ElGamal signature scheme in Go

This repo contains implementation for the full cycle ELGamal scheme algorithms working with bigInts. For digest function was used SHA256. Package contains group parameters generator (working on fast PCs only).

Default params

By default this ElGamal implementation working with this group:

p:       FromHex("FFFFFFFFFFFFFFFFC90FDAA22168C234C4C6628B80DC1CD129024E088A67CC74020BBEA63B139B22514A08798E3404DDEF9519B3CD3A431B302B0A6DF25F14374FE1356D6D51C245E485B576625E7EC6F44C42E9A637ED6B0BFF5CB6F406B7EDEE386BFB5A899FA5AE9F24117C4B1FE649286651ECE45B3DC2007CB8A163BF0598DA48361C55D39A69163FA8FD24CF5F83655D23DCA3AD961C62F356208552BB9ED529077096966D670C354E4ABC9804F1746C08CA18217C32905E462E36CE3BE39E772C180E86039B2783A2EC07A28FB5C55DF06F4C52C9DE2BCBF6955817183995497CEA956AE515D2261898FA051015728E5A8AAAC42DAD33170D04507A33A85521ABDF1CBA64ECFB850458DBEF0A8AEA71575D060C7DB3970F85A6E1E4C7ABF5AE8CDB0933D71E8C94E04A25619DCEE3D2261AD2EE6BF12FFA06D98A0864D87602733EC86A64521F2B18177B200CBBE117577A615D6C770988C0BAD946E208E24FA074E5AB3143DB5BFCE0FD108E4B82D120A92108011A723C12A787E6D788719A10BDBA5B2699C327186AF4E23C1A946834B6150BDA2583E9CA2AD44CE8DBBBC2DB04DE8EF92E8EFC141FBECAA6287C59474E6BC05D99B2964FA090C3A2233BA186515BE7ED1F612970CEE2D7AFB81BDD762170481CD0069127D5B05AA993B4EA988D8FDDC186FFB7DC90A6C08F4DF435C934063199FFFFFFFFFFFFFFFF"),
bitSize: 4096,
g: FromHex("2"),

The prime is: 2^4096 - 2^4032 - 1 + 2^64 * { [2^3966 pi] + 240904 } Its hexadecimal value is:

  FFFFFFFF FFFFFFFF C90FDAA2 2168C234 C4C6628B 80DC1CD1
  29024E08 8A67CC74 020BBEA6 3B139B22 514A0879 8E3404DD
  EF9519B3 CD3A431B 302B0A6D F25F1437 4FE1356D 6D51C245
  E485B576 625E7EC6 F44C42E9 A637ED6B 0BFF5CB6 F406B7ED
  EE386BFB 5A899FA5 AE9F2411 7C4B1FE6 49286651 ECE45B3D
  C2007CB8 A163BF05 98DA4836 1C55D39A 69163FA8 FD24CF5F
  83655D23 DCA3AD96 1C62F356 208552BB 9ED52907 7096966D
  670C354E 4ABC9804 F1746C08 CA18217C 32905E46 2E36CE3B
  E39E772C 180E8603 9B2783A2 EC07A28F B5C55DF0 6F4C52C9
  DE2BCBF6 95581718 3995497C EA956AE5 15D22618 98FA0510
  15728E5A 8AAAC42D AD33170D 04507A33 A85521AB DF1CBA64
  ECFB8504 58DBEF0A 8AEA7157 5D060C7D B3970F85 A6E1E4C7
  ABF5AE8C DB0933D7 1E8C94E0 4A25619D CEE3D226 1AD2EE6B
  F12FFA06 D98A0864 D8760273 3EC86A64 521F2B18 177B200C
  BBE11757 7A615D6C 770988C0 BAD946E2 08E24FA0 74E5AB31
  43DB5BFC E0FD108E 4B82D120 A9210801 1A723C12 A787E6D7
  88719A10 BDBA5B26 99C32718 6AF4E23C 1A946834 B6150BDA
  2583E9CA 2AD44CE8 DBBBC2DB 04DE8EF9 2E8EFC14 1FBECAA6
  287C5947 4E6BC05D 99B2964F A090C3A2 233BA186 515BE7ED
  1F612970 CEE2D7AF B81BDD76 2170481C D0069127 D5B05AA9
  93B4EA98 8D8FDDC1 86FFB7DC 90A6C08F 4DF435C9 34063199
  FFFFFFFF FFFFFFFF

The generator is: 2.

Signing and Verifying

Currently, package contains only unstable version of signature, that means that you can't sign message with your own key pair. To sign message you have to use UnstableSignature functions that takes []byte to sign and returns pointer to signature and key pair. To verify signature you have to know message itself and public key of user's signature.

Example:

message := "Modern programming languages are fast."

signature, keypair := elgamal.UnstableSignature(message)
// verify signature struct with public key
fmt.Println(signature.Verify([]byte(message), keypair.GetPublic()))

Encrypt and decrypt

To encrypt data in ElGamal scheme you have to know public key of recipient and to decrypt data recipient has to use encrypted data and his own private key. This encryption implementation returns pointer to []Cypher struct. System works with data of any length.

Example:

message := "Modern programming languages are fast. Call me Ishmael. Some years ago-never mind how long precisely-having little or no money in my purse, and nothing particular to interest me on shore, I thought I would sail about a little and see the watery part of the world. Call me Ishmael. Some years ago-never mind how long precisely-having little or no money in my purse, and nothing particular to interest me on shore, I thought I would sail about a little and see the watery part of the world. Modern programming languages are fast. "
	
// cypher our data through Encrypt function that returns list of Cypher structs
make_cypher := elgamal.Encrypt([]byte(message), alice_keyPair.GetPublic())
// decrypt data using decrypt function that takes *[]Cypher and private key of recipient
plain_data := elgamal.Decrypt(make_cypher, alice_keyPair.GetPrivate())

// check decrypted data
parseToText := string(plain_data)
fmt.Println(parseToText)