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DeprecatedBinary Weierstrass

sect571r1

sect571r1 (NIST B-571) is a pseudo-random curve over the binary field GF(2^571); NIST has deprecated it.

sect571r1 is a binary Weierstrass curve y² + xy = x³ + ax² + b over the binary field GF(2^571) with a 570-bit prime-order subgroup and cofactor 2; its estimated security level is 256 bits. Status: deprecated, do not use for new keys.

sect571r1 is y² + xy = x³ + x² + b over GF(2^571) 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 256 bits of security.

FIPS 186-2 to 186-4 listed it as B-571. 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 2sect571r1
NIST FIPS 186-4 (withdrawn)B-571

Object identifiers

Domain parameters

binary field GF(2^571) · about 256-bit security

Field degree m
0x23b
Reduction polynomial f
0x80000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000425
Coefficient a
0x1
Coefficient b
0x2f40e7e2221f295de297117b7f3d62f5c6a97ffcb8ceff1cd6ba8ce4a9a18ad84ffabbd8efa59332be7ad6756a66e294afd185a78ff12aa520e4de739baca0c7ffeff7f2955727a
Base point x
0x303001d34b856296c16c0d40d3cd7750a93d1d2955fa80aa5f40fc8db7b2abdbde53950f4c0d293cdd711a35b67fb1499ae60038614f1394abfa3b4c850d927e1e7769c8eec2d19
Base point y
0x37bf27342da639b6dccfffeb73d69d78c6c27a6009cbbca1980f8533921e8a684423e43bab08a576291af8f461bb2a8b3531d2f0485c19b16e2f1516e23dd3c1a4827af1b8ac15b
Order n of the base point
0x3ffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffe661ce18ff55987308059b186823851ec7dd9ca1161de93d5174d66e8382e9bb2fe84e47
Cofactor h
0x2
Seed
0x2aa058f73a0e33ab486b0f610410c53a7f132310

Used in

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

Identifiers in registries

TLS supported groups
sect571r1 0x000E

Standards and references

All curves