Key generation of algebraic-code cryptosystems

The purpose of this paper is to efficiently generate large nonsingular matrix (S, S^-1) pairs and permutation matrices over the binary field using short keys. The motivation of this work is to provide a solution to the long-key problem in algebraic-code cryptosystems. A special class of matrices which have exactly two 1's in each row and each column is defined, and their properties are investigated to facilitate the construction of these algorithms. The time complexities of these algorithms are studied and found to have O(n) n-bit word operations.