sect163k1 (NIST K-163) is a Koblitz curve over the binary field GF(2^163); NIST has deprecated it.
sect163k1 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.
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). sect163k1 uses a = 1, the degree-163 reduction polynomial f shown above and cofactor 2, for about 80 bits of security.
FIPS 186-2 to 186-4 listed it as K-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).