Cryptanalysis of a key exchange protocol based on the endomorphisms ring End(Z(p) x Z(p2))
Climent et al. (Appl Algebra Eng Commun Comput 22:91-108, 2011) identified the elements of the endomorphisms ring End(Z(p) x Z(p2)) with elements in a set, E (p) , of matrices of size 2 x 2, whose elements in the first row belong to Z(p) and the elements in the second row belong to Z(p2). By taking advantage of matrix arithmetic, they proposed a key exchange protocol using polynomial functions over E-p defined by polynomials in Z[X]. In this note, we show that this protocol is insecure; it can be broken by solving a set of 10 consistent homogeneous linear equations in 8 unknowns over Z(p2).
cryptanalysis key exchange protocol endomorphism noncommutative ring