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DeprecatedBinary Weierstrass

sect283k1

sect283k1 (NIST K-283) is a Koblitz curve over the binary field GF(2^283); NIST has deprecated it.

sect283k1 is a binary Weierstrass curve y² + xy = x³ + ax² + b over the binary field GF(2^283) with a 281-bit prime-order subgroup and cofactor 4; its estimated security level is 128 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). sect283k1 uses a = 0, the degree-283 reduction polynomial f shown above and cofactor 4, for about 128 bits of security.

FIPS 186-2 to 186-4 listed it as K-283. 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 2sect283k1
NIST FIPS 186-4 (withdrawn)K-283

Object identifiers

Domain parameters

binary field GF(2^283) · about 128-bit security

Field degree m
0x11b
Reduction polynomial f
0x800000000000000000000000000000000000000000000000000000000000000000010a1
Coefficient a
0x0
Coefficient b
0x1
Base point x
0x503213f78ca44883f1a3b8162f188e553cd265f23c1567a16876913b0c2ac2458492836
Base point y
0x1ccda380f1c9e318d90f95d07e5426fe87e45c0e8184698e45962364e34116177dd2259
Order n of the base point
0x1ffffffffffffffffffffffffffffffffffe9ae2ed07577265dff7f94451e061e163c61
Cofactor h
0x4

Used in

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

Identifiers in registries

TLS supported groups
sect283k1 0x0009

Standards and references

All curves