Fix DH_get_nid() so that it does not cache values.

DH_set0_pqg() is now responsible for caching the nid, q and length.

DH with or without named safe prime groups now default to using the maximum private key length (BN_num_bits(q) - 1)
when generating a DH private key. The code is now shared between fips and non fips mode for DH key generation.

The OSSL_PKEY_PARAM_DH_PRIV_LEN parameter can be used during keygen to override the maximum private key length to be
in the range (2 * strength ... bits(q) - 1). Where the strength depends on the length of p.

Added q = (p - 1) / 2 safe prime BIGNUMS so that the code is data driven (To simplify adding new names).
The BIGNUMS were code generated.

Fix error in documented return value for DH_get_nid

Reviewed-by: Richard Levitte <levitte@openssl.org>
(Merged from https://github.com/openssl/openssl/pull/11562)

8 files changed, 510 insertions, 154 deletions

diff --git a/crypto/bn/bn_dh.c b/crypto/bn/bn_dh.c
index 2dfa5a09ca..9ffb6d8d83 100644
--- a/crypto/bn/bn_dh.c
+++ b/crypto/bn/bn_dh.c
@@ -45,9 +45,23 @@ static const BN_ULONG modp_1536_p[] = {
     BN_DEF(0x8A67CC74, 0x29024E08), BN_DEF(0x80DC1CD1, 0xC4C6628B),
     BN_DEF(0x2168C234, 0xC90FDAA2), BN_DEF(0xFFFFFFFF, 0xFFFFFFFF)
 };
+/* q = (p - 1) / 2 */
+static const BN_ULONG modp_1536_q[] = {
+    BN_DEF(0xFFFFFFFF, 0xFFFFFFFF), BN_DEF(0x6511B993, 0x78BA3604),
+    BN_DEF(0x255E4C02, 0xB3861AA7), BN_DEF(0xB84B4B36, 0xCF6A9483),
+    BN_DEF(0x1042A95D, 0x0E3179AB), BN_DEF(0xEE51D6CB, 0xC1B2AE91),
+    BN_DEF(0x7E9267AF, 0x348B1FD4), BN_DEF(0x0E2AE9CD, 0xCC6D241B),
+    BN_DEF(0x50B1DF82, 0xE1003E5C), BN_DEF(0xF6722D9E, 0x24943328),
+    BN_DEF(0xBE258FF3, 0xD74F9208), BN_DEF(0xAD44CFD2, 0xF71C35FD),
+    BN_DEF(0x7A035BF6, 0x85FFAE5B), BN_DEF(0xD31BF6B5, 0x7A262174),
+    BN_DEF(0x312F3F63, 0xF242DABB), BN_DEF(0xB6A8E122, 0xA7F09AB6),
+    BN_DEF(0xF92F8A1B, 0x98158536), BN_DEF(0xE69D218D, 0xF7CA8CD9),
+    BN_DEF(0xC71A026E, 0x28A5043C), BN_DEF(0x1D89CD91, 0x0105DF53),
+    BN_DEF(0x4533E63A, 0x94812704), BN_DEF(0xC06E0E68, 0x62633145),
+    BN_DEF(0x10B4611A, 0xE487ED51), BN_DEF(0xFFFFFFFF, 0x7FFFFFFF)
+};
 # endif /* FIPS_MODE */
 
-
 /*-
  * "2048-bit MODP Group" from RFC3526, Section 3.
  *
@@ -73,6 +87,25 @@ static const BN_ULONG modp_2048_p[] = {
     BN_DEF(0x8A67CC74, 0x29024E08), BN_DEF(0x80DC1CD1, 0xC4C6628B),
     BN_DEF(0x2168C234, 0xC90FDAA2), BN_DEF(0xFFFFFFFF, 0xFFFFFFFF)
 };
+/* q = (p - 1) / 2 */
+static const BN_ULONG modp_2048_q[] = {
+    BN_DEF(0xFFFFFFFF,  0x7FFFFFFF), BN_DEF(0x45565534,  0x0AB9472D),
+    BN_DEF(0x4C7D0288,  0x8AE9130C), BN_DEF(0x754AB572,  0x1CCAA4BE),
+    BN_DEF(0x4AAC0B8C,  0xEF15E5FB), BN_DEF(0x37A62964,  0xDAE2AEF8),
+    BN_DEF(0x7603D147,  0xCD93C1D1), BN_DEF(0x0C074301,  0xF1CF3B96),
+    BN_DEF(0x171B671D,  0x19482F23), BN_DEF(0x650C10BE,  0x78BA3604),
+    BN_DEF(0x255E4C02,  0xB3861AA7), BN_DEF(0xB84B4B36,  0xCF6A9483),
+    BN_DEF(0x1042A95D,  0x0E3179AB), BN_DEF(0xEE51D6CB,  0xC1B2AE91),
+    BN_DEF(0x7E9267AF,  0x348B1FD4), BN_DEF(0x0E2AE9CD,  0xCC6D241B),
+    BN_DEF(0x50B1DF82,  0xE1003E5C), BN_DEF(0xF6722D9E,  0x24943328),
+    BN_DEF(0xBE258FF3,  0xD74F9208), BN_DEF(0xAD44CFD2,  0xF71C35FD),
+    BN_DEF(0x7A035BF6,  0x85FFAE5B), BN_DEF(0xD31BF6B5,  0x7A262174),
+    BN_DEF(0x312F3F63,  0xF242DABB), BN_DEF(0xB6A8E122,  0xA7F09AB6),
+    BN_DEF(0xF92F8A1B,  0x98158536), BN_DEF(0xE69D218D,  0xF7CA8CD9),
+    BN_DEF(0xC71A026E,  0x28A5043C), BN_DEF(0x1D89CD91,  0x0105DF53),
+    BN_DEF(0x4533E63A,  0x94812704), BN_DEF(0xC06E0E68,  0x62633145),
+    BN_DEF(0x10B4611A,  0xE487ED51), BN_DEF(0xFFFFFFFF,  0x7FFFFFFF),
+};
 
 /*-
  * "3072-bit MODP Group" from RFC3526, Section 4.
@@ -107,7 +140,33 @@ static const BN_ULONG modp_3072_p[] = {
     BN_DEF(0x8A67CC74, 0x29024E08), BN_DEF(0x80DC1CD1, 0xC4C6628B),
     BN_DEF(0x2168C234, 0xC90FDAA2), BN_DEF(0xFFFFFFFF, 0xFFFFFFFF)
 };
-
+/* q = (p - 1) / 2 */
+static const BN_ULONG modp_3072_q[] = {
+    BN_DEF(0xFFFFFFFF,  0x7FFFFFFF), BN_DEF(0x549D6965,  0x25C16890),
+    BN_DEF(0x707E8847,  0xA1EDADFE), BN_DEF(0x3A72D598,  0x047127D0),
+    BN_DEF(0x5D6CA371,  0x3B84C460), BN_DEF(0xBD30AEB6,  0x5DF08BAB),
+    BN_DEF(0x0BBD9006,  0x290F958C), BN_DEF(0x9F643532,  0x6C3B0139),
+    BN_DEF(0x6CC50432,  0xF897FD03), BN_DEF(0x0D697735,  0xE771E913),
+    BN_DEF(0x2512B0CE,  0x8F464A70), BN_DEF(0x6D8499EB,  0xD5FAD746),
+    BN_DEF(0xD370F263,  0xD9CB87C2), BN_DEF(0xAE83063E,  0x457538AB),
+    BN_DEF(0x2C6DF785,  0x767DC282), BN_DEF(0xEF8E5D32,  0xD42A90D5),
+    BN_DEF(0x82283D19,  0xD6998B86), BN_DEF(0x45556216,  0x0AB9472D),
+    BN_DEF(0x4C7D0288,  0x8AE9130C), BN_DEF(0x754AB572,  0x1CCAA4BE),
+    BN_DEF(0x4AAC0B8C,  0xEF15E5FB), BN_DEF(0x37A62964,  0xDAE2AEF8),
+    BN_DEF(0x7603D147,  0xCD93C1D1), BN_DEF(0x0C074301,  0xF1CF3B96),
+    BN_DEF(0x171B671D,  0x19482F23), BN_DEF(0x650C10BE,  0x78BA3604),
+    BN_DEF(0x255E4C02,  0xB3861AA7), BN_DEF(0xB84B4B36,  0xCF6A9483),
+    BN_DEF(0x1042A95D,  0x0E3179AB), BN_DEF(0xEE51D6CB,  0xC1B2AE91),
+    BN_DEF(0x7E9267AF,  0x348B1FD4), BN_DEF(0x0E2AE9CD,  0xCC6D241B),
+    BN_DEF(0x50B1DF82,  0xE1003E5C), BN_DEF(0xF6722D9E,  0x24943328),
+    BN_DEF(0xBE258FF3,  0xD74F9208), BN_DEF(0xAD44CFD2,  0xF71C35FD),
+    BN_DEF(0x7A035BF6,  0x85FFAE5B), BN_DEF(0xD31BF6B5,  0x7A262174),
+    BN_DEF(0x312F3F63,  0xF242DABB), BN_DEF(0xB6A8E122,  0xA7F09AB6),
+    BN_DEF(0xF92F8A1B,  0x98158536), BN_DEF(0xE69D218D,  0xF7CA8CD9),
+    BN_DEF(0xC71A026E,  0x28A5043C), BN_DEF(0x1D89CD91,  0x0105DF53),
+    BN_DEF(0x4533E63A,  0x94812704), BN_DEF(0xC06E0E68,  0x62633145),
+    BN_DEF(0x10B4611A,  0xE487ED51), BN_DEF(0xFFFFFFFF,  0x7FFFFFFF),
+};
 
