Construct Public Key Encryption Scheme Using Ergodic Matrices over GF(2)

摘要

This paper proposes a new public key encryption scheme. It is based on the difficulty of deducing x and y from A and B = x · A · y in a specific monoid (m, ·) which is noncommutative. So we select and do research work on the certain monoid which is formed by all the n×n matrices over finite field F_2 under multiplication. By the cryptographic properties of an "ergodic matrix", we propose a hard problem based on the ergodic matrices over F_2, and use it construct a public key encryption scheme.