paramSetB, published with paramSetA in RFC 7836 §5.1.1, is y² = x³ − 3x + b over the prime 2^511 + 111 and has prime order.
TLS lists it as group GC512B with signature scheme gostr34102012_512b (RFC 9189, RFC 9367).
AcceptableShort Weierstrass
GC512B
GC512B (id-tc26-gost-3410-12-512-paramSetB) is a 512-bit curve of GOST R 34.10-2012.
GC512B is a short Weierstrass curve y² = x³ + ax + b over a 512-bit prime field with a 512-bit prime-order subgroup and cofactor 1; its estimated security level is 256 bits. Status: secure, but regional or niche.
Names in standards
| Standard | Name |
|---|---|
| IANA TLS (RFC 9189) | GC512B |
| TC 26 | id-tc26-gost-3410-12-512-paramSetB |
Object identifiers
- 1.2.643.7.1.2.1.2.2id-tc26-gost-3410-12-512-paramSetB
Domain parameters
512-bit prime field · about 256-bit security
- Field prime p
- 0x8000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000006f
- Coefficient a
- 0x8000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000006c
- Coefficient b
- 0x687d1b459dc841457e3e06cf6f5e2517b97c7d614af138bcbf85dc806c4b289f3e965d2db1416d217f8b276fad1ab69c50f78bee1fa3106efb8ccbc7c5140116
- Base point x
- 0x2
- Base point y
- 0x1a8f7eda389b094c2c071e3647a8940f3c123b697578c213be6dd9e6c8ec7335dcb228fd1edf4a39152cbcaaf8c0398828041055f94ceeec7e21340780fe41bd
- Order n of the base point
- 0x800000000000000000000000000000000000000000000000000000000000000149a1ec142565a545acfdb77bd9d40cfa8b996712101bea0ec6346c54374f25bd
- 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
- GC512B 0x0027
- TLS signature schemes
- gostr34102012_512b 0x070E
Standards and references
- RFC 7836 §5.1.1: Guidelines on the Cryptographic Algorithms to Accompany the Usage of Standards GOST R 34.10-2012 and GOST R 34.11-2012
- RFC 9215 §4.2: Using GOST R 34.10-2012 and GOST R 34.11-2012 Algorithms with the Internet X.509 PKI
- RFC 9189: GOST Cipher Suites for TLS Protocol Version 1.2
- RFC 9367: GOST Cipher Suites for TLS Protocol Version 1.3