 /*-
  * "4096-bit MODP Group" from RFC3526, Section 5.
@@ -150,6 +209,41 @@ static const BN_ULONG modp_4096_p[] = {
     BN_DEF(0x8A67CC74, 0x29024E08), BN_DEF(0x80DC1CD1, 0xC4C6628B),
     BN_DEF(0x2168C234, 0xC90FDAA2), BN_DEF(0xFFFFFFFF, 0xFFFFFFFF)
 };
+/* q = (p - 1) / 2 */
+static const BN_ULONG modp_4096_q[] = {
+    BN_DEF(0xFFFFFFFF,  0xFFFFFFFF), BN_DEF(0x9A0318CC,  0xA6FA1AE4),
+    BN_DEF(0x48536047,  0xC37FDBEE), BN_DEF(0x46C7EEE0,  0xC9DA754C),
+    BN_DEF(0xEAD82D54,  0x68034893), BN_DEF(0x10B8240E,  0xDC0DEEBB),
+    BN_DEF(0x67716BD7,  0x8FB094B8), BN_DEF(0x28ADF3F6,  0x119DD0C3),
+    BN_DEF(0xD04861D1,  0xCCD94B27), BN_DEF(0xA735E02E,  0x143E2CA3),
+    BN_DEF(0x0FDF6553,  0x97477E0A), BN_DEF(0x826F477C,  0x6DDDE16D),
+    BN_DEF(0x156A2674,  0x12C1F4E5), BN_DEF(0x5B0A85ED,  0x0D4A341A),
+    BN_DEF(0x357A711E,  0x4CE1938C), BN_DEF(0x5EDD2D93,  0xC438CD08),
+    BN_DEF(0x53C3F36B,  0x8D391E09), BN_DEF(0x54908400,  0x25C16890),
+    BN_DEF(0x707E8847,  0xA1EDADFE), BN_DEF(0x3A72D598,  0x047127D0),
+    BN_DEF(0x5D6CA371,  0x3B84C460), BN_DEF(0xBD30AEB6,  0x5DF08BAB),
+    BN_DEF(0x0BBD9006,  0x290F958C), BN_DEF(0x9F643532,  0x6C3B0139),
+    BN_DEF(0x6CC50432,  0xF897FD03), BN_DEF(0x0D697735,  0xE771E913),
+    BN_DEF(0x2512B0CE,  0x8F464A70), BN_DEF(0x6D8499EB,  0xD5FAD746),
+    BN_DEF(0xD370F263,  0xD9CB87C2), BN_DEF(0xAE83063E,  0x457538AB),
+    BN_DEF(0x2C6DF785,  0x767DC282), BN_DEF(0xEF8E5D32,  0xD42A90D5),
+    BN_DEF(0x82283D19,  0xD6998B86), BN_DEF(0x45556216,  0x0AB9472D),
+    BN_DEF(0x4C7D0288,  0x8AE9130C), BN_DEF(0x754AB572,  0x1CCAA4BE),
+    BN_DEF(0x4AAC0B8C,  0xEF15E5FB), BN_DEF(0x37A62964,  0xDAE2AEF8),
+    BN_DEF(0x7603D147,  0xCD93C1D1), BN_DEF(0x0C074301,  0xF1CF3B96),
+    BN_DEF(0x171B671D,  0x19482F23), BN_DEF(0x650C10BE,  0x78BA3604),
+    BN_DEF(0x255E4C02,  0xB3861AA7), BN_DEF(0xB84B4B36,  0xCF6A9483),
+    BN_DEF(0x1042A95D,  0x0E3179AB), BN_DEF(0xEE51D6CB,  0xC1B2AE91),
+    BN_DEF(0x7E9267AF,  0x348B1FD4), BN_DEF(0x0E2AE9CD,  0xCC6D241B),
+    BN_DEF(0x50B1DF82,  0xE1003E5C), BN_DEF(0xF6722D9E,  0x24943328),
+    BN_DEF(0xBE258FF3,  0xD74F9208), BN_DEF(0xAD44CFD2,  0xF71C35FD),
+    BN_DEF(0x7A035BF6,  0x85FFAE5B), BN_DEF(0xD31BF6B5,  0x7A262174),
+    BN_DEF(0x312F3F63,  0xF242DABB), BN_DEF(0xB6A8E122,  0xA7F09AB6),
+    BN_DEF(0xF92F8A1B,  0x98158536), BN_DEF(0xE69D218D,  0xF7CA8CD9),
+    BN_DEF(0xC71A026E,  0x28A5043C), BN_DEF(0x1D89CD91,  0x0105DF53),
+    BN_DEF(0x4533E63A,  0x94812704), BN_DEF(0xC06E0E68,  0x62633145),
+    BN_DEF(0x10B4611A,  0xE487ED51), BN_DEF(0xFFFFFFFF,  0x7FFFFFFF),
+};
 
 /*-
  * "6144-bit MODP Group" from RFC3526, Section 6.
@@ -208,6 +302,57 @@ static const BN_ULONG modp_6144_p[] = {
     BN_DEF(0x8A67CC74, 0x29024E08), BN_DEF(0x80DC1CD1, 0xC4C6628B),
     BN_DEF(0x2168C234, 0xC90FDAA2), BN_DEF(0xFFFFFFFF, 0xFFFFFFFF)
 };
+/* q = (p - 1) / 2 */
+static const BN_ULONG modp_6144_q[] = {
+    BN_DEF(0xFFFFFFFF,  0x7FFFFFFF), BN_DEF(0x36E62012,  0x734A7C8F),
+    BN_DEF(0x85BA3A6B,  0x095F96AD), BN_DEF(0x1FA43077,  0x021F47B3),
+    BN_DEF(0xB71E0234,  0x1C3FF46B), BN_DEF(0x17794B19,  0x6D2B64F6),
+    BN_DEF(0xD189EAAE,  0x758CE658), BN_DEF(0xC50FDFF8,  0x7AA8551E),
+    BN_DEF(0xDBE2ED3B,  0x0350EAC5), BN_DEF(0x794DF194,  0x53CB8AF7),
+    BN_DEF(0x07C01BF0,  0x0A662F69), BN_DEF(0x5FA470EC,  0x6647B6BF),
+    BN_DEF(0x15A0AA55,  0xA5EA03D9), BN_DEF(0xFFAC2D62,  0x078EA2DB),
+    BN_DEF(0x1B66445F,  0x91D4BD3F), BN_DEF(0xDF63F479,  0x2CF3E4BF),
+    BN_DEF(0xC8058E4F,  0x5AD42018), BN_DEF(0xA34C0641,  0x6AAF3817),
+    BN_DEF(0x373A7F7B,  0xFA416BE7), BN_DEF(0xE8B90E81,  0x7819750A),
+    BN_DEF(0xE325C976,  0xACC1E500), BN_DEF(0x9BC6695F,  0x37DC7A00),
+    BN_DEF(0x95EBD7A1,  0x999028A8), BN_DEF(0xF36612A5,  0xEDBF8A23),
+    BN_DEF(0x676A5D8D,  0xA267365D), BN_DEF(0xE7CD8A76,  0x6D1F6DF5),
+    BN_DEF(0x432D448C,  0x8BCB93D8), BN_DEF(0xC813EC18,  0x583529F6),
+    BN_DEF(0xA09800D7,  0x72ED9C17), BN_DEF(0x56CF2987,  0xFC7FCA03),
+    BN_DEF(0x1EDD1BDE,  0x64BA8F3B), BN_DEF(0x3013236F,  0x60EA6E59),
+    BN_DEF(0x693E3813,  0x1B61FD5A), BN_DEF(0x9A014249,  0xA6FA1AE4),
+    BN_DEF(0x48536047,  0xC37FDBEE), BN_DEF(0x46C7EEE0,  0xC9DA754C),
+    BN_DEF(0xEAD82D54,  0x68034893), BN_DEF(0x10B8240E,  0xDC0DEEBB),
+    BN_DEF(0x67716BD7,  0x8FB094B8), BN_DEF(0x28ADF3F6,  0x119DD0C3),
+    BN_DEF(0xD04861D1,  0xCCD94B27), BN_DEF(0xA735E02E,  0x143E2CA3),
+    BN_DEF(0x0FDF6553,  0x97477E0A), BN_DEF(0x826F477C,  0x6DDDE16D),
+    BN_DEF(0x156A2674,  0x12C1F4E5), BN_DEF(0x5B0A85ED,  0x0D4A341A),
+    BN_DEF(0x357A711E,  0x4CE1938C), BN_DEF(0x5EDD2D93,  0xC438CD08),
+    BN_DEF(0x53C3F36B,  0x8D391E09), BN_DEF(0x54908400,  0x25C16890),
+    BN_DEF(0x707E8847,  0xA1EDADFE), BN_DEF(0x3A72D598,  0x047127D0),
+    BN_DEF(0x5D6CA371,  0x3B84C460), BN_DEF(0xBD30AEB6,  0x5DF08BAB),
+    BN_DEF(0x0BBD9006,  0x290F958C), BN_DEF(0x9F643532,  0x6C3B0139),
+    BN_DEF(0x6CC50432,  0xF897FD03), BN_DEF(0x0D697735,  0xE771E913),
+    BN_DEF(0x2512B0CE,  0x8F464A70), BN_DEF(0x6D8499EB,  0xD5FAD746),
+    BN_DEF(0xD370F263,  0xD9CB87C2), BN_DEF(0xAE83063E,  0x457538AB),
+    BN_DEF(0x2C6DF785,  0x767DC282), BN_DEF(0xEF8E5D32,  0xD42A90D5),
+    BN_DEF(0x82283D19,  0xD6998B86), BN_DEF(0x45556216,  0x0AB9472D),
+    BN_DEF(0x4C7D0288,  0x8AE9130C), BN_DEF(0x754AB572,  0x1CCAA4BE),
+    BN_DEF(0x4AAC0B8C,  0xEF15E5FB), BN_DEF(0x37A62964,  0xDAE2AEF8),
+    BN_DEF(0x7603D147,  0xCD93C1D1), BN_DEF(0x0C074301,  0xF1CF3B96),
+    BN_DEF(0x171B671D,  0x19482F23), BN_DEF(0x650C10BE,  0x78BA3604),
+    BN_DEF(0x255E4C02,  0xB3861AA7), BN_DEF(0xB84B4B36,  0xCF6A9483),
+    BN_DEF(0x1042A95D,  0x0E3179AB), BN_DEF(0xEE51D6CB,  0xC1B2AE91),
+    BN_DEF(0x7E9267AF,  0x348B1FD4), BN_DEF(0x0E2AE9CD,  0xCC6D241B),
+    BN_DEF(0x50B1DF82,  0xE1003E5C), BN_DEF(0xF6722D9E,  0x24943328),
+    BN_DEF(0xBE258FF3,  0xD74F9208), BN_DEF(0xAD44CFD2,  0xF71C35FD),
+    BN_DEF(0x7A035BF6,  0x85FFAE5B), BN_DEF(0xD31BF6B5,  0x7A262174),
+    BN_DEF(0x312F3F63,  0xF242DABB), BN_DEF(0xB6A8E122,  0xA7F09AB6),
+    BN_DEF(0xF92F8A1B,  0x98158536), BN_DEF(0xE69D218D,  0xF7CA8CD9),
+    BN_DEF(0xC71A026E,  0x28A5043C), BN_DEF(0x1D89CD91,  0x0105DF53),
+    BN_DEF(0x4533E63A,  0x94812704), BN_DEF(0xC06E0E68,  0x62633145),
+    BN_DEF(0x10B4611A,  0xE487ED51), BN_DEF(0xFFFFFFFF,  0x7FFFFFFF),
+};
 
