shigoto-dev19 / classic-elgamal-circom

This repository is featuring a classic ElGamal Scheme implementation in Circom with focus on experimenting with exponentiation in a circuit. Note that this implementation is intentionally insecure and designed for educational purposes.

Description

• Classic ElGamal Scheme Circuit in Circom
• Additively Homomorphic Properties (secret encoding => generator^secret)
• Mainly for playing around with Exponentiation which is quite challenging in circom.
• Note:
  • This implementation is not secure and only meant for learning purposes!
  • For further details, refer to the Security section.

Documentation

See this notion page that I wrote for better Understanding Secure ElGamal Encryption Scheme.

Build

npm install to install all dependencies

Test

npm test to run Typescript & Circuit tests.

Note: If you have an error complaining about circom version run rm -rf "./node_modules/circom" to fix the error.

Security

• Similar to DH encryption, the security of ElGamal Encryption Scheme is based on the assumption of the Discrete Logarithm Problem (DLP).

• The recommended size for both private keys and public keys should be at least 2,048 bits size-wise (617digits).

• The private & public keys are constrained to the size of the field element which is around 254 bits ==> The Classic ElGamal implementation in circom is not secure!

• 2²⁵³ already overflows 253-bit unsigned integer ==> to prevent overflows, the possible maximum exponent value is 252.

• Since 2²⁵³ can be described inside the circom integer range(the circom prime number is larger than 2²⁵³) ==> not secure for cryptographic algorithms based on the DLP assupmtion.

• For this POC implementation, the maximum size for the secret is chosen to be ~254 bits which increased the security a little bit but caused overflows that inhibited the homomorphic properties of ElGamal Scheme.