Cryptanalysis of Some Protocols Using Matrices over Group Rings
نویسنده
چکیده
It is important to search for easily implementable groups, for which the DL problem is hard and there is no known subexponential time algorithm for computing DL. The group of points over Fq of an elliptic curve is such a group. In [8], the group of invertible matrices with coefficients in a finite field was considered for such a key exchange. In [6], using the Jordan form it was shown that the discrete logarithm problem on such matrices can be reduced to the same problem over some small extensions of the finite base field. In [4], the authors consider the semigroup of matrices ( 3-by-3 matrices) over the group ring F7[S5], where S5 is the group of permutation of {1, 2, 3, 4, 5}. The security of this protocol is based on the supposed difficulty of the discrete logarithm problem in the (semi) group of matrices with coefficients in F7[S5].
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