Pseudo-Chaotic Lossy Compressors for True Random Number Generation

Abstract

This paper presents a compression method that\ud exploits pseudo-chaotic systems, to be applied to True Random\ud Bit Generators (TRBGs). The theoretical explanation of the\ud proposed compression scheme required the projection of some\ud results achieved within the Ergodic Theory for chaotic systems\ud on the world of digital pseudo-chaos. To this aim, a weaker and\ud more general interpretation of the Shadowing Theory has been\ud proposed, focusing on probability measures, rather than on single chaotic trajectories. The design of the compression scheme has been theoretically discussed in order to assure the final entropy of the compressed TRBG to be arbitrarily close to the maximum\ud limit of 1 bit/time-step. The proposed solution requires extremely\ud low-complex hardware circuits for being implemented, assures a\ud constant throughput and is based on theoretical results of general validity

Pseudo-chaotic lossy compression of TRBGs

“…The similarity between (10) and (13) Let us focus on the Average Shannon Entropy of this source. It can be shown [3] that in order to assure the ASE8 to be greater than 0.95 bit/time-step, it suffices that for each interval of the partition P8 the probability for 8(x) to belong to any interval Ii satisfies In this Section we propose to use a pseudo-chaotic digitized version of the Renyi chaotic map T(x) = 6x mod 1 for the definition of a lossy compressor to process TRBGs. We focus on the Renyi chaotic map since it is a not continuos map and its pseudo-chaotic implementation involves efficient hardware circuits [5], [6].…”

“…The discretized Renyi map approximates the Renyi map in the sense specified by the following [3] Theorem 2: Let us consider the interval…”

“…Accordingly, we assume the map 5 to be the p-th iterate of the Renyi map T, i.e., 5 = TP : [ 0,1) ---> [ 0,1). Since the Renyi map is strongly mixing [3], [7], in most cases of practical interest a small number of iterations (p � 5) assures that the random variable 5 (x) is almost uniformly distributed.…”

Generalized Hardware Post-processing Technique for Chaos-Based Pseudorandom Number Generators

“…With a deterministic yet unpredictable nature, chaos-based PRNGs (CB-PRNGs) implement a chaotic equation that produces randomized symbols when initialized by a seed. Many CBPRNGs have been digitally realized using chaotic maps [5]- [8] and recently using the numerical solution of differential equations [9], [10], while other chaos-based true random bit generators have also been proposed [11]. Digital design provides several benefits over analog implementation in terms of area efficiency, repeatability, portability, power consumption, and integrability with IC technology [12].…”

Fully digital jerk-based chaotic oscillators for high throughput pseudo-random number generators up to 8.77Gbits/s

“…Chaos generation has been widely considered for a broad range of applications in instrumentation [1], communication systems (chaos shift-keying) [2,3], baseband modulation [4], image encryption [5], and random number generation [6][7][8][9][10][11][12], designed as both fully MOS-based [13][14][15][16] and integrated circuits [17][18][19][20]. Random number generators (RNGs) remain a critical component in communications, cryptography [21] and microprocessors [22].…”