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DeprecatedBinary Weierstrass

sect233r1

sect233r1 (NIST B-233) is a pseudo-random curve over the binary field GF(2^233); NIST has deprecated it.

sect233r1 is a binary Weierstrass curve y² + xy = x³ + ax² + b over the binary field GF(2^233) with a 233-bit prime-order subgroup and cofactor 2; its estimated security level is 112 bits. Status: deprecated, do not use for new keys.

sect233r1 is y² + xy = x³ + x² + b over GF(2^233) with the reduction polynomial f shown above; b was derived from the listed seed with SHA-1 (ANSI X9.62). The group has cofactor 2 and about 112 bits of security.

FIPS 186-2 to 186-4 listed it as B-233. NIST SP 800-186 (2023) deprecates every curve over a binary field, and RFC 8422 deprecated them for TLS. OpenSSL can be built without binary-curve support (no-ec2m).

Names in standards

StandardName
SEC 2sect233r1
NIST FIPS 186-4 (withdrawn)B-233

Object identifiers

Domain parameters

binary field GF(2^233) · about 112-bit security

Field degree m
0xe9
Reduction polynomial f
0x20000000000000000000000000000000000000004000000000000000001
Coefficient a
0x1
Coefficient b
0x66647ede6c332c7f8c0923bb58213b333b20e9ce4281fe115f7d8f90ad
Base point x
0xfac9dfcbac8313bb2139f1bb755fef65bc391f8b36f8f8eb7371fd558b
Base point y
0x1006a08a41903350678e58528bebf8a0beff867a7ca36716f7e01f81052
Order n of the base point
0x1000000000000000000000000000013e974e72f8a6922031d2603cfe0d7
Cofactor h
0x2
Seed
0x74d59ff07f6b413d0ea14b344b20a2db049b50c3

Used in

  • Legacy TLS 1.2 (RFC 8422)
  • Legacy X.509 certificates

Identifiers in registries

TLS supported groups
sect233r1 0x0007

Standards and references

All curves