openssl ec 命令查看椭圆曲线参数信息

openssl 列出所有曲线

openssl ecparam -list_curves

secp112r1 : SECG/WTLS curve over a 112 bit prime field
secp112r2 : SECG curve over a 112 bit prime field
secp128r1 : SECG curve over a 128 bit prime field
secp128r2 : SECG curve over a 128 bit prime field
secp160k1 : SECG curve over a 160 bit prime field
secp160r1 : SECG curve over a 160 bit prime field
secp160r2 : SECG/WTLS curve over a 160 bit prime field
secp192k1 : SECG curve over a 192 bit prime field
secp224k1 : SECG curve over a 224 bit prime field
secp224r1 : NIST/SECG curve over a 224 bit prime field
secp256k1 : SECG curve over a 256 bit prime field
secp384r1 : NIST/SECG curve over a 384 bit prime field
secp521r1 : NIST/SECG curve over a 521 bit prime field
prime192v1: NIST/X9.62/SECG curve over a 192 bit prime field
prime192v2: X9.62 curve over a 192 bit prime field
prime192v3: X9.62 curve over a 192 bit prime field
prime239v1: X9.62 curve over a 239 bit prime field
prime239v2: X9.62 curve over a 239 bit prime field
prime239v3: X9.62 curve over a 239 bit prime field
prime256v1: X9.62/SECG curve over a 256 bit prime field
sect113r1 : SECG curve over a 113 bit binary field
sect113r2 : SECG curve over a 113 bit binary field
sect131r1 : SECG/WTLS curve over a 131 bit binary field
sect131r2 : SECG curve over a 131 bit binary field
sect163k1 : NIST/SECG/WTLS curve over a 163 bit binary field
sect163r1 : SECG curve over a 163 bit binary field
sect163r2 : NIST/SECG curve over a 163 bit binary field
sect193r1 : SECG curve over a 193 bit binary field
sect193r2 : SECG curve over a 193 bit binary field
sect233k1 : NIST/SECG/WTLS curve over a 233 bit binary field
sect233r1 : NIST/SECG/WTLS curve over a 233 bit binary field
sect239k1 : SECG curve over a 239 bit binary field
sect283k1 : NIST/SECG curve over a 283 bit binary field
sect283r1 : NIST/SECG curve over a 283 bit binary field
sect409k1 : NIST/SECG curve over a 409 bit binary field
sect409r1 : NIST/SECG curve over a 409 bit binary field
sect571k1 : NIST/SECG curve over a 571 bit binary field
sect571r1 : NIST/SECG curve over a 571 bit binary field
c2pnb163v1: X9.62 curve over a 163 bit binary field
c2pnb163v2: X9.62 curve over a 163 bit binary field
c2pnb163v3: X9.62 curve over a 163 bit binary field
c2pnb176v1: X9.62 curve over a 176 bit binary field
c2tnb191v1: X9.62 curve over a 191 bit binary field
c2tnb191v2: X9.62 curve over a 191 bit binary field
c2tnb191v3: X9.62 curve over a 191 bit binary field
c2pnb208w1: X9.62 curve over a 208 bit binary field
c2tnb239v1: X9.62 curve over a 239 bit binary field
c2tnb239v2: X9.62 curve over a 239 bit binary field
c2tnb239v3: X9.62 curve over a 239 bit binary field
c2pnb272w1: X9.62 curve over a 272 bit binary field
c2pnb304w1: X9.62 curve over a 304 bit binary field
c2tnb359v1: X9.62 curve over a 359 bit binary field
c2pnb368w1: X9.62 curve over a 368 bit binary field
c2tnb431r1: X9.62 curve over a 431 bit binary field
wap-wsg-idm-ecid-wtls1: WTLS curve over a 113 bit binary field
wap-wsg-idm-ecid-wtls3: NIST/SECG/WTLS curve over a 163 bit binary field
wap-wsg-idm-ecid-wtls4: SECG curve over a 113 bit binary field
wap-wsg-idm-ecid-wtls5: X9.62 curve over a 163 bit binary field
wap-wsg-idm-ecid-wtls6: SECG/WTLS curve over a 112 bit prime field
wap-wsg-idm-ecid-wtls7: SECG/WTLS curve over a 160 bit prime field
wap-wsg-idm-ecid-wtls8: WTLS curve over a 112 bit prime field
wap-wsg-idm-ecid-wtls9: WTLS curve over a 160 bit prime field
wap-wsg-idm-ecid-wtls10: NIST/SECG/WTLS curve over a 233 bit binary field
wap-wsg-idm-ecid-wtls11: NIST/SECG/WTLS curve over a 233 bit binary field
wap-wsg-idm-ecid-wtls12: WTLS curve over a 224 bit prime field
Oakley-EC2N-3:
Oakley-EC2N-4:
brainpoolP160r1: RFC 5639 curve over a 160 bit prime field
brainpoolP160t1: RFC 5639 curve over a 160 bit prime field
brainpoolP192r1: RFC 5639 curve over a 192 bit prime field
brainpoolP192t1: RFC 5639 curve over a 192 bit prime field
brainpoolP224r1: RFC 5639 curve over a 224 bit prime field
brainpoolP224t1: RFC 5639 curve over a 224 bit prime field
brainpoolP256r1: RFC 5639 curve over a 256 bit prime field
brainpoolP256t1: RFC 5639 curve over a 256 bit prime field
brainpoolP320r1: RFC 5639 curve over a 320 bit prime field
brainpoolP320t1: RFC 5639 curve over a 320 bit prime field
brainpoolP384r1: RFC 5639 curve over a 384 bit prime field
brainpoolP384t1: RFC 5639 curve over a 384 bit prime field
brainpoolP512r1: RFC 5639 curve over a 512 bit prime field
brainpoolP512t1: RFC 5639 curve over a 512 bit prime field
SM2 : SM2 curve over a 256 bit prime field

