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Title

Bijective Function with Domain in N and Image in the Set of Permutations: An Application to Cryptography

Author

V?ctor M. SilvaGarc?a, Cornelio Y??ezM?rquez, Juan L. D?az de Le?nSantiago

Citation 
Vol. 7 No. 4 pp. 117124

Abstract

In this work an algorithm is constructed that counts n! permutations in n1 steps. Actually, the algorithm defines a bijective function from the natural numbers to the set of permutations. In addition, for any permutation ¥ðL defined over the positions of a string of length L, where L is a multiple of 3, this permutation may be constructed by means of 3 permutations over strings of length ¨øL. This allows for the definition of an iterative cryptosystem over blocks of 96 characters, with numbers in the range of 1090 instead of 10154, approximately. It is also shown that the set of keys grows factorially, so that the number of elements of the set reaches 2500 when working with strings of 96 characters. Finally, by means of an example the iterative cryptosystem using the DES boxes and strings of 96 characters is illustrated.

Keywords

JV Theorem, Factorial Theorem, Factorial Cryptosystem, Permutations.

URL

http://paper.ijcsns.org/07_book/200704/20070416.pdf

