Abstract.
A symmetric key cryptosystem based on logarithmic signature s for finite permutation groups was described by the first author in [6], and its algebraic properties were studied in [7]. In this paper we describe two possible approaches to the construction of new public key cryptosystems with message space a large finite group G , using logarithmic signature s and their generalizations. The first approach relies on the fact that permutations of the message space G induced by transversal logarithmic signature s almost always generate the full symmetric group S G on the message space. The second approach could potentially lead to new ElGamal-like systems based on trapdoor, one-way functions induced by logarithmic signature -like objects we call meshes , which are uniform covers for G .
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Magliveras, Stinson & van Trung, T. New Approaches to Designing Public Key Cryptosystems Using One-Way Functions and Trapdoors in Finite Groups . J. Cryptology 15, 285–297 (2002). https://doi.org/10.1007/s00145-001-0018-3
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DOI: https://doi.org/10.1007/s00145-001-0018-3