Applications of probabilistic combiners on linear feedback shift register sequences

Abstract

Cryptography forms the backbone of modern secure communication. Many different methods are available for encrypting and decrypting data, each with advantages and disadvantages. If communicating parties require speed of encryption more than incredibly robust security, they may use a stream cipher, which is based on generating long strings of bits with linear feedback shift registers (LFSRs), then making those strings cryptographically secure by combining them with a nonlinear Boolean function called a combiner. In this thesis, we investigate a modification to the classical combiner method by introducing a (nonsecure) probabilistic randomization to the order in which the LFSRs are input into the combiner function at each bit. We implemented two different designs for the probabilistic combiner: one that randomly ordered four LFSRs and put them into a four-variable Boolean function, and another that selected only three out of four LFSRs to use as inputs in a three-variable function. Our tests on the resulting output strings show a drastic increase in complexity, while simultaneously passing the stringent randomness tests required by the National Institute of Standards and Technology for pseudorandom numbers.