Journal of Applied Mathematics & Bioinformatics
Handling problems in cryptography with matrix factorization
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Abstract
Matrix manipulations of cryptographic functions are revisited. TheDiscrete logarithm function and the Diffie Hellman mapping can be expressed as products of Vandermonde matrices. First we consider orbits of repeated applications of the cryptographic transformations. The difficulty to compute the cryptographic function (in other terms the robustness of the cryptosystem) is related to the length of the orbit. We determine it either by computational experiments or with theoretical tools. We investigate the behaviour of powers of matrices constructed from the generators á of the multiplicative group for several primes p in Zp. We study how the sequence of powers of these matrices leads to the identity matrix in respect to the generator á, the prime numbers p and the elements of the main diagonal of the matrices. Finally, the matrix factorization approach (LU factorization) is revisited.
