In this paper we study the MOR cryptosystem with finite Chevalley groups. There are four infinite families of finite classical Chevalley groups. These are: special linear groups SL(d, q), orthogonal groups O(d, q) and symplectic groups Sp(d, q). The family O(d, q) splits to two different families of Chevalley groups depending on the parity of d. The MOR cryptosystem over SL(d, q) was studied by...

In this paper, which is a sequel of PSV], we develop a completely elementary approach to calculations in Chevalley groups G = G((; R) of types = E 6 and E 7 over a commutative ring R using only the weight diagrams (alias, crystal graphs) of their minimal modules. After an elementary construction of a crystal base we explicitly describe action of root subgroups and of the extended Weyl group, mu...