In this paper, we establish, as a generalization of a result on the classical homological dimensions of commutative rings, an upper bound on the Gorenstein global dimension of commutative rings using the global cotorsion dimension of rings. We use this result to compute the Gorenstein global dimension of some particular cases of trivial extensions of rings and of group rings.

The objective of this work is to survey several digital signatures proposed in the last decade using non-commuta-tive groups and rings and propose a digital signature using non-commutative groups and analyze its security.