Generate secp256k1 Keys with OpenSSL

EC Cryptography Tutorials - Herong's Tutorial Examples

∟Generate secp256k1 Keys with OpenSSL

This section provides a tutorial example on how to generate EC (Elliptic Curve) private and public key pairs using secp256k1 domain parameters.

You can also use OpenSSL command line tool to generate EC (Elliptic Curve) private and public key pairs using secp256k1 domain parameters. For example:

herong> openssl ecparam -genkey -name secp256k1 \
   -out ec_key.pem -param_enc explicit

herong> openssl ec -in ec_key.pem -noout -text

read EC key
Private-Key: (256 bit)
priv:
    00:90:f4:55:61:b5:a4:3d:a2:7f:35:70:63:48:bf:
    86:a4:75:9b:23:8a:58:a0:ed:db:24:2a:a2:64:d0:
    f0:2f:55
pub:
    04:f2:56:c6:e6:c8:0b:21:3f:2a:a0:b0:17:44:23:
    5d:51:5c:59:44:35:be:65:1b:15:88:3a:10:dd:47:
    2f:a6:46:ce:62:ea:f3:67:0d:c5:cb:91:00:a0:ca:
    2a:55:b2:c1:47:c1:e9:a3:8c:e4:28:87:8e:7d:46:
    e1:fb:71:4a:99
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)

Note that OpenSSL prints out the generator point G as single value by combining its 2 coordinates in a format of: 0x04<G.x><G.y>. So the above Generator value is really:

G = (x, y)
  = (0x79be667ef9dcbbac55a06295ce870b07029bfcdb2dce28d959f2815b16f81798,
     0x483ada7726a3c4655da4fbfc0e1108a8fd17b448a68554199c47d08ffb10d4b8)

The public key is also a point and printed as a single value by combining its 2 coordinates in a format of: 0x04<x><y>. So the above "pub" value is really:

pub = (x, y)
  = (0xf256c6e6c80b213f2aa0b01744235d515c594435be651b15883a10dd472fa646,
     0xce62eaf3670dc5cb9100a0ca2a55b2c147c1e9a38ce428878e7d46e1fb714a99)

This private is called a 256-bit key, because it has 64 hexadecimal digits, which is 32-byte/256-bit long, or 2²⁵⁶ large. Note that the first two 0x00 digits should not be counted.