Elgamal

Implementation of Elgamal algorithm in Python, based on these series of videos (the parameter nomenclature is based on them).

Public and private keys are composed of 3 elements each:

• Kpub = (p, alfa, B)

• Kpriv = (p, alfa, b)

These parameters are:

• p (parameter -m): A random integer

• alfa (parameter -a): A generator of Zp

• b (parameter -b): A secret integer between 2 and (p-2)

• B (parameter -B): A public modular exponentiation calculated as B = (alfa^(b))mod(p)

Encryption

For the encryption process, it is necessary to add --encrypt, the parameters of the public key (-p, -a and -B) and the plaintext message (parameter -m). The verbose parameter (-vv) is optional:

python3 main.py --encrypt -p 79 -a 30 -B 59 -m 44 -vv

Decryption

For the decryption process, it is necessary to add --decrypt, the parameters of the private key (-p, -a and -b), the encrypted message (parameter -m) and the ephemeral key received with the message (-ke). The verbose parameter (-vv) is optional:

python3 main.py --decrypt -p 79 -a 30 -b 61 -m 73 -ke 13 -vv

Signature

For the signing process, it is necessary to add --sign, the parameters of the private key (-p, -a and -b) and the plaintext message (parameter -m). The verbose parameter (-vv) is optional:

python3 main.py --sign -p 541 -a 128 -b 105 -m 95 -vv

Signature verification

For the signature verification process, it is necessary to add --verify, the parameters of the public key (-p, -a and -B), the plaintext message (parameter -m) and the signature parameters (-r and -s):

python3 main.py --verify -p 541 -a 128 -B 239 -m 95 -r 280 -s 65 -vv