements ECC over Z/pZ for curve y^2 = x^3 + a*x + b
  *
  * All curves taken from NIST recommendation paper of July 1999
  * Available at http://csrc.nist.gov/cryptval/dss.htm
diff --git a/src/ltc/pk/ecc/ecc_sign_hash.c b/src/ltc/pk/ecc/ecc_sign_hash.c
index a01dfad3..fb7a0890 100644
--- a/src/ltc/pk/ecc/ecc_sign_hash.c
+++ b/src/ltc/pk/ecc/ecc_sign_hash.c
@@ -9,7 +9,7 @@
  * Tom St Denis, tomstdenis@gmail.com, http://libtom.org
  */
 
-/* Implements ECC over Z/pZ for curve y^2 = x^3 - 3x + b
+/* Implements ECC over Z/pZ for curve y^2 = x^3 + a*x + b
  *
  * All curves taken from NIST recommendation paper of July 1999
  * Available at http://csrc.nist.gov/cryptval/dss.htm
diff --git a/src/ltc/pk/ecc/ecc_sizes.c b/src/ltc/pk/ecc/ecc_sizes.c
index b02a9f9e..c13ca67c 100644
--- a/src/ltc/pk/ecc/ecc_sizes.c
+++ b/src/ltc/pk/ecc/ecc_sizes.c
@@ -9,7 +9,7 @@
  * Tom St Denis, tomstdenis@gmail.com, http://libtom.org
  */
 
-/* Implements ECC over Z/pZ for curve y^2 = x^3 - 3x + b
+/* Implements ECC over Z/pZ for curve y^2 = x^3 + a*x + b
  *
  * All curves taken from NIST recommendation paper of July 1999
  * Available at http://csrc.nist.gov/cryptval/dss.htm
diff --git a/src/ltc/pk/ecc/ecc_verify_hash.c b/src/ltc/pk/ecc/ecc_verify_hash.c
index ba7bba55..c23b1333 100644
--- a/src/ltc/pk/ecc/ecc_verify_hash.c
+++ b/src/ltc/pk/ecc/ecc_verify_hash.c
@@ -9,7 +9,7 @@
  * Tom St Denis, tomstdenis@gmail.com, http://libtom.org
  */
 
-/* Implements ECC over Z/pZ for curve y^2 = x^3 - 3x + b
+/* Implements ECC over Z/pZ for curve y^2 = x^3 + a*x + b
  *
  * All curves taken from NIST recommendation paper of July 1999
  * Available at http://csrc.nist.gov/cryptval/dss.htm
diff --git a/src/ltc/pk/ecc/ltc_ecc_is_valid_idx.c b/src/ltc/pk/ecc/ltc_ecc_is_valid_idx.c
index 4a020688..ffef9674 100644
--- a/src/ltc/pk/ecc/ltc_ecc_is_valid_idx.c
+++ b/src/ltc/pk/ecc/ltc_ecc_is_valid_idx.c
@@ -9,7 +9,7 @@
  * Tom St Denis, tomstdenis@gmail.com, http://libtom.org
  */
 
-/* Implements ECC over Z/pZ for curve y^2 = x^3 - 3x + b
+/* Implements ECC over Z/pZ for curve y^2 = x^3 + a*x + b
  *
  * All curves taken from NIST recommendation paper of July 1999
  * Available at http://csrc.nist.gov/cryptval/dss.htm
diff --git a/src/ltc/pk/ecc/ltc_ecc_map.c b/src/ltc/pk/ecc/ltc_ecc_map.c
index 4f3ec09c..e1c53a68 100644
--- a/src/ltc/pk/ecc/ltc_ecc_map.c
+++ b/src/ltc/pk/ecc/ltc_ecc_map.c
@@ -9,7 +9,7 @@
  * Tom St Denis, tomstdenis@gmail.com, http://libtom.org
  */
 
-/* Implements ECC over Z/pZ for curve y^2 = x^3 - 3x + b
+/* Implements ECC over Z/pZ for curve y^2 = x^3 + a*x + b
  *
  * All curves taken from NIST recommendation paper of July 1999
  * Available at http://csrc.nist.gov/cryptval/dss.htm
diff --git a/src/ltc/pk/ecc/ltc_ecc_mul2add.c b/src/ltc/pk/ecc/ltc_ecc_mul2add.c
index a6d1aab8..e3d5e79a 100644
--- a/src/ltc/pk/ecc/ltc_ecc_mul2add.c
+++ b/src/ltc/pk/ecc/ltc_ecc_mul2add.c
@@ -9,7 +9,7 @@
  * Tom St Denis, tomstdenis@gmail.com, http://libtom.org
  */
 
