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DeprecatedBinary Weierstrass

sect283r1

sect283r1 (NIST B-283) is a pseudo-random curve over the binary field GF(2^283); NIST has deprecated it.

sect283r1 is a binary Weierstrass curve y² + xy = x³ + ax² + b over the binary field GF(2^283) with a 282-bit prime-order subgroup and cofactor 2; its estimated security level is 128 bits. Status: deprecated, do not use for new keys.

sect283r1 is y² + xy = x³ + x² + b over GF(2^283) 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 128 bits of security.

FIPS 186-2 to 186-4 listed it as B-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 2sect283r1
NIST FIPS 186-4 (withdrawn)B-283

Object identifiers

Domain parameters

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

Field degree m
0x11b
Reduction polynomial f
0x800000000000000000000000000000000000000000000000000000000000000000010a1
Coefficient a
0x1
Coefficient b
0x27b680ac8b8596da5a4af8a19a0303fca97fd7645309fa2a581485af6263e313b79a2f5
Base point x
0x5f939258db7dd90e1934f8c70b0dfec2eed25b8557eac9c80e2e198f8cdbecd86b12053
Base point y
0x3676854fe24141cb98fe6d4b20d02b4516ff702350eddb0826779c813f0df45be8112f4
Order n of the base point
0x3ffffffffffffffffffffffffffffffffffef90399660fc938a90165b042a7cefadb307
Cofactor h
0x2
Seed
0x77e2b07370eb0f832a6dd5b62dfc88cd06bb84be

Used in

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

Identifiers in registries

TLS supported groups
sect283r1 0x000A

Standards and references

All curves