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DeprecatedBinary Weierstrass

sect233k1

sect233k1 (NIST K-233) is a Koblitz curve over the binary field GF(2^233); NIST has deprecated it.

sect233k1 is a binary Weierstrass curve y² + xy = x³ + ax² + b over the binary field GF(2^233) with a 232-bit prime-order subgroup and cofactor 4; its estimated security level is 112 bits. Status: deprecated, do not use for new keys.

Koblitz curves are binary curves y² + xy = x³ + ax² + 1 with a = 0 or 1; their Frobenius endomorphism lets implementations replace point doublings with cheap squarings (τ-adic scalar multiplication). sect233k1 uses a = 0, the degree-233 reduction polynomial f shown above and cofactor 4, for about 112 bits of security.

FIPS 186-2 to 186-4 listed it as K-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 2sect233k1
NIST FIPS 186-4 (withdrawn)K-233

Object identifiers

Domain parameters

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

Field degree m
0xe9
Reduction polynomial f
0x20000000000000000000000000000000000000004000000000000000001
Coefficient a
0x0
Coefficient b
0x1
Base point x
0x17232ba853a7e731af129f22ff4149563a419c26bf50a4c9d6eefad6126
Base point y
0x1db537dece819b7f70f555a67c427a8cd9bf18aeb9b56e0c11056fae6a3
Order n of the base point
0x8000000000000000000000000000069d5bb915bcd46efb1ad5f173abdf
Cofactor h
0x4

Used in

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

Identifiers in registries

TLS supported groups
sect233k1 0x0006

Standards and references

All curves