A secret key cryptosystem based on certain factorization bases (called logarithmic signature) for finite permutation groups was described by Magliveras in the late 1970's and its algebraic properties were studied by Magliveras and Memon in 1989. We presently announce a new method whereby logarithmic signatures can be used to construct a new type of public key cryptosystem. The new system relies on the fact that there exist non-transversal logarithmic signatures which (loosely speaking) can be written as the (functional) composition of a small number (usually two) transversal logarithmic signatures. Since transversal logarithmic signatures can be inverted efficiently, while non-transversal ones can not, such a factorization can be used as a trap door for a public key cryptosystem. Examples are constructed in the smallest carrier group where this is possible, and algorithms for constructing such trap doors in the general case are discussed.

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