 /*
  * "8192-bit MODP Group" from RFC3526, Section 7.
@@ -282,6 +427,73 @@ static const BN_ULONG modp_8192_p[] = {
     BN_DEF(0x8A67CC74, 0x29024E08), BN_DEF(0x80DC1CD1, 0xC4C6628B),
     BN_DEF(0x2168C234, 0xC90FDAA2), BN_DEF(0xFFFFFFFF, 0xFFFFFFFF)
 };
+/* q = (p - 1) / 2 */
+static const BN_ULONG modp_8192_q[] = {
+    BN_DEF(0xFFFFFFFF,  0xFFFFFFFF), BN_DEF(0xCC76E9EF,  0xB064C06E),
+    BN_DEF(0x405CB738,  0xE40FAB74), BN_DEF(0x3B2B4A6F,  0x4F182871),
+    BN_DEF(0xAB3BF4D5,  0xCAAC7223), BN_DEF(0x7E013723,  0xE48C86D3),
+    BN_DEF(0x6AF71C15,  0xC44D0017), BN_DEF(0xA40E366B,  0x2004A1C5),
+    BN_DEF(0x75C3CFC9,  0x1AC8237A), BN_DEF(0x8F67D134,  0xFD79B5E1),
+    BN_DEF(0xBF73A6B9,  0xD8EA885E), BN_DEF(0xAEF6BF50,  0xFCD5A40C),
+    BN_DEF(0x8423428E,  0xB2798E62), BN_DEF(0xD012AEE0,  0x22CBF44C),
+    BN_DEF(0x3A55B51B,  0xEF988770), BN_DEF(0x1FA27C16,  0x369509FC),
+    BN_DEF(0xD9D13C53,  0x03159E7A), BN_DEF(0xF6ADEE9D,  0x3CB41981),
+    BN_DEF(0xD16043F4,  0xFD4EA5BF), BN_DEF(0x17C1C2EE,  0xA5E5E443),
+    BN_DEF(0x36751835,  0x9A39FE32), BN_DEF(0x0D11F863,  0x89F5ABD4),
+    BN_DEF(0x5201BE03,  0x91111702), BN_DEF(0x7E42456C,  0xF1FEDC5F),
+    BN_DEF(0xF1CEB296,  0x11C78B65), BN_DEF(0x15F8E4BC,  0x1A11DA3A),
+    BN_DEF(0x2D727AB4,  0x1D55B1CE), BN_DEF(0xB5D21233,  0x92BB7B49),
+    BN_DEF(0xC57E23F6,  0x3A0FD3DF), BN_DEF(0x46CEE980,  0x1DE4195B),
+    BN_DEF(0x39DC98DD,  0x6C5F6268), BN_DEF(0x54996FC6,  0x1C3BBE5B),
+    BN_DEF(0x897F72F2,  0xBA51C937), BN_DEF(0x36DF08AC,  0x734A7C8F),
+    BN_DEF(0x85BA3A6B,  0x095F96AD), BN_DEF(0x1FA43077,  0x021F47B3),
+    BN_DEF(0xB71E0234,  0x1C3FF46B), BN_DEF(0x17794B19,  0x6D2B64F6),
+    BN_DEF(0xD189EAAE,  0x758CE658), BN_DEF(0xC50FDFF8,  0x7AA8551E),
+    BN_DEF(0xDBE2ED3B,  0x0350EAC5), BN_DEF(0x794DF194,  0x53CB8AF7),
+    BN_DEF(0x07C01BF0,  0x0A662F69), BN_DEF(0x5FA470EC,  0x6647B6BF),
+    BN_DEF(0x15A0AA55,  0xA5EA03D9), BN_DEF(0xFFAC2D62,  0x078EA2DB),
+    BN_DEF(0x1B66445F,  0x91D4BD3F), BN_DEF(0xDF63F479,  0x2CF3E4BF),
+    BN_DEF(0xC8058E4F,  0x5AD42018), BN_DEF(0xA34C0641,  0x6AAF3817),
+    BN_DEF(0x373A7F7B,  0xFA416BE7), BN_DEF(0xE8B90E81,  0x7819750A),
+    BN_DEF(0xE325C976,  0xACC1E500), BN_DEF(0x9BC6695F,  0x37DC7A00),
+    BN_DEF(0x95EBD7A1,  0x999028A8), BN_DEF(0xF36612A5,  0xEDBF8A23),
+    BN_DEF(0x676A5D8D,  0xA267365D), BN_DEF(0xE7CD8A76,  0x6D1F6DF5),
+    BN_DEF(0x432D448C,  0x8BCB93D8), BN_DEF(0xC813EC18,  0x583529F6),
+    BN_DEF(0xA09800D7,  0x72ED9C17), BN_DEF(0x56CF2987,  0xFC7FCA03),
+    BN_DEF(0x1EDD1BDE,  0x64BA8F3B), BN_DEF(0x3013236F,  0x60EA6E59),
+    BN_DEF(0x693E3813,  0x1B61FD5A), BN_DEF(0x9A014249,  0xA6FA1AE4),
+    BN_DEF(0x48536047,  0xC37FDBEE), BN_DEF(0x46C7EEE0,  0xC9DA754C),
+    BN_DEF(0xEAD82D54,  0x68034893), BN_DEF(0x10B8240E,  0xDC0DEEBB),
+    BN_DEF(0x67716BD7,  0x8FB094B8), BN_DEF(0x28ADF3F6,  0x119DD0C3),
+    BN_DEF(0xD04861D1,  0xCCD94B27), BN_DEF(0xA735E02E,  0x143E2CA3),
+    BN_DEF(0x0FDF6553,  0x97477E0A), BN_DEF(0x826F477C,  0x6DDDE16D),
+    BN_DEF(0x156A2674,  0x12C1F4E5), BN_DEF(0x5B0A85ED,  0x0D4A341A),
+    BN_DEF(0x357A711E,  0x4CE1938C), BN_DEF(0x5EDD2D93,  0xC438CD08),
+    BN_DEF(0x53C3F36B,  0x8D391E09), BN_DEF(0x54908400,  0x25C16890),
+    BN_DEF(0x707E8847,  0xA1EDADFE), BN_DEF(0x3A72D598,  0x047127D0),
+    BN_DEF(0x5D6CA371,  0x3B84C460), BN_DEF(0xBD30AEB6,  0x5DF08BAB),
+    BN_DEF(0x0BBD9006,  0x290F958C), BN_DEF(0x9F643532,  0x6C3B0139),
+    BN_DEF(0x6CC50432,  0xF897FD03), BN_DEF(0x0D697735,  0xE771E913),
+    BN_DEF(0x2512B0CE,  0x8F464A70), BN_DEF(0x6D8499EB,  0xD5FAD746),
+    BN_DEF(0xD370F263,  0xD9CB87C2), BN_DEF(0xAE83063E,  0x457538AB),
+    BN_DEF(0x2C6DF785,  0x767DC282), BN_DEF(0xEF8E5D32,  0xD42A90D5),
+    BN_DEF(0x82283D19,  0xD6998B86), BN_DEF(0x45556216,  0x0AB9472D),
+    BN_DEF(0x4C7D0288,  0x8AE9130C), BN_DEF(0x754AB572,  0x1CCAA4BE),
+    BN_DEF(0x4AAC0B8C,  0xEF15E5FB), BN_DEF(0x37A62964,  0xDAE2AEF8),
+    BN_DEF(0x7603D147,  0xCD93C1D1), BN_DEF(0x0C074301,  0xF1CF3B96),
+    BN_DEF(0x171B671D,  0x19482F23), BN_DEF(0x650C10BE,  0x78BA3604),
+    BN_DEF(0x255E4C02,  0xB3861AA7), BN_DEF(0xB84B4B36,  0xCF6A9483),
+    BN_DEF(0x1042A95D,  0x0E3179AB), BN_DEF(0xEE51D6CB,  0xC1B2AE91),
+    BN_DEF(0x7E9267AF,  0x348B1FD4), BN_DEF(0x0E2AE9CD,  0xCC6D241B),
+    BN_DEF(0x50B1DF82,  0xE1003E5C), BN_DEF(0xF6722D9E,  0x24943328),
+    BN_DEF(0xBE258FF3,  0xD74F9208), BN_DEF(0xAD44CFD2,  0xF71C35FD),
+    BN_DEF(0x7A035BF6,  0x85FFAE5B), BN_DEF(0xD31BF6B5,  0x7A262174),
+    BN_DEF(0x312F3F63,  0xF242DABB), BN_DEF(0xB6A8E122,  0xA7F09AB6),
+    BN_DEF(0xF92F8A1B,  0x98158536), BN_DEF(0xE69D218D,  0xF7CA8CD9),
+    BN_DEF(0xC71A026E,  0x28A5043C), BN_DEF(0x1D89CD91,  0x0105DF53),
+    BN_DEF(0x4533E63A,  0x94812704), BN_DEF(0xC06E0E68,  0x62633145),
+    BN_DEF(0x10B4611A,  0xE487ED51), BN_DEF(0xFFFFFFFF,  0x7FFFFFFF),
+};
 
