Modified Public Key Cryptosystem Based On Circulant Matrix

Abstract

Experts believe that public key cryptosystems on non-commutative algebraic structures are resistant to the attack of quantum algorithms. In recent years, public key cryptosystems based on Polynomial Symmetrical Decomposition (PSD) on the non-commutative group have been developed. However, they are vulnerable to direct attack, linearization equations attack, and overdefined systems of multivariate polynomial equations attack. This cryptosystem has also been improved by experts. However, the operation of the proposed PSD Improvement still uses complex computing and untested. Therefore in this paper, we replace PSD on a non-commutative group into a non-commutative matrix group. We chose the circulant matrix on the key agreement protocol and the key distribution. The results show that the cryptosystem proposed on the circulant matrix is resistant to direct attack, linearization equations attack, and overdefined systems of multivariate polynomial equations attack.