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DeprecatedBinary Weierstrass

sect163r2

sect163r2 (NIST B-163) is a pseudo-random curve over the binary field GF(2^163); NIST has deprecated it.

sect163r2 is a binary Weierstrass curve y² + xy = x³ + ax² + b over the binary field GF(2^163) with a 163-bit prime-order subgroup and cofactor 2; its estimated security level is 80 bits. Status: deprecated, do not use for new keys.

sect163r2 is y² + xy = x³ + x² + b over GF(2^163) 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 80 bits of security.

FIPS 186-2 to 186-4 listed it as B-163. NIST SP 800-186 (2023) deprecates every curve over a binary field, and RFC 8422 deprecated them for TLS. At about 80 bits of security it is also below the 112-bit minimum, so NIST treats it as legacy-use only. OpenSSL can be built without binary-curve support (no-ec2m).

Names in standards

StandardName
SEC 2sect163r2
NIST FIPS 186-4 (withdrawn)B-163

Object identifiers

Domain parameters

binary field GF(2^163) · about 80-bit security

Field degree m
0xa3
Reduction polynomial f
0x800000000000000000000000000000000000000c9
Coefficient a
0x1
Coefficient b
0x20a601907b8c953ca1481eb10512f78744a3205fd
Base point x
0x3f0eba16286a2d57ea0991168d4994637e8343e36
Base point y
0xd51fbc6c71a0094fa2cdd545b11c5c0c797324f1
Order n of the base point
0x40000000000000000000292fe77e70c12a4234c33
Cofactor h
0x2

Used in

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

Identifiers in registries

TLS supported groups
sect163r2 0x0003

Standards and references

All curves