 /* DH parameters from RFC5114 */
 static const BN_ULONG dh1024_160_p[] = {
@@ -294,7 +506,10 @@ static const BN_ULONG dh1024_160_p[] = {
     BN_DEF(0x52D23B61, 0x9A6A9DCA), BN_DEF(0xFB06A3C6, 0x52C99FBC),
     BN_DEF(0xAE5D54EC, 0xDE92DE5E), BN_DEF(0xA080E01D, 0xB10B8F96)
 };
-
+static const BN_ULONG dh1024_160_q[] = {
+    BN_DEF(0x49462353, 0x64B7CB9D), BN_DEF(0x8ABA4E7D, 0x81A8DF27),
+    (BN_ULONG)0xF518AA87
+};
 static const BN_ULONG dh1024_160_g[] = {
     BN_DEF(0x22B3B2E5, 0x855E6EEB), BN_DEF(0xF97C2A24, 0x858F4DCE),
     BN_DEF(0x18D08BC8, 0x2D779D59), BN_DEF(0x8E73AFA3, 0xD662A4D1),
@@ -306,11 +521,6 @@ static const BN_ULONG dh1024_160_g[] = {
     BN_DEF(0xEFB99905, 0x6765A442), BN_DEF(0xC3FD3412, 0xA4D1CBD5)
 };
 
-static const BN_ULONG dh1024_160_q[] = {
-    BN_DEF(0x49462353, 0x64B7CB9D), BN_DEF(0x8ABA4E7D, 0x81A8DF27),
-    (BN_ULONG)0xF518AA87
-};
-
 static const BN_ULONG dh2048_224_p[] = {
     BN_DEF(0x0C10E64F, 0x0AC4DFFE), BN_DEF(0x4E71B81C, 0xCF9DE538),
     BN_DEF(0xFFA31F71, 0x7EF363E2), BN_DEF(0x6B8E75B9, 0xE3FB73C1),
@@ -329,7 +539,10 @@ static const BN_ULONG dh2048_224_p[] = {
     BN_DEF(0xB61D0A75, 0xB54B1597), BN_DEF(0x683B9FD1, 0xA20D64E5),
     BN_DEF(0x9559C51F, 0xD660FAA7), BN_DEF(0x9123A9D0, 0xAD107E1E)
 };
-
+static const BN_ULONG dh2048_224_q[] = {
+    BN_DEF(0xB36371EB, 0xBF389A99), BN_DEF(0x4738CEBC, 0x1F80535A),
+    BN_DEF(0x99717710, 0xC58D93FE), (BN_ULONG)0x801C0D34
+};
 static const BN_ULONG dh2048_224_g[] = {
     BN_DEF(0x191F2BFA, 0x84B890D3), BN_DEF(0x2A7065B3, 0x81BC087F),
     BN_DEF(0xF6EC0179, 0x19C418E1), BN_DEF(0x71CFFF4C, 0x7B5A0F1C),
@@ -349,11 +562,6 @@ static const BN_ULONG dh2048_224_g[] = {
     BN_DEF(0x8FFDAC50, 0x9DF30B5C), BN_DEF(0x4F2D9AE3, 0xAC4032EF)
 };
 
-static const BN_ULONG dh2048_224_q[] = {
-    BN_DEF(0xB36371EB, 0xBF389A99), BN_DEF(0x4738CEBC, 0x1F80535A),
-    BN_DEF(0x99717710, 0xC58D93FE), (BN_ULONG)0x801C0D34
-};
-
 static const BN_ULONG dh2048_256_p[] = {
     BN_DEF(0x1E1A1597, 0xDB094AE9), BN_DEF(0xD7EF09CA, 0x693877FA),
     BN_DEF(0x6E11715F, 0x6116D227), BN_DEF(0xC198AF12, 0xA4B54330),
@@ -372,7 +580,10 @@ static const BN_ULONG dh2048_256_p[] = {
     BN_DEF(0x435E3B00, 0x5D2CEED4), BN_DEF(0x660DD0F2, 0x8CEEF608),
     BN_DEF(0x65195999, 0xFFBBD19C), BN_DEF(0xB4B6663C, 0x87A8E61D)
 };
-
+static const BN_ULONG dh2048_256_q[] = {
+    BN_DEF(0x64F5FBD3, 0xA308B0FE), BN_DEF(0x1EB3750B, 0x99B1A47D),
+    BN_DEF(0x40129DA2, 0xB4479976), BN_DEF(0xA709A097, 0x8CF83642)
+};
 static const BN_ULONG dh2048_256_g[] = {
     BN_DEF(0x6CC41659, 0x664B4C0F), BN_DEF(0xEF98C582, 0x5E2327CF),
     BN_DEF(0xD4795451, 0xD647D148), BN_DEF(0x90F00EF8, 0x2F630784),
@@ -392,12 +603,6 @@ static const BN_ULONG dh2048_256_g[] = {
     BN_DEF(0x60EDBD48, 0x2E775066), BN_DEF(0x73134D0B, 0x3FB32C9B)
 };
 
-static const BN_ULONG dh2048_256_q[] = {
-    BN_DEF(0x64F5FBD3, 0xA308B0FE), BN_DEF(0x1EB3750B, 0x99B1A47D),
-    BN_DEF(0x40129DA2, 0xB4479976), BN_DEF(0xA709A097, 0x8CF83642)
-
-};
-
 /* Primes from RFC 7919 */
 static const BN_ULONG ffdhe2048_p[] = {
     BN_DEF(0xFFFFFFFF, 0xFFFFFFFF), BN_DEF(0x61285C97, 0x886B4238),
@@ -417,6 +622,25 @@ static const BN_ULONG ffdhe2048_p[] = {
     BN_DEF(0xCE2D3695, 0xD8B9C583), BN_DEF(0x273D3CF1, 0xAFDC5620),
     BN_DEF(0xA2BB4A9A, 0xADF85458), BN_DEF(0xFFFFFFFF, 0xFFFFFFFF)
 };
+/* q = (p - 1) / 2 */
+static const BN_ULONG ffdhe2048_q[] = {
+    BN_DEF(0xFFFFFFFF,  0xFFFFFFFF), BN_DEF(0x30942E4B,  0x4435A11C),
+    BN_DEF(0x60D977FD,  0x6379A513), BN_DEF(0xBE8B41D9,  0xE2C778C1),
+    BN_DEF(0x17611002,  0x9DDAFE5E), BN_DEF(0xA637D6B9,  0xE1FF1D8D),
+    BN_DEF(0x777940C1,  0xC7278919), BN_DEF(0x74C2C1FF,  0xC8B97F4E),
+    BN_DEF(0x941A17B0,  0x601A0266), BN_DEF(0xE6FBF176,  0x4F017E70),
+    BN_DEF(0x770536B8,  0x8583D3E4), BN_DEF(0xB1B95D8C,  0x572B76F3),
+    BN_DEF(0xEF1CA6FA,  0x0EA7A151), BN_DEF(0xB06BFA34,  0xDCB56D5B),
+    BN_DEF(0xD96471FD,  0xE88454A5), BN_DEF(0x59927DB0,  0x5E0558C1),
+    BN_DEF(0xA41D3CBD,  0x98566527), BN_DEF(0x9B56F39A,  0x0EF8AC50),
+    BN_DEF(0x79F7F439,  0xF15344ED), BN_DEF(0x707345BB,  0xCC278638),
+    BN_DEF(0x3FABE49A,  0xDAAB89AF), BN_DEF(0x9EF68D79,  0x42B1B2AA),
+    BN_DEF(0xAF833768,  0x9219FA8F), BN_DEF(0xEAFEB2B0,  0x69EF8F6A),
+    BN_DEF(0x576230BD,  0x7B40D901), BN_DEF(0xB1863AEC,  0xBE97F1B1),
+    BN_DEF(0x124D9F7C,  0xE649CEE7), BN_DEF(0x8A3219FD,  0xD4F09B20),
+    BN_DEF(0xE7169B4A,  0xEC5CE2C1), BN_DEF(0x139E9E78,  0x57EE2B10),
+    BN_DEF(0x515DA54D,  0xD6FC2A2C), BN_DEF(0xFFFFFFFF,  0x7FFFFFFF),
+};
 
 static const BN_ULONG ffdhe3072_p[] = {
     BN_DEF(0xFFFFFFFF, 0xFFFFFFFF), BN_DEF(0x66C62E37, 0x25E41D2B),
@@ -444,6 +668,33 @@ static const BN_ULONG ffdhe3072_p[] = {
     BN_DEF(0xCE2D3695, 0xD8B9C583), BN_DEF(0x273D3CF1, 0xAFDC5620),
     BN_DEF(0xA2BB4A9A, 0xADF85458), BN_DEF(0xFFFFFFFF, 0xFFFFFFFF)
 };
+/* q = (p - 1) / 2 */
+static const BN_ULONG ffdhe3072_q[] = {
+    BN_DEF(0xFFFFFFFF,  0xFFFFFFFF), BN_DEF(0xB363171B,  0x12F20E95),
+    BN_DEF(0x1FEACEBE,  0x9E0D9077), BN_DEF(0xFD29EEF7,  0x055E6835),
+    BN_DEF(0x6AE22427,  0x0EDFCD21), BN_DEF(0xCD86F56D,  0xD5E290CB),
+    BN_DEF(0x911B1D06,  0x743695E2), BN_DEF(0xCE4EFB4F,  0xAE574155),
+    BN_DEF(0x38FAA5FF,  0xB279710F), BN_DEF(0x716BA6E9,  0x7A7EA229),
+    BN_DEF(0xDE21BCA2,  0x5A098649), BN_DEF(0xC289C938,  0x577F0984),
+    BN_DEF(0x60C36C8E,  0x2CC6587D), BN_DEF(0x48FBFBF7,  0xBD6C8E93),
+    BN_DEF(0xEB736483,  0x30DA37E4), BN_DEF(0x7CCE011C,  0xDE1A7A6F),
+    BN_DEF(0xB28C81AD,  0x6F1AAD9D), BN_DEF(0x308FE7EE,  0x4435A11C),
+    BN_DEF(0x60D977FD,  0x6379A513), BN_DEF(0xBE8B41D9,  0xE2C778C1),
+    BN_DEF(0x17611002,  0x9DDAFE5E), BN_DEF(0xA637D6B9,  0xE1FF1D8D),
+    BN_DEF(0x777940C1,  0xC7278919), BN_DEF(0x74C2C1FF,  0xC8B97F4E),
+    BN_DEF(0x941A17B0,  0x601A0266), BN_DEF(0xE6FBF176,  0x4F017E70),
+    BN_DEF(0x770536B8,  0x8583D3E4), BN_DEF(0xB1B95D8C,  0x572B76F3),
+    BN_DEF(0xEF1CA6FA,  0x0EA7A151), BN_DEF(0xB06BFA34,  0xDCB56D5B),
+    BN_DEF(0xD96471FD,  0xE88454A5), BN_DEF(0x59927DB0,  0x5E0558C1),
+    BN_DEF(0xA41D3CBD,  0x98566527), BN_DEF(0x9B56F39A,  0x0EF8AC50),
+    BN_DEF(0x79F7F439,  0xF15344ED), BN_DEF(0x707345BB,  0xCC278638),
+    BN_DEF(0x3FABE49A,  0xDAAB89AF), BN_DEF(0x9EF68D79,  0x42B1B2AA),
+    BN_DEF(0xAF833768,  0x9219FA8F), BN_DEF(0xEAFEB2B0,  0x69EF8F6A),
+    BN_DEF(0x576230BD,  0x7B40D901), BN_DEF(0xB1863AEC,  0xBE97F1B1),
+    BN_DEF(0x124D9F7C,  0xE649CEE7), BN_DEF(0x8A3219FD,  0xD4F09B20),
+    BN_DEF(0xE7169B4A,  0xEC5CE2C1), BN_DEF(0x139E9E78,  0x57EE2B10),
+    BN_DEF(0x515DA54D,  0xD6FC2A2C), BN_DEF(0xFFFFFFFF,  0x7FFFFFFF),
+};
 
