On Public Key Cryptosystem Based On The Word Problem In A Group


  • Nacer Ghadbane Laboratory of Pure and Applied Mathematics, Department of Mathematics, University of M’sila, Algeria




Group, Word in a group, Word problem in a group, Combinatorial group theory, Public key cryptography


One of the classical problems in mathematics is the word problem in a group. The difficulty and complexity for solving this problem is used in most of the cryptosystems. For a fixed set of elements S = {S1, … , Sn} in group G, a word in S is any expression of the sort    …  where the exponents  are positive or negative integers, and . The word problem in a group G with respect to a subset S = {S1, … , Sn} is the question of telling whether two words in S are equal. It is known that in general the word problem is undecidable, meaning that there is no algorithm to solve it. In this paper, we introduce a cryptosystem based on the word problem in a group G.