**EC Cryptography Tutorials - Herong's Tutorial Examples** - v1.02, by Dr. Herong Yang

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 2^{256} large.
Note that the first two 0x00 digits should not be counted.

Table of Contents

Geometric Introduction to Elliptic Curves

Algebraic Introduction to Elliptic Curves

Abelian Group and Elliptic Curves

Discrete Logarithm Problem (DLP)

Generators and Cyclic Subgroups

tinyec - Python Library for ECC

EC Private and Public Key Pair

EC Private Key Example - secp256k1

►Generate secp256k1 Keys with OpenSSL

ECDH (Elliptic Curve Diffie-Hellman) Key Exchange

ECDSA (Elliptic Curve Digital Signature Algorithm)