 static const BN_ULONG ffdhe4096_p[] = {
     BN_DEF(0xFFFFFFFF, 0xFFFFFFFF), BN_DEF(0x5E655F6A, 0xC68A007E),
@@ -479,6 +730,41 @@ static const BN_ULONG ffdhe4096_p[] = {
     BN_DEF(0xCE2D3695, 0xD8B9C583), BN_DEF(0x273D3CF1, 0xAFDC5620),
     BN_DEF(0xA2BB4A9A, 0xADF85458), BN_DEF(0xFFFFFFFF, 0xFFFFFFFF)
 };
+/* q = (p - 1) / 2 */
+static const BN_ULONG ffdhe4096_q[] = {
+    BN_DEF(0xFFFFFFFF,  0x7FFFFFFF), BN_DEF(0x2F32AFB5,  0xE345003F),
+    BN_DEF(0xFA20C170,  0xA6DAD428), BN_DEF(0x3FC45235,  0xC764DAAD),
+    BN_DEF(0xE764BEE7,  0x054148E6), BN_DEF(0xFCC68566,  0x15276754),
+    BN_DEF(0xB8A0001E,  0x0D0EDC9E), BN_DEF(0x99E5C5BD,  0x0494CCD1),
+    BN_DEF(0xB8D6801C,  0x36E3BC7C), BN_DEF(0x48C09862,  0x5483B005),
+    BN_DEF(0x96CF3419,  0x76B50F00), BN_DEF(0x77DA18C5,  0x389AE443),
+    BN_DEF(0xBF18E63D,  0x43FAADD2), BN_DEF(0xAA81A002,  0x3BB1E78E),
+    BN_DEF(0x6B4FB68C,  0x563EAFA1), BN_DEF(0x72C42BDB,  0xBC9874F2),
+    BN_DEF(0x8B26FA7D,  0xB737A961), BN_DEF(0xB34F0F78,  0x12F20E95),
+    BN_DEF(0x1FEACEBE,  0x9E0D9077), BN_DEF(0xFD29EEF7,  0x055E6835),
+    BN_DEF(0x6AE22427,  0x0EDFCD21), BN_DEF(0xCD86F56D,  0xD5E290CB),
+    BN_DEF(0x911B1D06,  0x743695E2), BN_DEF(0xCE4EFB4F,  0xAE574155),
+    BN_DEF(0x38FAA5FF,  0xB279710F), BN_DEF(0x716BA6E9,  0x7A7EA229),
+    BN_DEF(0xDE21BCA2,  0x5A098649), BN_DEF(0xC289C938,  0x577F0984),
+    BN_DEF(0x60C36C8E,  0x2CC6587D), BN_DEF(0x48FBFBF7,  0xBD6C8E93),
+    BN_DEF(0xEB736483,  0x30DA37E4), BN_DEF(0x7CCE011C,  0xDE1A7A6F),
+    BN_DEF(0xB28C81AD,  0x6F1AAD9D), BN_DEF(0x308FE7EE,  0x4435A11C),
+    BN_DEF(0x60D977FD,  0x6379A513), BN_DEF(0xBE8B41D9,  0xE2C778C1),
+    BN_DEF(0x17611002,  0x9DDAFE5E), BN_DEF(0xA637D6B9,  0xE1FF1D8D),
+    BN_DEF(0x777940C1,  0xC7278919), BN_DEF(0x74C2C1FF,  0xC8B97F4E),
+    BN_DEF(0x941A17B0,  0x601A0266), BN_DEF(0xE6FBF176,  0x4F017E70),
+    BN_DEF(0x770536B8,  0x8583D3E4), BN_DEF(0xB1B95D8C,  0x572B76F3),
+    BN_DEF(0xEF1CA6FA,  0x0EA7A151), BN_DEF(0xB06BFA34,  0xDCB56D5B),
+    BN_DEF(0xD96471FD,  0xE88454A5), BN_DEF(0x59927DB0,  0x5E0558C1),
+    BN_DEF(0xA41D3CBD,  0x98566527), BN_DEF(0x9B56F39A,  0x0EF8AC50),
+    BN_DEF(0x79F7F439,  0xF15344ED), BN_DEF(0x707345BB,  0xCC278638),
+    BN_DEF(0x3FABE49A,  0xDAAB89AF), BN_DEF(0x9EF68D79,  0x42B1B2AA),
+    BN_DEF(0xAF833768,  0x9219FA8F), BN_DEF(0xEAFEB2B0,  0x69EF8F6A),
+    BN_DEF(0x576230BD,  0x7B40D901), BN_DEF(0xB1863AEC,  0xBE97F1B1),
+    BN_DEF(0x124D9F7C,  0xE649CEE7), BN_DEF(0x8A3219FD,  0xD4F09B20),
+    BN_DEF(0xE7169B4A,  0xEC5CE2C1), BN_DEF(0x139E9E78,  0x57EE2B10),
+    BN_DEF(0x515DA54D,  0xD6FC2A2C), BN_DEF(0xFFFFFFFF,  0x7FFFFFFF),
+};
 
