A genetic algorithm for computing the k-error linear complexity of cryptographic sequences

Some cryptographical applications use pseudorandom sequences and require that the sequences are secure in the sense that they cannot be recovered by only knowing a small amount of consecutive terms. Such sequences should therefore have a large linear complexity and also a large k-error linear complexity. Efficient algorithms for computing the kerror linear complexity of a sequence over a finite field only exist for sequences of period equal to a power of the characteristic of the field. It is therefore useful to find a general and efficient algorithm to compute a good approximation of the k-error linear complexity. In this paper we investigate the design of a genetic algorithm to approximate the k-error linear complexity of a sequence. Our preliminary experiments show that the genetic algorithm approach is suitable to the problem and that a good scheme would use a medium sized population, an elitist type of selection, a special design of the two point random crossover and a standard random mutation. The algorithm outputs an approximative value of the k-error linear complexity which is on average only 19.5% higher than the exact value. This paper intends to be a proof of concept that the genetic algorithm technique is suitable for the problem in hand and future research will further refine the choice of parameters.