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DeprecatedShort Weierstrass

brainpoolP192r1

brainpoolP192r1 is the 192-bit Brainpool curve of RFC 5639, with parameters derived verifiably from the digits of π and e.

brainpoolP192r1 is a short Weierstrass curve y² = x³ + ax + b over a 192-bit prime field with a 192-bit prime-order subgroup and cofactor 1; its estimated security level is 96 bits. Status: deprecated, do not use for new keys.

The Brainpool curves (RFC 5639) were generated in a verifiably pseudo-random way: the primes come from the digits of π and the curve coefficients from the digits of e, so anyone can recompute them (RFC 5639 Appendix A). brainpoolP192r1 is the 192-bit random curve; it has prime order (cofactor 1) and about 96 bits of security.

At about 96 bits of security it is too small for new keys (NIST SP 800-57 requires at least 112 bits). NIST SP 800-186 lists the Brainpool curves solely for interoperability.

Names in standards

StandardName
RFC 5639brainpoolP192r1

Object identifiers

Domain parameters

192-bit prime field · about 96-bit security

Field prime p
0xc302f41d932a36cda7a3463093d18db78fce476de1a86297
Coefficient a
0x6a91174076b1e0e19c39c031fe8685c1cae040e5c69a28ef
Coefficient b
0x469a28ef7c28cca3dc721d044f4496bcca7ef4146fbf25c9
Base point x
0xc0a0647eaab6a48753b033c56cb0f0900a2f5c4853375fd6
Base point y
0x14b690866abd5bb88b5f4828c1490002e6773fa2fa299b8f
Order n of the base point
0xc302f41d932a36cda7a3462f9e9e916b5be8f1029ac4acc1
Cofactor h
0x1

Standards and references

All curves