 static const BN_ULONG ffdhe6144_p[] = {
     BN_DEF(0xFFFFFFFF, 0xFFFFFFFF), BN_DEF(0xD0E40E65, 0xA40E329C),
@@ -530,6 +816,57 @@ static const BN_ULONG ffdhe6144_p[] = {
     BN_DEF(0xCE2D3695, 0xD8B9C583), BN_DEF(0x273D3CF1, 0xAFDC5620),
     BN_DEF(0xA2BB4A9A, 0xADF85458), BN_DEF(0xFFFFFFFF, 0xFFFFFFFF)
 };
+/* q = (p - 1) / 2 */
+static const BN_ULONG ffdhe6144_q[] = {
+    BN_DEF(0xFFFFFFFF,  0xFFFFFFFF), BN_DEF(0x68720732,  0x5207194E),
+    BN_DEF(0xBC9C6D6A,  0xD20EAB86), BN_DEF(0x6A18B0E0,  0xB1534A93),
+    BN_DEF(0x4D6D8F34,  0x1FEEA547), BN_DEF(0xEE35C06B,  0x2D9DB8FC),
+    BN_DEF(0x63139582,  0xF64E8C08), BN_DEF(0xE5677A01,  0xC66796EA),
+    BN_DEF(0xE4ADC88B,  0x724FA91A), BN_DEF(0xDC2A19C5,  0x282EE416),
+    BN_DEF(0x8AB15423,  0x31149618), BN_DEF(0x3573BFAF,  0x6B9581BA),
+    BN_DEF(0xA316A9C6,  0x7CE4848D), BN_DEF(0x23D33E5F,  0x05746DAC),
+    BN_DEF(0x91308B41,  0x59D39CE0), BN_DEF(0x95140DFB,  0x77556011),
+    BN_DEF(0x3BE57CC9,  0xCA63328F), BN_DEF(0xCA595DE0,  0x3B1F2725),
+    BN_DEF(0x003BECDA,  0xAC3F1C6D), BN_DEF(0x0C1811E1,  0x3FD94FC6),
+    BN_DEF(0xFCF1D137,  0x855F60FF), BN_DEF(0x1A8288F1,  0x50077849),
+    BN_DEF(0x6DB1A06C,  0x5C2A9917), BN_DEF(0xD4D4B488,  0xD29238FB),
+    BN_DEF(0xA67EDA3B,  0x9C40A3FD), BN_DEF(0x2723020F,  0xCD8FAE1F),
+    BN_DEF(0xFE67F638,  0x66D6832B), BN_DEF(0xA6380E1D,  0x59C74619),
+    BN_DEF(0x58E07EA6,  0x48BDEEB2), BN_DEF(0x4DBB1264,  0x1DDA2A19),
+    BN_DEF(0x657A9F53,  0x11DD2221), BN_DEF(0x1C29951D,  0x2733BE96),
+    BN_DEF(0x2281B63D,  0x05FEB25B), BN_DEF(0x2F06EC81,  0xE345003F),
+    BN_DEF(0xFA20C170,  0xA6DAD428), BN_DEF(0x3FC45235,  0xC764DAAD),
+    BN_DEF(0xE764BEE7,  0x054148E6), BN_DEF(0xFCC68566,  0x15276754),
+    BN_DEF(0xB8A0001E,  0x0D0EDC9E), BN_DEF(0x99E5C5BD,  0x0494CCD1),
+    BN_DEF(0xB8D6801C,  0x36E3BC7C), BN_DEF(0x48C09862,  0x5483B005),
+    BN_DEF(0x96CF3419,  0x76B50F00), BN_DEF(0x77DA18C5,  0x389AE443),
+    BN_DEF(0xBF18E63D,  0x43FAADD2), BN_DEF(0xAA81A002,  0x3BB1E78E),
+    BN_DEF(0x6B4FB68C,  0x563EAFA1), BN_DEF(0x72C42BDB,  0xBC9874F2),
+    BN_DEF(0x8B26FA7D,  0xB737A961), BN_DEF(0xB34F0F78,  0x12F20E95),
+    BN_DEF(0x1FEACEBE,  0x9E0D9077), BN_DEF(0xFD29EEF7,  0x055E6835),
+    BN_DEF(0x6AE22427,  0x0EDFCD21), BN_DEF(0xCD86F56D,  0xD5E290CB),
+    BN_DEF(0x911B1D06,  0x743695E2), BN_DEF(0xCE4EFB4F,  0xAE574155),
+    BN_DEF(0x38FAA5FF,  0xB279710F), BN_DEF(0x716BA6E9,  0x7A7EA229),
+    BN_DEF(0xDE21BCA2,  0x5A098649), BN_DEF(0xC289C938,  0x577F0984),
+    BN_DEF(0x60C36C8E,  0x2CC6587D), BN_DEF(0x48FBFBF7,  0xBD6C8E93),
+    BN_DEF(0xEB736483,  0x30DA37E4), BN_DEF(0x7CCE011C,  0xDE1A7A6F),
+    BN_DEF(0xB28C81AD,  0x6F1AAD9D), BN_DEF(0x308FE7EE,  0x4435A11C),
+    BN_DEF(0x60D977FD,  0x6379A513), BN_DEF(0xBE8B41D9,  0xE2C778C1),
+    BN_DEF(0x17611002,  0x9DDAFE5E), BN_DEF(0xA637D6B9,  0xE1FF1D8D),
+    BN_DEF(0x777940C1,  0xC7278919), BN_DEF(0x74C2C1FF,  0xC8B97F4E),
+    BN_DEF(0x941A17B0,  0x601A0266), BN_DEF(0xE6FBF176,  0x4F017E70),
+    BN_DEF(0x770536B8,  0x8583D3E4), BN_DEF(0xB1B95D8C,  0x572B76F3),
+    BN_DEF(0xEF1CA6FA,  0x0EA7A151), BN_DEF(0xB06BFA34,  0xDCB56D5B),
+    BN_DEF(0xD96471FD,  0xE88454A5), BN_DEF(0x59927DB0,  0x5E0558C1),
+    BN_DEF(0xA41D3CBD,  0x98566527), BN_DEF(0x9B56F39A,  0x0EF8AC50),
+    BN_DEF(0x79F7F439,  0xF15344ED), BN_DEF(0x707345BB,  0xCC278638),
+    BN_DEF(0x3FABE49A,  0xDAAB89AF), BN_DEF(0x9EF68D79,  0x42B1B2AA),
+    BN_DEF(0xAF833768,  0x9219FA8F), BN_DEF(0xEAFEB2B0,  0x69EF8F6A),
+    BN_DEF(0x576230BD,  0x7B40D901), BN_DEF(0xB1863AEC,  0xBE97F1B1),
+    BN_DEF(0x124D9F7C,  0xE649CEE7), BN_DEF(0x8A3219FD,  0xD4F09B20),
+    BN_DEF(0xE7169B4A,  0xEC5CE2C1), BN_DEF(0x139E9E78,  0x57EE2B10),
+    BN_DEF(0x515DA54D,  0xD6FC2A2C), BN_DEF(0xFFFFFFFF,  0x7FFFFFFF),
+};
 
 static const BN_ULONG ffdhe8192_p[] = {
     BN_DEF(0xFFFFFFFF, 0xFFFFFFFF), BN_DEF(0xC5C6424C, 0xD68C8BB7),
@@ -597,6 +934,73 @@ static const BN_ULONG ffdhe8192_p[] = {
     BN_DEF(0xCE2D3695, 0xD8B9C583), BN_DEF(0x273D3CF1, 0xAFDC5620),
     BN_DEF(0xA2BB4A9A, 0xADF85458), BN_DEF(0xFFFFFFFF, 0xFFFFFFFF)
 };
+/* q = (p - 1) / 2 */
+static const BN_ULONG ffdhe8192_q[] = {
+    BN_DEF(0xFFFFFFFF,  0x7FFFFFFF), BN_DEF(0xE2E32126,  0x6B4645DB),
+    BN_DEF(0x41C7FC46,  0x008F154A), BN_DEF(0x54FA30A7,  0x84117283),
+    BN_DEF(0xFBD4221E,  0xCBE88EA4), BN_DEF(0x9833BF86,  0x535DFEF2),
+    BN_DEF(0x60FF437F,  0x17BA0F7C), BN_DEF(0x2EB8D43F,  0x7D7D5F0E),
+    BN_DEF(0xFDF2C518,  0x6F697DD5), BN_DEF(0x39585337,  0x5B42AEFF),
+    BN_DEF(0x5D4527F4,  0x8F7E4670), BN_DEF(0x1F97D22B,  0xC1FC0EA5),
+    BN_DEF(0xD2BBF118,  0x50FF183A), BN_DEF(0x446CE050,  0xEADC00CA),
+    BN_DEF(0xD6CD4AFC,  0xB1240B66), BN_DEF(0x286090BD,  0x4CF4F18B),
+    BN_DEF(0x07211E7E,  0x28D5348F), BN_DEF(0x1C137296,  0x0E10BF36),
+    BN_DEF(0x84B81FF7,  0x28D45498), BN_DEF(0xB523073A,  0x5DB84CC3),
+    BN_DEF(0x4E435811,  0xAA0FE346), BN_DEF(0x237EC128,  0x2C8B0660),
+    BN_DEF(0x1AE1AFAE,  0x1423605D), BN_DEF(0xC5BAC141,  0x2A282563),
+    BN_DEF(0xE95782F2,  0x149C441C), BN_DEF(0x600DEB81,  0xE596078E),
+    BN_DEF(0x3E499332,  0xAAAD97BA), BN_DEF(0x51D5C414,  0xC35B18A1),
+    BN_DEF(0xFB258877,  0x05C661DE), BN_DEF(0xF6E8E62F,  0xB43FF5B4),
+    BN_DEF(0x64A84EA1,  0x7ED91FE7), BN_DEF(0xECA8D732,  0x0F212D18),
+    BN_DEF(0x7B00641C,  0x1B568026), BN_DEF(0x67FA3555,  0x5207194E),
+    BN_DEF(0xBC9C6D6A,  0xD20EAB86), BN_DEF(0x6A18B0E0,  0xB1534A93),
+    BN_DEF(0x4D6D8F34,  0x1FEEA547), BN_DEF(0xEE35C06B,  0x2D9DB8FC),
+    BN_DEF(0x63139582,  0xF64E8C08), BN_DEF(0xE5677A01,  0xC66796EA),
+    BN_DEF(0xE4ADC88B,  0x724FA91A), BN_DEF(0xDC2A19C5,  0x282EE416),
+    BN_DEF(0x8AB15423,  0x31149618), BN_DEF(0x3573BFAF,  0x6B9581BA),
+    BN_DEF(0xA316A9C6,  0x7CE4848D), BN_DEF(0x23D33E5F,  0x05746DAC),
+    BN_DEF(0x91308B41,  0x59D39CE0), BN_DEF(0x95140DFB,  0x77556011),
+    BN_DEF(0x3BE57CC9,  0xCA63328F), BN_DEF(0xCA595DE0,  0x3B1F2725),
+    BN_DEF(0x003BECDA,  0xAC3F1C6D), BN_DEF(0x0C1811E1,  0x3FD94FC6),
+    BN_DEF(0xFCF1D137,  0x855F60FF), BN_DEF(0x1A8288F1,  0x50077849),
+    BN_DEF(0x6DB1A06C,  0x5C2A9917), BN_DEF(0xD4D4B488,  0xD29238FB),
+    BN_DEF(0xA67EDA3B,  0x9C40A3FD), BN_DEF(0x2723020F,  0xCD8FAE1F),
+    BN_DEF(0xFE67F638,  0x66D6832B), BN_DEF(0xA6380E1D,  0x59C74619),
+    BN_DEF(0x58E07EA6,  0x48BDEEB2), BN_DEF(0x4DBB1264,  0x1DDA2A19),
+    BN_DEF(0x657A9F53,  0x11DD2221), BN_DEF(0x1C29951D,  0x2733BE96),
+    BN_DEF(0x2281B63D,  0x05FEB25B), BN_DEF(0x2F06EC81,  0xE345003F),
+    BN_DEF(0xFA20C170,  0xA6DAD428), BN_DEF(0x3FC45235,  0xC764DAAD),
+    BN_DEF(0xE764BEE7,  0x054148E6), BN_DEF(0xFCC68566,  0x15276754),
+    BN_DEF(0xB8A0001E,  0x0D0EDC9E), BN_DEF(0x99E5C5BD,  0x0494CCD1),
+    BN_DEF(0xB8D6801C,  0x36E3BC7C), BN_DEF(0x48C09862,  0x5483B005),
+    BN_DEF(0x96CF3419,  0x76B50F00), BN_DEF(0x77DA18C5,  0x389AE443),
+    BN_DEF(0xBF18E63D,  0x43FAADD2), BN_DEF(0xAA81A002,  0x3BB1E78E),
+    BN_DEF(0x6B4FB68C,  0x563EAFA1), BN_DEF(0x72C42BDB,  0xBC9874F2),
+    BN_DEF(0x8B26FA7D,  0xB737A961), BN_DEF(0xB34F0F78,  0x12F20E95),
+    BN_DEF(0x1FEACEBE,  0x9E0D9077), BN_DEF(0xFD29EEF7,  0x055E6835),
+    BN_DEF(0x6AE22427,  0x0EDFCD21), BN_DEF(0xCD86F56D,  0xD5E290CB),
+    BN_DEF(0x911B1D06,  0x743695E2), BN_DEF(0xCE4EFB4F,  0xAE574155),
+    BN_DEF(0x38FAA5FF,  0xB279710F), BN_DEF(0x716BA6E9,  0x7A7EA229),
+    BN_DEF(0xDE21BCA2,  0x5A098649), BN_DEF(0xC289C938,  0x577F0984),
+    BN_DEF(0x60C36C8E,  0x2CC6587D), BN_DEF(0x48FBFBF7,  0xBD6C8E93),
+    BN_DEF(0xEB736483,  0x30DA37E4), BN_DEF(0x7CCE011C,  0xDE1A7A6F),
+    BN_DEF(0xB28C81AD,  0x6F1AAD9D), BN_DEF(0x308FE7EE,  0x4435A11C),
+    BN_DEF(0x60D977FD,  0x6379A513), BN_DEF(0xBE8B41D9,  0xE2C778C1),
+    BN_DEF(0x17611002,  0x9DDAFE5E), BN_DEF(0xA637D6B9,  0xE1FF1D8D),
+    BN_DEF(0x777940C1,  0xC7278919), BN_DEF(0x74C2C1FF,  0xC8B97F4E),
+    BN_DEF(0x941A17B0,  0x601A0266), BN_DEF(0xE6FBF176,  0x4F017E70),
+    BN_DEF(0x770536B8,  0x8583D3E4), BN_DEF(0xB1B95D8C,  0x572B76F3),
+    BN_DEF(0xEF1CA6FA,  0x0EA7A151), BN_DEF(0xB06BFA34,  0xDCB56D5B),
+    BN_DEF(0xD96471FD,  0xE88454A5), BN_DEF(0x59927DB0,  0x5E0558C1),
+    BN_DEF(0xA41D3CBD,  0x98566527), BN_DEF(0x9B56F39A,  0x0EF8AC50),
+    BN_DEF(0x79F7F439,  0xF15344ED), BN_DEF(0x707345BB,  0xCC278638),
+    BN_DEF(0x3FABE49A,  0xDAAB89AF), BN_DEF(0x9EF68D79,  0x42B1B2AA),
+    BN_DEF(0xAF833768,  0x9219FA8F), BN_DEF(0xEAFEB2B0,  0x69EF8F6A),
+    BN_DEF(0x576230BD,  0x7B40D901), BN_DEF(0xB1863AEC,  0xBE97F1B1),
+    BN_DEF(0x124D9F7C,  0xE649CEE7), BN_DEF(0x8A3219FD,  0xD4F09B20),
+    BN_DEF(0xE7169B4A,  0xEC5CE2C1), BN_DEF(0x139E9E78,  0x57EE2B10),
+    BN_DEF(0x515DA54D,  0xD6FC2A2C), BN_DEF(0xFFFFFFFF,  0x7FFFFFFF),
+};
 
