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 cl ass of matrices which have exactly two 1's in each row and each column is defined, and their properties are investigated to facilitate the c onstruction of these algorithms. The time complexities of these algori thms are studied and found to have O(n) n-bit word operations.