openssl 生成EC 参数文件

openssl ecparam -name secp256k1

-----BEGIN EC PARAMETERS-----
BgUrgQQACg==
-----END EC PARAMETERS-----

openssl ecparam -name secp256k1 -out secp256k1.pem

openssl 查看同线的基点(Generator)，阶(Order)

openssl ecparam -in secp256k1.pem -text -param_enc explicit -noout

Field Type: prime-field
Prime:
00:ff:ff:ff:ff:ff:ff:ff:ff:ff:ff:ff:ff:ff:ff:
ff:ff:ff:ff:ff:ff:ff:ff:ff:ff:ff:ff:ff:fe:ff:
ff:fc:2f
A: 0
B: 7 (0x7)
Generator (uncompressed):
04:79:be:66:7e:f9:dc:bb:ac:55:a0:62:95:ce:87:
0b:07:02:9b:fc:db:2d:ce:28:d9:59:f2:81:5b:16:
f8:17:98:48:3a:da:77:26:a3:c4:65:5d:a4:fb:fc:
0e:11:08:a8:fd:17:b4:48:a6:85:54:19:9c:47:d0:
8f:fb:10:d4:b8
Order:
00:ff:ff:ff:ff:ff:ff:ff:ff:ff:ff:ff:ff:ff:ff:
ff:fe:ba:ae:dc:e6:af:48:a0:3b:bf:d2:5e:8c:d0:
36:41:41
Cofactor: 1 (0x1)

openssl 查看　NISTp256的曲线参数

openssl ecparam -name prime256v1
openssl ecparam -name prime256v1 -out prime256v1.pem

openssl ecparam -in prime256v1.pem -text -param_enc explicit -noout

Field Type: prime-field
Prime:
00:ff:ff:ff:ff:00:00:00:01:00:00:00:00:00:00:
00:00:00:00:00:00:ff:ff:ff:ff:ff:ff:ff:ff:ff:
ff:ff:ff
A:
00:ff:ff:ff:ff:00:00:00:01:00:00:00:00:00:00:
00:00:00:00:00:00:ff:ff:ff:ff:ff:ff:ff:ff:ff:
ff:ff:fc
B:
5a:c6:35:d8:aa:3a:93:e7:b3:eb:bd:55:76:98:86:
bc:65:1d:06:b0:cc:53:b0:f6:3b:ce:3c:3e:27:d2:
60:4b
Generator (uncompressed):
04:6b:17:d1:f2:e1:2c:42:47:f8:bc:e6:e5:63:a4:
40:f2:77:03:7d:81:2d:eb:33:a0:f4:a1:39:45:d8:
98:c2:96:4f:e3:42:e2:fe:1a:7f:9b:8e:e7:eb:4a:
7c:0f:9e:16:2b:ce:33:57:6b:31:5e:ce:cb:b6:40:
68:37:bf:51:f5
Order:
00:ff:ff:ff:ff:00:00:00:00:ff:ff:ff:ff:ff:ff:
ff:ff:bc:e6:fa:ad:a7:17:9e:84:f3:b9:ca:c2:fc:
63:25:51
Cofactor: 1 (0x1)
Seed:
c4:9d:36:08:86:e7:04:93:6a:66:78:e1:13:9d:26:
b7:81:9f:7e:90

