Matrix manipulations of cryptographic functions arerevisited. TheDiscrete logarithm function and the Diffie Hellman mapping can beexpressed as products of Vandermonde matrices. First we consider orbits ofrepeated applications of the cryptographic transformations. The difficulty tocompute the cryptographic function (in other terms the robustness of the cryptosystem)is related to the length of the orbit. We determine it either by computationalexperiments or with theoretical tools. We investigate the behaviour of powersof matrices constructed from the generators α of the multiplicative group forseveral primes p in Zp. We study how the sequence of powers of these matricesleads to the identity matrix in respect to the generator α, the prime numbers pand the elements of the main diagonal of the matrices. Finally, the matrix factorizationapproach (LU factorization) is revisited.
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