Cryptographic Hardening of d-Sequences

This paper shows how a one-way mapping using majority information on adjacent bits will improve the randomness of d-sequences. Introduction In a recent article, Anthes [1] summarizes recent results in generating true random numbers. In particular, it mentions the work at Intel Corp. to use thermal noise on the central processing unit of the computer as random number generator (RNG) [2]. This is not unlike the RNGs based on quantum processes that have been proposed elsewhere [3]. Quantum processes come with their own uncertainty [4]-[7]. Randomness is generally measured in terms of probability or of complexity. From the lens of probability, all binary sequences of length n are equivalent. From the point of view of complexity, randomness will depend on the algorithm that has been used to generate the sequence. Ritter provides a summary of several measures of algorithmic complexity [8] and, therefore, also of randomness. In this article, we will investigate results of a method of cryptographic strengthening of RNGs. Basically, the idea is to apply a many–to-one mapping to the binary output of the RNG, increasing the complexity of reverse process. We show that by using a 3-to-1 mapping where each group of three 0s and 1s is replaced by whatever the majority improves the autocorrelation function of the resultant sequence in some cases. This will be tried both for the Windows based RNGs as well as d-sequences [9-17], that are “decimal sequences” in an arbitrary base, although binary (base-2) sequences are the ones considered here. D-sequences have found several applications in cryptography and they are of particular interest since any random sequence can be represented as a d-sequence (Figure 1). Randomness measured by Autocorrelation Function For simplicity, we consider only the autocorrelation function as measure of randomness. The value of the autocorrelation is defined as in the equation below: