EC Cryptography Tutorials - Herong's Tutorial Examples

∟EC (Elliptic Curve) Key Pair

∟EC Key File with Curve Name

This section provides a tutorial example on the EC private key file with curve name only. Actuall domain parameters are not stored in the key file.

If your private key is generated from a named elliptic curve, you can store the curve name instead of domain parameters to reduce the key file size.

Let's generate another EC private key with OpenSSL and keep the curve name only: 

herong> openssl ecparam -genkey -name secp256k1 \
   -out ec_key_with_name.pem

herong> type ec_key_with_name.pem
-----BEGIN EC PARAMETERS-----
BgUrgQQACg==
-----END EC PARAMETERS-----
-----BEGIN EC PRIVATE KEY-----
MHQCAQEEICT5ZF/xctNhmSRpX9c05KnCwQDxHLUWz0CK9rSZQKbqoAcGBSuBBAAK
oUQDQgAEvQinrrTC12K1irns23vh7VR//Z/hXR0Yx545HNDZ/hm4rhRjj1T3X3Pe
KITUKm1oUC1zs5nphvkN+4mhNI14ew==
-----END EC PRIVATE KEY-----

herong> openssl ec -in ec_key_with_name
.pem -noout -text
read EC key
Private-Key: (256 bit)
priv:
    24:f9:64:5f:f1:72:d3:61:99:24:69:5f:d7:34:e4:
    a9:c2:c1:00:f1:1c:b5:16:cf:40:8a:f6:b4:99:40:
    a6:ea
pub:
    04:bd:08:a7:ae:b4:c2:d7:62:b5:8a:b9:ec:db:7b:
    e1:ed:54:7f:fd:9f:e1:5d:1d:18:c7:9e:39:1c:d0:
    d9:fe:19:b8:ae:14:63:8f:54:f7:5f:73:de:28:84:
    d4:2a:6d:68:50:2d:73:b3:99:e9:86:f9:0d:fb:89:
    a1:34:8d:78:7b
ASN1 OID: secp256k1

As you can see, domain parameters are replaced with the curve name: secp256k1.

ec_key_with_name.pem is a valid EC private key, as long as your application knows domain parameters of the given curve name: secp256k1.

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)

 EC Cryptography in Java

 Standard Elliptic Curves

 Terminology

 References

 Full Version in PDF/EPUB