Abstract
Let G be a finite group and let A i 1 ≤ i ≤ s, be subsets of G where ¦A i ¦ ≥ 2, 1 ≤ i ≤ s and s ≥ 2. We say that (A1, A2,..., A3) is a factorization of G if and only if for each g ε G there is exactly one way to express g = a 1 a 1 a 2··· a 3, where a j ε A i , 1 ≤ i ≤ s.
The problem of finding factorizations of this type was first introduced by Hajos [3] in 1941. Since then a number of papers have appeared on the subject. More recently, Magliveras [6] has applied factorization of permutation groups to cryptography to obtain a private-key cryptosystem. Factorizations in the elementary abelian p-group were exploited (but not explicitly stated in these terms) by Webb [13] to produce a public-key cryptosystem conceptually similar to cryptosystems based on the knapsack problem.
Using the result that certain types of factorizations in the elementary abelian p-group are necessarily transversal (a term introduced by Magliveras), this paper shows that the public-key system proposed by Webb is insecure.
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Communicated by Johannes A. Buchmann
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Qu, M., Vanstone, S.A. Factorizations in the elementary Abelian p-group and their cryptographic significance. J. Cryptology 7, 201–212 (1994). https://doi.org/10.1007/BF00203963
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DOI: https://doi.org/10.1007/BF00203963