 /* Macro to make a BIGNUM from static data */
 
@@ -608,32 +1012,44 @@ static const BN_ULONG ffdhe8192_p[] = {
 
 static const BN_ULONG value_2 = 2;
 
-const BIGNUM _bignum_const_2 =
-    { (BN_ULONG *)&value_2, 1, 1, 0, BN_FLG_STATIC_DATA };
+const BIGNUM _bignum_const_2 = {
+    (BN_ULONG *)&value_2, 1, 1, 0, BN_FLG_STATIC_DATA
+};
 
 make_dh_bn(dh1024_160_p)
-make_dh_bn(dh1024_160_g)
 make_dh_bn(dh1024_160_q)
+make_dh_bn(dh1024_160_g)
 make_dh_bn(dh2048_224_p)
-make_dh_bn(dh2048_224_g)
 make_dh_bn(dh2048_224_q)
+make_dh_bn(dh2048_224_g)
 make_dh_bn(dh2048_256_p)
-make_dh_bn(dh2048_256_g)
 make_dh_bn(dh2048_256_q)
+make_dh_bn(dh2048_256_g)
 
 make_dh_bn(ffdhe2048_p)
+make_dh_bn(ffdhe2048_q)
 make_dh_bn(ffdhe3072_p)
+make_dh_bn(ffdhe3072_q)
 make_dh_bn(ffdhe4096_p)
+make_dh_bn(ffdhe4096_q)
 make_dh_bn(ffdhe6144_p)
+make_dh_bn(ffdhe6144_q)
 make_dh_bn(ffdhe8192_p)
+make_dh_bn(ffdhe8192_q)
 
 # ifndef FIPS_MODE
 make_dh_bn(modp_1536_p)
+make_dh_bn(modp_1536_q)
 # endif
 make_dh_bn(modp_2048_p)
+make_dh_bn(modp_2048_q)
 make_dh_bn(modp_3072_p)
+make_dh_bn(modp_3072_q)
 make_dh_bn(modp_4096_p)
+make_dh_bn(modp_4096_q)
 make_dh_bn(modp_6144_p)
+make_dh_bn(modp_6144_q)
 make_dh_bn(modp_8192_p)
+make_dh_bn(modp_8192_q)
 
 #endif /* OPENSSL_NO_DH */
diff --git a/crypto/dh/dh_ameth.c b/crypto/dh/dh_ameth.c
index ea92fc9db7..4d247dbba2 100644
--- a/crypto/dh/dh_ameth.c
+++ b/crypto/dh/dh_ameth.c
@@ -559,7 +559,7 @@ static int dh_pkey_import_from(const OSSL_PARAM params[], void *vpctx)
         return 0;
     }
 
-    if (!ffc_params_fromdata(dh_get0_params(dh), params)
+    if (!dh_ffc_params_fromdata(dh, params)
         || !dh_key_fromdata(dh, params)
         || !EVP_PKEY_assign_DH(pkey, dh)) {
         DH_free(dh);
diff --git a/crypto/dh/dh_group_params.c b/crypto/dh/dh_group_params.c
index 1f5a58ed87..7221e806c5 100644
--- a/crypto/dh/dh_group_params.c
+++ b/crypto/dh/dh_group_params.c
@@ -23,19 +23,18 @@
 #include <openssl/objects.h>
 #include "crypto/bn_dh.h"
 #include "crypto/dh.h"
-#include "crypto/security_bits.h"
 #include "e_os.h" /* strcasecmp */
 
 #define FFDHE(sz) {                                                            \
     SN_ffdhe##sz, NID_ffdhe##sz,                                               \
     sz,                                                                        \
-    &_bignum_ffdhe##sz##_p, NULL, &_bignum_const_2                             \
+    &_bignum_ffdhe##sz##_p, &_bignum_ffdhe##sz##_q, &_bignum_const_2           \
 }
 
 #define MODP(sz)  {                                                            \
     SN_modp_##sz, NID_modp_##sz,                                               \
     sz,                                                                        \
-    &_bignum_modp_##sz##_p, NULL,  &_bignum_const_2                            \
+    &_bignum_modp_##sz##_p, &_bignum_modp_##sz##_q,  &_bignum_const_2          \
 }
 
 #define RFC5114(name, uid, sz, tag)  {                                         \
@@ -102,30 +101,18 @@ const char *ffc_named_group_from_uid(int uid)
 }
 
 static DH *dh_param_init(OPENSSL_CTX *libctx, int uid, const BIGNUM *p,
-                         const BIGNUM *q, const BIGNUM *g,
-                         int32_t nbits)
+                         const BIGNUM *q, const BIGNUM *g)
 {
-    BIGNUM *qtmp = NULL;
     DH *dh = dh_new_with_libctx(libctx);
 
     if (dh == NULL)
         return NULL;
 
-    if (q == NULL) {
-        qtmp = BN_dup(p);
-        /* Set q = (p - 1) / 2 (p is known to be odd so just shift right ) */
-        if (qtmp == NULL || !BN_rshift1(qtmp, qtmp)) {
-            BN_free(qtmp);
-            DH_free(dh);
-            return NULL;
-        }
-    }
     dh->params.nid = uid;
     dh->params.p = (BIGNUM *)p;
-    dh->params.q = (q != NULL ? (BIGNUM *)q : qtmp);
+    dh->params.q = (BIGNUM *)q;
     dh->params.g = (BIGNUM *)g;
-    /* Private key length = 2 * max_target_security_strength */
-    dh->length = nbits;
+    dh->length = BN_num_bits(q);
     dh->dirty_cnt++;
     return dh;
 }
@@ -139,19 +126,10 @@ static DH *dh_new_by_group_name(OPENSSL_CTX *libctx, const char *name)
 
     for (i = 0; i < (int)OSSL_NELEM(dh_named_groups); ++i) {
         if (strcasecmp(dh_named_groups[i].name, name) == 0) {
-            int max_target_security_strength =
-                ifc_ffc_compute_security_bits(dh_named_groups[i].nbits);
-
-            /*
-             * The last parameter specified here is
-             * 2 * max_target_security_strength.
-             * See SP800-56Ar3 Table(s) 25 & 26.
-             */
             return dh_param_init(libctx, dh_named_groups[i].uid,
                                  dh_named_groups[i].p,
                                  dh_named_groups[i].q,
-                                 dh_named_groups[i].g,
-                                 2 * max_target_security_strength);
+                                 dh_named_groups[i].g);
         }
     }
     DHerr(0, DH_R_INVALID_PARAMETER_NID);
@@ -180,23 +158,10 @@ int ffc_set_group_pqg(FFC_PARAMS *ffc, const char *group_name)
 
     for (i = 0; i < (int)OSSL_NELEM(dh_named_groups); ++i) {
         if (strcasecmp(dh_named_groups[i].name, group_name) == 0) {
-            if (dh_named_groups[i].q != NULL) {
-                /* For groups with a q */
-                ffc_params_set0_pqg(ffc,
-                                    (BIGNUM *)dh_named_groups[i].p,
-                                    (BIGNUM *)dh_named_groups[i].q,
-                                    (BIGNUM *)dh_named_groups[i].g);
-            } else {
-                /* For SAFE PRIME GROUPS */
-                /* Set q = (p - 1) / 2 (p is known to be odd so just shift right) */
-                q = BN_dup(dh_named_groups[i].p);
-                if (q == NULL || !BN_rshift1(q, q))
-                    break; /* exit with failure */
-
-                ffc_params_set0_pqg(ffc,
-                                    (BIGNUM *)dh_named_groups[i].p, q,
-                                    (BIGNUM *)dh_named_groups[i].g);
-            }
+            ffc_params_set0_pqg(ffc,
+                                (BIGNUM *)dh_named_groups[i].p,
+                                (BIGNUM *)dh_named_groups[i].q,
+                                (BIGNUM *)dh_named_groups[i].g);
             /* flush the cached nid, The DH layer is responsible for caching */
             ffc->nid = NID_undef;
             return 1;
@@ -207,63 +172,43 @@ int ffc_set_group_pqg(FFC_PARAMS *ffc, const char *group_name)
     return 0;
 }
 
