MQ based identification signatures

This project is a part of an term paper project in my 4th semester course E0 213 (Quantum safe cryptography) instructed by Prof. Sanjit Chatterjee at IISc Bangalore. It is a joint report with Shubh Prakash, a senior student at IISc. A small abstract is presented below:

“MQDSS (Multivariate Quadratic Digital Signature Scheme) is a cryptographic signature scheme based on the hardness of solving multivariate quadratic (MQ) equations, a problem considered resistant to attacks by quantum computers. Unlike traditional cryptographic methods, which rely on number-theoretic problems like factoring or discrete logarithms, MQDSS leverages the difficulty of solving systems of quadratic equations over finite fields, making it a strong candidate for post-quantum cryptography.

MQDSS is particularly notable for its efficiency and compactness, offering relatively small signature sizes compared to other post-quantum signature schemes. It utilizes a Fiat-Shamir transform applied to an identification scheme based on the MQ problem, which ensures security by reducing the signature verification process to checking the validity of a quadratic equation system. Due to its robust security guarantees and efficiency, MQDSS is a promising candidate for securing communications in the post-quantum era, where quantum-resistant cryptographic methods will be essential.”