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:

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

C:\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.

Last update: 2019.

Table of Contents

 About This Book

 Geometric Introduction to Elliptic Curves

 Algebraic Introduction to Elliptic Curves

 Abelian Group and Elliptic Curves

 Discrete Logarithm Problem (DLP)

 Finite Fields

 Generators and Cyclic Subgroups

 Reduced Elliptic Curve Groups

 Elliptic Curve Subgroups

 tinyec - Python Library for ECC

EC (Elliptic Curve) Key Pair

 EC Private and Public Key Pair

 Is EC Private Key Secure

 EC Private Key Example - secp256k1

Generate secp256k1 Keys with OpenSSL

 EC Key in PEM File Format

 EC Key File with Curve Name

 Create EC Public Key File

 ECDH (Elliptic Curve Diffie-Hellman) Key Exchange

 ECDSA (Elliptic Curve Digital Signature Algorithm)

 ECES (Elliptic Curve Encryption Scheme)

 Terminology

 References

 Full Version in PDF/EPUB