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AcceptableShort Weierstrass

GC256C

GC256C is the 256-bit GOST curve CryptoPro-B (id-GostR3410-2001-CryptoPro-B-ParamSet).

GC256C is a short Weierstrass curve y² = x³ + ax + b over a 256-bit prime field with a 256-bit prime-order subgroup and cofactor 1; its estimated security level is 128 bits. Status: secure, but regional or niche.

GC256C was defined for GOST R 34.10-2001 in RFC 4357 §11.4 and is kept as paramSetC by GOST R 34.10-2012 (RFC 9215). It is y² = x³ − 3x + b over the prime 2^255 + 3225, with prime order.

TLS lists it as group GC256C with signature scheme gostr34102012_256c (RFC 9189, RFC 9367).

Names in standards

StandardName
IANA TLS (RFC 9189)GC256C
TC 26id-tc26-gost-3410-2012-256-paramSetC
RFC 4357id-GostR3410-2001-CryptoPro-B-ParamSet

Object identifiers

Domain parameters

256-bit prime field · about 128-bit security

Field prime p
0x8000000000000000000000000000000000000000000000000000000000000c99
Coefficient a
0x8000000000000000000000000000000000000000000000000000000000000c96
Coefficient b
0x3e1af419a269a5f866a7d3c25c3df80ae979259373ff2b182f49d4ce7e1bbc8b
Base point x
0x1
Base point y
0x3fa8124359f96680b83d1c3eb2c070e5c545c9858d03ecfb744bf8d717717efc
Order n of the base point
0x800000000000000000000000000000015f700cfff1a624e5e497161bcc8a198f
Cofactor h
0x1

Used in

  • GOST R 34.10-2012 signatures
  • TLS 1.2 and 1.3 GOST cipher suites (RFC 9189, RFC 9367)
  • Russian government PKI

Identifiers in registries

TLS supported groups
GC256C 0x0024
TLS signature schemes
gostr34102012_256c 0x070B

Standards and references

All curves