Pseudorandom Number Generator (PRNG) Design Using Hyper-Chaotic Modified Robust Logistic Map (HC-MRLM)

Abstract

Robust chaotic systems, due to their inherent properties of mixing, ergodicity, and larger chaotic parameter space, constitute a perfect candidate for cryptography. This paper reports a novel method to generate random numbers using modified robust logistic map (MRLM). The non-smooth probability distribution function of robust logistic map (RLM) trajectories gives an un-even binary distribution in randomness test. To overcome this disadvantage in RLM, control of chaos (CoC) is proposed for smooth probability distribution function of RLM. For testing the proposed design, cryptographic random numbers generated by MRLM were vetted with National Institute of Standards and Technology statistical test suite (NIST 800-22). The results showed that proposed MRLM generates cryptographically secure random numbers (CSPRNG).

Function Composition from Sine Function and Skew Tent Map and Its Application to Pseudorandom Number Generators

“…Several works related to the PRNG design have been proposed; for example, there are strategies that implement PRNGs using linear feedback shift registers (LFSR) [1][2][3][4][5], while other strategies are based on block cipher [6], stream cipher [7], quantum walks [8], cellular automata [9,10], chaotic oscillators and artificial neural networks (ANN) [11], or chaotic maps [12][13][14][15]. There are also PRNG design approaches that combine several of the above strategies [16].…”

“…Therefore, many cryptographic systems and modules have been proposed based on chaotic systems [22][23][24][25][26][27][28][29][30][31][32][33]. In particular, chaotic maps have been successfully applied in the implementation of PRNGs [14,15,31,[34][35][36][37][38][39][40][41][42].…”

“…After the work developed by Li et al [47], many other researchers proposed PRNGs based on chaotic maps using different approaches [12][13][14][15]31,[34][35][36][37][38][39][40][41][42]48]. In this extensive variety of proffers, several implementations were identified with security disadvantages attributed to one or more of the following features: non-uniform statistical distribution [49], digital degradation [50] and predictability [51] of the produced number sequences, as well as the small-sized seed space of the chaotic map [21].…”

“…Therefore, although efforts are being made to overcome the security disadvantages of implementing PRNGs based on chaotic maps, there are still PRNGs based on chaotic maps that have security shortcomings. For example, some chaotic maps have stability islands within the parameter domains for chaotic behavior, adversely affecting the system security, other chaotic maps produce number sequences with non-uniform statistical distribution, and other chaotic maps only work by using a limited size of initial conditions space [15,53]. Therefore, to safely use a PRNG based on chaotic maps, we must carefully select the initial conditions ensuring that the map will always produce pseudorandom sequences with uniform statistical distribution and it will operate into the parameter domains for chaotic behavior avoiding the annulling chaos conditions; and when the chaotic system is implemented electronically, the dynamic degradation of the digital sequences must be considered.…”

Modification of the Logistic Map Using Fuzzy Numbers with Application to Pseudorandom Number Generation and Image Encryption

“…The resulting map presents more complex chaos related phenomena compared to the classic map as mentioned above, as well as achieves a higher value for its Lyapunov exponent. Furthermore, to showcase the applicability of the map to chaos related applications, the problems of pseudo random bit generation [ 4 , 5 , 10 , 11 , 13 , 29 , 30 , 31 , 32 , 33 , 34 , 35 , 36 , 37 , 38 , 39 , 40 , 41 , 42 , 43 ] and image encryption [ 4 , 7 , 9 , 14 , 15 , 33 , 35 , 39 , 44 , 45 , 46 , 47 , 48 ] are considered. It is seen that the bit sequence generated from the modified map using a simple rule passes all 15 tests of the National Institute of Standards and Technology (NIST) statistical test suite [ 49 ].…”