openssl 查看　SM2曲线的参数

openssl ecparam -name SM2 -out SM2.pem
openssl ecparam -in SM2.pem -text -param_enc explicit -noout

Field Type: prime-field
Prime:
00:ff:ff:ff:fe:ff:ff:ff:ff:ff:ff:ff:ff:ff:ff:
ff:ff:ff:ff:ff:ff:00:00:00:00:ff:ff:ff:ff:ff:
ff:ff:ff
A:
00:ff:ff:ff:fe:ff:ff:ff:ff:ff:ff:ff:ff:ff:ff:
ff:ff:ff:ff:ff:ff:00:00:00:00:ff:ff:ff:ff:ff:
ff:ff:fc
B:
28:e9:fa:9e:9d:9f:5e:34:4d:5a:9e:4b:cf:65:09:
a7:f3:97:89:f5:15:ab:8f:92:dd:bc:bd:41:4d:94:
0e:93
Generator (uncompressed):
04:32:c4:ae:2c:1f:19:81:19:5f:99:04:46:6a:39:
c9:94:8f:e3:0b:bf:f2:66:0b:e1:71:5a:45:89:33:
4c:74:c7:bc:37:36:a2:f4:f6:77:9c:59:bd:ce:e3:
6b:69:21:53:d0:a9:87:7c:c6:2a:47:40:02:df:32:
e5:21:39:f0:a0
Order:
00:ff:ff:ff:fe:ff:ff:ff:ff:ff:ff:ff:ff:ff:ff:
ff:ff:72:03:df:6b:21:c6:05:2b:53:bb:f4:09:39:
d5:41:23
Cofactor: 1 (0x1)

openssl 生成EC 私钥

openssl ecparam -in secp256k1.pem -genkey -noout -out secp256k1-key.pem
openssl ecparam -name secp256k1 -genkey -noout -out secp256k1-key.pem
cat secp256k1-key.pem 

-----BEGIN EC PRIVATE KEY-----
MHQCAQEEIC3sGk59MeFBA4sZQLJ2XHzhSIhFMmsxJChp6TKfrAtOoAcGBSuBBAAK
oUQDQgAExrW0lB2mH5ROP6u7eTH7N4/SKBRn9CGyS/p/3hMTjOGz3vwnH+35ymmv
+HiERIl7Zy+EfACJ6EO8fSTGrI8jrA==
-----END EC PRIVATE KEY-----

openssl ecparam -in SM2.pem -text -noout

ASN1 OID: SM2

openssl ecparam -in secp256k1.pem -text -noout

ASN1 OID: secp256k1

openssl EC 根据私钥生成公钥

openssl ec -in secp256k1-key.pem -pubout

read EC key
writing EC key
-----BEGIN PUBLIC KEY-----
MFYwEAYHKoZIzj0CAQYFK4EEAAoDQgAExrW0lB2mH5ROP6u7eTH7N4/SKBRn9CGy
S/p/3hMTjOGz3vwnH+35ymmv+HiERIl7Zy+EfACJ6EO8fSTGrI8jrA==
-----END PUBLIC KEY-----

openssl ec -in secp256k1-key.pem -pubout -out secp256k1-pubkey.pem

cat secp256k1-pubkey.pem
-----BEGIN PUBLIC KEY-----
MFYwEAYHKoZIzj0CAQYFK4EEAAoDQgAExrW0lB2mH5ROP6u7eTH7N4/SKBRn9CGy
S/p/3hMTjOGz3vwnH+35ymmv+HiERIl7Zy+EfACJ6EO8fSTGrI8jrA==
-----END PUBLIC KEY-----

openssl ec -in secp256k1-key.pem -pubout -outform DER -out secp256k1-key.der

openssl ec 帮助查看　

openssl ecparam help
openssl ec help

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