Linear Feedback Shift Register Optimizations

Abstract

One actual problem in cryptography is to find a generator which must carry out some conditions asked by the beneficiary. There are presented some interesting and new results concerning the complexity of the combinations of linear feedback shift registers (Schneier [7]). These combination can be described in terms of boolean function theory using the logical operators like sum and product. There are also introduced the notion of spliting (a generalization of classical term of decimation) and the inverse operator called interleave. The presented results have applications in cryptography, more exactly, to the construction of some chipher system which are used in simetric-key encryption for high-level safety-comunications(Zeng [3]). Also, the present exposure approaches the power of the generator to attack.

2000 Mathematics Subject Classification. Primary 94A55; Secondary 11T71, 68P25.
Key words and phrases. LFSR. Berlekamp Massey Cryptographyc attack.