SM2 Curve

SM2 algorithm is an extension based on ecc (Elliptic Curves Cryptography).

TIP

1. For an introduction to the curve principle, refer to SM2 Algorithm Understanding, or refer to SM2 Official Document (National Cryptography Administration December 2010).

2. GM/T 0003-2012 The standard recommended parameter is sm2p256v1 (NID_sm2).

3. If you need to use other curves for SM2, call [GMSm2Utils setCurveType:] and pass in the int type.

4. The three most common curves listed in the GMSm2Utils header file enumeration are sm2p256v1, secp256k1, and secp256r1.

5. If you need other curves, you can find them in the OpenSSL source code crypto/ec/ec_curve.c and pass in the int type.

GMCurveType definition

The GMCurveType defined in the GMSm2Utils.h header file corresponds to the curve parameters as shown below:

ECC recommended parameters: sm2p256v1 (corresponding to NID_sm2 in OpenSSL)
p   = FFFFFFFE FFFFFFFF FFFFFFFF FFFFFFFF FFFFFFFF 00000000 FFFFFFFF FFFFFFFF
a   = FFFFFFFE FFFFFFFF FFFFFFFF FFFFFFFF FFFFFFFF 00000000 FFFFFFFF FFFFFFFC
b   = 28E9FA9E 9D9F5E34 4D5A9E4B CF6509A7 F39789F5 15AB8F92 DDBCBD41 4D940E93
n   = FFFFFFFE FFFFFFFF FFFFFFFF FFFFFFFF 7203DF6B 21C6052B 53BBF409 39D54123
Gx =  32C4AE2C 1F198119 5F990446 6A39C994 8FE30BBF F2660BE1 715A4589 334C74C7
Gy =  BC3736A2 F4F6779C 59BDCEE3 6B692153 D0A9877C C62A4740 02DF32E5 2139F0A0

ECC recommended parameters: secp256k1 (corresponding to NID_secp256k1 in OpenSSL)
p   = FFFFFFFF FFFFFFFF FFFFFFFF FFFFFFFF FFFFFFFF FFFFFFFF FFFFFFFE FFFFFC2F
a   = 00000000 00000000 00000000 00000000 00000000 00000000 00000000 00000000
b   = 00000000 00000000 00000000 00000000 00000000 00000000 00000000 00000007
n   = FFFFFFFF FFFFFFFF FFFFFFFF FFFFFFFE BAAEDCE6 AF48A03B BFD25E8C D0364141
Gx =  79BE667E F9DCBBAC 55A06295 CE870B07 029BFCDB 2DCE28D9 59F2815B 16F81798
Gy =  483ADA77 26A3C465 5DA4FBFC 0E1108A8 FD17B448 A6855419 9C47D08F FB10D4B8

ECC recommended parameters: secp256r1 (corresponding to NID_X9_62_prime256v1 in OpenSSL)
p   = FFFFFFFF 00000001 00000000 00000000 00000000 FFFFFFFF FFFFFFFF FFFFFFFF
a   = FFFFFFFF 00000001 00000000 00000000 00000000 FFFFFFFF FFFFFFFF FFFFFFFC
b   = 5AC635D8 AA3A93E7 B3EBBD55 769886BC 651D06B0 CC53B0F6 3BCE3C3E 27D2604B
n   = FFFFFFFF 00000000 FFFFFFFF FFFFFFFF BCE6FAAD A7179E84 F3B9CAC2 FC632551
Gx  = 6B17D1F2 E12C4247 F8BCE6E5 63A440F2 77037D81 2DEB33A0 F4A13945 D898C296
Gy  = 4FE342E2 FE1A7F9B 8EE7EB4A 7C0F9E16 2BCE3357 6B315ECE CBB64068 37BF51F5