Are Matrices Useful in Public-Key Cryptography?

Abstract

The discrete logarithm problem is the most prolific cryptographic primitive in use. Though the most important ones are the DiffieHellman problem and the decision Diffie-Hellman problem. In this paper, we discuss the discrete logarithm problem in circulant matrices – providing many particular secure instances. We compare the discrete logarithm problem in circulant matrices with that of the discrete logarithm problem in finite fields and with the discrete logarithm problem in the group of rational points of an elliptic curve.