Chaos-Based Bitwise Dynamical Pseudorandom Number Generator on FPGA
Abstract : In this paper, a new pseudorandom number generator (PRNG) based on the logistic map has been proposed. To prevent the system to fall into short period orbits as well as increasing the randomness of the generated sequences, the proposed algorithm dynamically changes the parameters of the chaotic system. This PRNG has been implemented in a Virtex 7 field-programmable gate array (FPGA) with a 32-bit fixed point precision, using a total of 510 lookup tables (LUTs) and 120 registers. The sequences generated by the proposed algorithm have been subjected to the National Institute of Standards and Technology (NIST) randomness tests, passing all of them. By comparing the randomness with the sequences generated by a raw 32-bit logistic map, it is shown that, by using only an additional 16% of LUTs, the proposed PRNG obtains a much better performance in terms of randomness, increasing the NIST passing rate from 0.252 to 0.989. Finally, the proposed bitwise dynamical PRNG is compared with other chaos-based realizations previously proposed, showing great improvement in terms of resources and randomness.
? Many of these systems, however, present some correlations or short periods, which make them unsuitable for many applications.
? In this context, chaos-based PRNGs have arisen as a good alternative, thanks to their properties of pergodicity, and random like behavior.
? In this paper, we propose a random generator based on the logistic map that, in order to improve its statistical properties, dynamically changes its chaotic parameter.
? The sequences have passed all of these tests, proving that they are undistinguishable from a truly random sequence.
? It has been applied to a simpler chaotic map than the skew tent map the logistic map, obtaining a cost-effective high-performance PRNG.
? A possible strategy to reduce this problem consists on using bigger word lengths.
? In this paper, this issue has been solved using an alternative approach that improves the random properties of a chaotic PRNG by using a small number of extra resources.
? These generators are usually slow, requiring considerably more storage space and lose their chaotic properties during computations. These major problems restrict their use as generators.
? However, despite a large number of papers published in the field of chaos-based pseudorandom generators, the impact of this research is rather marginal.
• In this paper, we propose a random generator based on the logistic map that, in order to improve its statistical properties, dynamically changes its chaotic parameter.
• The main contribution of this work will presents better randomness results than other PRNG with required very small amount of resources to implementation on FPGA.
• This new technique of Galois and Fibonacci will increases better randomness in this Enhanced PRNG and it will take very less resources of area, delay and power.
• The proposed PRNG achieves better randomness than other commonly used PRNGs such as a 32-order LFSR or a glibc LCG.
? It has been applied to a simpler chaotic map than the skew tent map, the logistic map, obtaining a cost-effective high-performance PRNG.
? This PRNG with previously proposed chaos-based PRNGs proves the good performance of the proposed system, especially in terms of resources and quality of randomness.
? Some of the most commonly used PRNGs are based on linear congruential generators (LCG) or linear feedback shift registers (LFSR).
? To be able to compare the number of used resources with other previously proposed algorithms, the number of slices has been estimated from the number of LUTs and registers assuming unrelated logic.
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