One Random Jump and One Permutation: Sufficient Conditions to Chaotic, Statistically Faultless, and Large Throughput PRNG for FPGA

Abstract

Sub-categories of mathematical topology, like the mathematical theory of chaos, offer interesting applications devoted to information security. In this research work, we have introduced a new chaos-based pseudorandom number generator implemented in FPGA, which is mainly based on the deletion of a Hamilton cycle within the n-cube (or on the vectorial negation), plus one single permutation. By doing so, we produce a kind of post-treatment on hardware pseudorandom generators, but the obtained generator has usually a better statistical profile than its input, while running at a similar speed. We tested 6 combinations of Boolean functions and strategies that all achieve to pass the most stringent TestU01 battery of tests. This generation can reach a throughput/latency ratio equal to 6.7 Gbps, being thus the second fastest FPGA generator that can pass TestU01.

Survey on hardware implementation of random number generators on FPGA: Theory and experimental analyses

“…Two new families have then been proposed, which are based on chaotic iterations [111] [112] (CIPRNG-XOR) on FPGA/ASIC on the one hand, and on the deletion of an Hamilton Cycle [113] on the other hand. This latter has to satisfy some balance properties: the associated Markov chain on the ncube must be close enough to the uniform distribution.…”

“…PRNGs based on chaotic iterations, for their part, need to embed linear PRNGs for their strategies: on the one hand, CIPRNG-XOR uses 3 PRNGs, while on the other hand ICGPRNG manipulates only one, but with a permutation function. Figure 17b illustrates the superiority of chaotic iterations family, in which the differential PRNG based Euler optimization [103], an optimized logistic map [82], and these PRNG based chaotic iterations [113] have the largest throughput in this category of chaotic generators. Regarding the Throughput/Area ratio in Figure 17c, the chaotic PRNG based on LCGM [79] outperforms all the other linear PRNGs: the ratio is 4.1 times more efficient than the second best one [107], which is a chaotic iterations generator based on BBS and XORshift.…”

A Mathematically Generated Noise Technique for Ultrasound Systems

“…Two-post modules in hardware-based number generators were implemented to improve the randomness of linear PRNGs [20]. A chaos-based random number generator in a field-programmable gate array (FPGA) was implemented to achieve higher statistical capability in hardware [21]. Recent random-bit generation techniques for medical imaging applications between years 2018 and 2022 are summarized here.…”

Dynamics on Binary Relations over Topological Spaces

“…It is worth mentioning that the study of dynamics over finite graphs has been recently considered by Bahi et al by setting links between Devaney chaos and strong connectivity in order to provide an algorithm for the generation of strongly connected graphs and to construct Pseudo Random Number Generators (PRNGs) [6]. This approach has also allowed for the obtainment of PRNGs based on the construction of Hamiltonian cycles over an N-cube [7,8]. It is also worth mentioning that such results can also be considered in connection with finite state machines [9] and explained using Turing machines [10].…”