brainpoolP224t1 is a short Weierstrass curve y² = x³ + ax + b over a 224-bit prime field with a 224-bit prime-order subgroup and cofactor 1; its estimated security level is 112 bits. Status: still secure, being phased out.
Each Brainpool 'r1' curve has a 't1' counterpart obtained through an isomorphism over GF(p) — the parameter Z of RFC 5639 §3 maps (x, y) to (Z²x, Z³y) — that turns a into −3, which allows faster point doubling. The two curves have isomorphic groups of the same prime order and the same security level (about 112 bits). See brainpoolP224r1.
TLS, JOSE and COSE register only the r1 curves; the t1 forms appear as X.509 OIDs (RFC 5639 §4.1) and in libraries such as OpenSSL and Bouncy Castle.
Names in standards
| Standard | Name |
|---|
| RFC 5639 | brainpoolP224t1 |
Domain parameters
224-bit prime field · about 112-bit security
- Field prime p
- 0xd7c134aa264366862a18302575d1d787b09f075797da89f57ec8c0ff
- Coefficient a
- 0xd7c134aa264366862a18302575d1d787b09f075797da89f57ec8c0fc
- Coefficient b
- 0x4b337d934104cd7bef271bf60ced1ed20da14c08b3bb64f18a60888d
- Base point x
- 0x6ab1e344ce25ff3896424e7ffe14762ecb49f8928ac0c76029b4d580
- Base point y
- 0x374e9f5143e568cd23f3f4d7c0d4b1e41c8cc0d1c6abd5f1a46db4c
- Order n of the base point
- 0xd7c134aa264366862a18302575d0fb98d116bc4b6ddebca3a5a7939f
- Cofactor h
- 0x1
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