"Secret- and Public-key Cryptosystems from Group Factorizations"
We describe two possible approaches to the construction of new, secret- and
public-key cryptosystems with message space a large finite group G. These
schemes utilize certain factorization bases for G, called "logarithmic
signatures", and their generalizations. The first scheme relies on the
fact that the permutations on G induced by transversal logarithmic signatures
almost always generate the full symmetric group on G. The second approach
is based on trap-door, one-way functions, induced by objects we call "meshes"
which cover G uniformly. This approach could potentially lead to new, general,
Spyros Magliveras is "Henson Professor Emeritus" at the University of Nebraska -
Lincoln, and Professor of Mathematical Sciences at Florida Atlantic University.
He is Coordinator of the Applied Mathematics Program, and Director of the
"Cryptology and Computer Security Initiative" at Florida Atlantic University.