-int DH_get_nid(DH *dh)
+void dh_cache_named_group(DH *dh)
 {
-    BIGNUM *q = NULL;
-    int i, nid;
+    int i;
 
     if (dh == NULL)
-        return NID_undef;
+        return;
+
+    dh->params.nid = NID_undef; /* flush cached value */
 
-    nid = dh->params.nid;
-    /* Just return if it is already cached */
-    if (nid != NID_undef)
-        return nid;
+    /* Exit if p or g is not set */
+    if (dh->params.p == NULL
+        || dh->params.g == NULL)
+        return;
 
     for (i = 0; i < (int)OSSL_NELEM(dh_named_groups); ++i) {
-        /* Keep searching until a matching p is found */
-        if (BN_cmp(dh->params.p, dh_named_groups[i].p) != 0)
-            continue;
-
-        /* Return an error if g is not matching */
-        if (BN_cmp(dh->params.g, dh_named_groups[i].g) != 0)
-            break;
-        if (dh_named_groups[i].q != NULL) {
-            /* RFC5114 NAMED GROUPS have q defined */
-
-            /* Verify q is correct if it exists */
-            if (dh->params.q != NULL) {
-                if (BN_cmp(dh->params.q, dh_named_groups[i].q) != 0)
-                    break;  /* returns nid = NID_undef if q does not match */
-            } else {
-                dh->params.q = (BIGNUM *)dh_named_groups[i].q;
-            }
-        } else {
-            /* For SAFE PRIME GROUPS */
-
-            /* Set q = (p - 1) / 2 (p is known to be odd so just shift right) */
-            q = BN_dup(dh->params.p);
-
-            if (q == NULL || !BN_rshift1(q, q))
-                break; /* returns nid = NID_undef on failure */
-
-            /* Verify q is correct if it exists */
-            if (dh->params.q != NULL) {
-                if (BN_cmp(dh->params.q, q) != 0)
-                    break;  /* returns nid = NID_undef if q does not match */
-            } else {
-                /* assign the calculated q */
-                dh->params.q = q;
-                q = NULL; /* set to NULL so it is not freed */
-            }
+        /* Keep searching until a matching p and g is found */
+        if (BN_cmp(dh->params.p, dh_named_groups[i].p) == 0
+            && BN_cmp(dh->params.g, dh_named_groups[i].g) == 0) {
+                /* Verify q is correct if it exists */
+                if (dh->params.q != NULL) {
+                    if (BN_cmp(dh->params.q, dh_named_groups[i].q) != 0)
+                        continue;  /* ignore if q does not match */
+                } else {
+                    dh->params.q = (BIGNUM *)dh_named_groups[i].q;
+                }
+                dh->params.nid = dh_named_groups[i].uid; /* cache the nid */
+                dh->length = BN_num_bits(dh->params.q);
+                dh->dirty_cnt++;
+                break;
         }
-        nid = dh->params.nid = dh_named_groups[i].uid; /* cache the nid */
-        dh->length =
-            2 * ifc_ffc_compute_security_bits(dh_named_groups[i].nbits);
-        dh->dirty_cnt++;
-        /* A matching p was found so break out of the loop */
-        break;
     }
-    BN_free(q);
-    return nid;
+}
+
+int DH_get_nid(const DH *dh)
+{
+    if (dh == NULL)
+        return NID_undef;
+
+    return dh->params.nid;
 }
diff --git a/crypto/dh/dh_key.c b/crypto/dh/dh_key.c
index e46946153b..918949d953 100644
--- a/crypto/dh/dh_key.c
+++ b/crypto/dh/dh_key.c
@@ -18,6 +18,7 @@
 #include "dh_local.h"
 #include "crypto/bn.h"
 #include "crypto/dh.h"
+#include "crypto/security_bits.h"
 
 #ifdef FIPS_MODE
 # define MIN_STRENGTH 112
@@ -252,16 +253,15 @@ static int generate_key(DH *dh)
     if (generate_new_key) {
         /* Is it an approved safe prime ?*/
         if (DH_get_nid(dh) != NID_undef) {
-            /*
-             * The safe prime group code sets N = 2*s
-             * (where s = max security strength supported).
-             * N = dh->length (N = maximum bit length of private key)
-             */
+            int max_strength =
+                    ifc_ffc_compute_security_bits(BN_num_bits(dh->params.p));
+
             if (dh->params.q == NULL
                 || dh->length > BN_num_bits(dh->params.q))
                 goto err;
+            /* dh->length = maximum bit length of generated private key */
             if (!ffc_generate_private_key(ctx, &dh->params, dh->length,
-                                          dh->length / 2, priv_key))
+                                          max_strength, priv_key))
                 goto err;
         } else {
 #ifdef FIPS_MODE
diff --git a/crypto/dh/dh_lib.c b/crypto/dh/dh_lib.c
index 3643cb1471..7e42d13f3c 100644
--- a/crypto/dh/dh_lib.c
+++ b/crypto/dh/dh_lib.c
@@ -209,7 +209,8 @@ void DH_get0_pqg(const DH *dh,
 
 int DH_set0_pqg(DH *dh, BIGNUM *p, BIGNUM *q, BIGNUM *g)
 {
-    /* If the fields p and g in d are NULL, the corresponding input
+    /*
+     * If the fields p and g in d are NULL, the corresponding input
      * parameters MUST be non-NULL.  q may remain NULL.
      */
     if ((dh->params.p == NULL && p == NULL)
@@ -217,7 +218,9 @@ int DH_set0_pqg(DH *dh, BIGNUM *p, BIGNUM *q, BIGNUM *g)
         return 0;
 
     ffc_params_set0_pqg(&dh->params, p, q, g);
-    dh->params.nid = NID_undef;
+    dh_cache_named_group(dh);
+    if (q != NULL)
+        dh->length = BN_num_bits(q);
     /*
      * Check if this is a named group. If it finds a named group then the
      * 'q' and 'length' value are either already set or are set by the
@@ -260,6 +263,7 @@ int DH_set0_key(DH *dh, BIGNUM *pub_key, BIGNUM *priv_key)
     if (priv_key != NULL) {
         BN_clear_free(dh->priv_key);
         dh->priv_key = priv_key;
+        dh->length = BN_num_bits(priv_key);
     }
 
     dh->dirty_cnt++;
@@ -335,7 +339,7 @@ int dh_ffc_params_fromdata(DH *dh, const OSSL_PARAM params[])
 
     ret = ffc_params_fromdata(ffc, params);
     if (ret) {
-        DH_get_nid(dh);
+        dh_cache_named_group(dh);
         dh->dirty_cnt++;
     }
     return ret;
diff --git a/crypto/dh/dh_local.h b/crypto/dh/dh_local.h
index 7fefcf76f3..3b0181f76a 100644
--- a/crypto/dh/dh_local.h
+++ b/crypto/dh/dh_local.h
@@ -21,7 +21,8 @@ struct dh_st {
     int pad;
     int version;
     FFC_PARAMS params;
-    int32_t length;             /* optional value of N (if there is no q) */
+    /* max generated private key length (can be less than len(q)) */
+    int32_t length;
     BIGNUM *pub_key;            /* g^x % p */
     BIGNUM *priv_key;           /* x */
     int flags;
diff --git a/crypto/dsa/dsa_key.c b/crypto/dsa/dsa_key.c
index 1d625272e5..f9bb3470f6 100644
--- a/crypto/dsa/dsa_key.c
+++ b/crypto/dsa/dsa_key.c
@@ -74,6 +74,11 @@ static int dsa_keygen(DSA *dsa, int pairwise_test)
         priv_key = dsa->priv_key;
     }
 
+    /*
+     * For FFC FIPS 186-4 keygen
+     * security strength s = 112,
+     * Max Private key size N = len(q)
+     */
     if (!ffc_generate_private_key(ctx, &dsa->params, BN_num_bits(dsa->params.q),
                                   MIN_STRENGTH, priv_key))
         goto err;
diff --git a/crypto/ffc/ffc_key_generate.c b/crypto/ffc/ffc_key_generate.c
index 4e2f231d83..aeabae010f 100644
--- a/crypto/ffc/ffc_key_generate.c
+++ b/crypto/ffc/ffc_key_generate.c
@@ -10,7 +10,6 @@
 #include "internal/ffc.h"
 
 /*
- * For Fips mode:
  * SP800-56Ar3 5.6.1.1.4 Key pair generation by testing candidates.
  * Generates a private key in the interval [1, min(2 ^ N - 1, q - 1)].
  *
@@ -23,32 +22,18 @@
 int ffc_generate_private_key(BN_CTX *ctx, const FFC_PARAMS *params,
                              int N, int s, BIGNUM *priv)
 {
-#ifdef FIPS_MODE
-    return ffc_generate_private_key_fips(ctx, params, N, s, priv);
-#else
-    do {
-        if (!BN_priv_rand_range_ex(priv, params->q, ctx))
-            return 0;
-    } while (BN_is_zero(priv) || BN_is_one(priv));
-    return 1;
-#endif /* FIPS_MODE */
-}
-
-int ffc_generate_private_key_fips(BN_CTX *ctx, const FFC_PARAMS *params,
-                                  int N, int s, BIGNUM *priv)
-{
     int ret = 0, qbits = BN_num_bits(params->q);
     BIGNUM *m, *two_powN = NULL;
 
-    /* Step (2) : check range of N */
-    if (N < 2 * s || N > qbits)
-        return 0;
-
     /* Deal with the edge case where the value of N is not set */
-    if (N == 0) {
+    if (N == 0)
         N = qbits;
+    if (s == 0)
         s = N / 2;
-    }
+
+    /* Step (2) : check range of N */
+    if (N < 2 * s || N > qbits)
+        return 0;
 
     two_powN = BN_new();
     /* 2^N */