-/* Implements ECC over Z/pZ for curve y^2 = x^3 - 3x + b
+/* Implements ECC over Z/pZ for curve y^2 = x^3 + a*x + b
  *
  * All curves taken from NIST recommendation paper of July 1999
  * Available at http://csrc.nist.gov/cryptval/dss.htm
diff --git a/src/ltc/pk/ecc/ltc_ecc_mulmod.c b/src/ltc/pk/ecc/ltc_ecc_mulmod.c
index 4b11392e..87b49356 100644
--- a/src/ltc/pk/ecc/ltc_ecc_mulmod.c
+++ b/src/ltc/pk/ecc/ltc_ecc_mulmod.c
@@ -9,7 +9,7 @@
  * Tom St Denis, tomstdenis@gmail.com, http://libtom.org
  */
 
-/* Implements ECC over Z/pZ for curve y^2 = x^3 - 3x + b
+/* Implements ECC over Z/pZ for curve y^2 = x^3 + a*x + b
  *
  * All curves taken from NIST recommendation paper of July 1999
  * Available at http://csrc.nist.gov/cryptval/dss.htm
diff --git a/src/ltc/pk/ecc/ltc_ecc_mulmod_timing.c b/src/ltc/pk/ecc/ltc_ecc_mulmod_timing.c
index 863ed07c..535db5dc 100644
--- a/src/ltc/pk/ecc/ltc_ecc_mulmod_timing.c
+++ b/src/ltc/pk/ecc/ltc_ecc_mulmod_timing.c
@@ -9,7 +9,7 @@
  * Tom St Denis, tomstdenis@gmail.com, http://libtom.org
  */
 
-/* Implements ECC over Z/pZ for curve y^2 = x^3 - 3x + b
+/* Implements ECC over Z/pZ for curve y^2 = x^3 + a*x + b
  *
  * All curves taken from NIST recommendation paper of July 1999
  * Available at http://csrc.nist.gov/cryptval/dss.htm
diff --git a/src/ltc/pk/ecc/ltc_ecc_points.c b/src/ltc/pk/ecc/ltc_ecc_points.c
index 9be9eff7..1f143115 100644
--- a/src/ltc/pk/ecc/ltc_ecc_points.c
+++ b/src/ltc/pk/ecc/ltc_ecc_points.c
@@ -9,7 +9,7 @@
  * Tom St Denis, tomstdenis@gmail.com, http://libtom.org
  */
 
-/* Implements ECC over Z/pZ for curve y^2 = x^3 - 3x + b
+/* Implements ECC over Z/pZ for curve y^2 = x^3 + a*x + b
  *
  * All curves taken from NIST recommendation paper of July 1999
  * Available at http://csrc.nist.gov/cryptval/dss.htm
diff --git a/src/ltc/pk/ecc/ltc_ecc_projective_add_point.c b/src/ltc/pk/ecc/ltc_ecc_projective_add_point.c
index c45a47b5..220860f3 100644
--- a/src/ltc/pk/ecc/ltc_ecc_projective_add_point.c
+++ b/src/ltc/pk/ecc/ltc_ecc_projective_add_point.c
@@ -9,7 +9,7 @@
  * Tom St Denis, tomstdenis@gmail.com, http://libtom.org
  */
 
-/* Implements ECC over Z/pZ for curve y^2 = x^3 - 3x + b
+/* Implements ECC over Z/pZ for curve y^2 = x^3 + a*x + b
  *
  * All curves taken from NIST recommendation paper of July 1999
  * Available at http://csrc.nist.gov/cryptval/dss.htm
diff --git a/src/ltc/pk/ecc/ltc_ecc_projective_dbl_point.c b/src/ltc/pk/ecc/ltc_ecc_projective_dbl_point.c
index ce31ccc2..350150a5 100644
--- a/src/ltc/pk/ecc/ltc_ecc_projective_dbl_point.c
+++ b/src/ltc/pk/ecc/ltc_ecc_projective_dbl_point.c
@@ -9,7 +9,7 @@
  * Tom St Denis, tomstdenis@gmail.com, http://libtom.org
  */
 
-/* Implements ECC over Z/pZ for curve y^2 = x^3 - 3x + b
+/* Implements ECC over Z/pZ for curve y^2 = x^3 + a*x + b
  *
  * All curves taken from NIST recommendation paper of July 1999
  * Available at http://csrc.nist.gov/cryptval/dss.htm