A new public-key cryptosystem family based on feedback shift registers

Abstract

Nearly all public-key cryptographic algorithms are based on hard problems of number theory, which are related to each other. That is to say, if one of these algorithms is broken, the other's security will be threatened. This work presents a new public-key ciphering mechanism that isn't based on any of the classic cryptographical problems. The method consists of permuting the elements of the field GF(2/sup L/). The permutation is constructed by composition of bijective transitions based on the feedback functions of the feedback shift registers. The permutation algorithm is transmitted as a nonlinear equation system, where the difficulty of solving it conveys the security of the cipher. At the implementation level, the proposed scheme makes use of NLFSR (non-linear feedback shift registers), modifying the feedback function at each iteration. The resulting ciphering mechanism is able to generate any permutation.