A post-processing method for true random number generators based on hyperchaos with applications in audio-based generators

Abstract

True random number generators (TRNG) are important counterparts to pseudorandom number generators (PRNG), especially for high security applications such as cryptography. They produce unpredictable, non-repeatable random sequences. However, most TRNGs require specialized hardware to extract entropy from physical phenomena and tend to be slower than PRNGs. These generators usually require post-processing algorithms to eliminate biases but in turn, reduces performance. In this paper, a new post-processing method based on hyperchaos is proposed for software-based TRNGs which not only eliminates statistical biases but also provides amplification in order to improve the performance of TRNGs. The proposed method utilizes the inherent characteristics of chaos such as hypersensitivity to input changes, diffusion, and confusion capabilities to achieve these goals. Quantized bits of a physical entropy source are used to perturb the parameters of a hyperchaotic map, which is then iterated to produce a set of random output bits. To depict the feasibility of the proposed post-processing algorithm, it is applied in designing TRNGs based on digital audio. The generators are analyzed to identify statistical defects in addition to forward and backward security. Results indicate that the proposed generators are able to produce secure true random sequences at a high throughput,which in turn reflects on the effectiveness of the proposed post-processing method.

Keywords

audio / chaos theory / chaotic map / entropy / hy-perchaos / post-processing / random number generator / security

References

[1] Cret O, Gyorfi T, Suciu A. Implementing true random number generators based on high fanout nets. Romanian Journal of Information Science and Technology, 2012, 15(3): 277–298

[2] Jun B, Kocher P. The intel random number generator. Cryptography Research Inc. White Paper, 1999, 27: 1–8

[3] Cicek I, Pusane A E, Dundar G. An integrated dual entropy core true random number generator. IEEE Transactions on Circuits and Systems II: Express Briefs, 2017, 64(3): 329–333

[4] Karakaya B, Çelik V, Gulten A. Chaotic cellular neural network-based true random number generator. International Journal of Circuit Theory and Applications, 2017, 45(11): 1885–1897

[5] Bonny T, Debsi R A, Majzoub S, Elwakil A S. Hardware optimized FPGA implementations of high-speed true random bit generators basedon switching-type chaotic oscillators. Circuits, Systems, and Signal Processing, 2018, 38(3): 1342–1359

[6] Mei F, Zhang L, Gu C, Cao Y, Wang C, Liu W. A highly flexible lightweight and high speed true random number generator on FPGA. In: Proceedings of IEEE Computer Society Annual Symposium on VLSI (ISVLSI). 2018

[7] Nguyen T T N, Kaddoum G, Gagnon F. Implementation of a chaotic true random number generator based on fuzzy modeling. In: Proceedings of the 16th IEEE International New Circuits and Systems Conference. 2018

[8] Kumar D, Nabi K, Misra P K, Goswami M. Modified tent map based design for true random number generator. In: Proceedings of IEEE International Symposium on Smart Electronic Systems. 2018

[9] Alcin M, Koyuncu I, Tuna M, Varan M, Pehlivan I. A novel high speed artificial neural network-based chaotic true random number generator on field programmable gate array. International Journal of Circuit Theory and Applications, 2018, 47(3): 365–378

[10] Hsueh J C, Chen V H C. An ultra-low voltage chaos-based true random number generator for IoT applications. Microelectronics Journal, 2019, 87: 55–64

[11] Gupta R, Pandey A, Baghel R K. FPGA implementation of chaosbased high-speed true random number generator. International Journal of Numerical Modelling: Electronic Networks, Devices and Fields, 2019, 32(5): e2604

[12] Karakaya B, Gulten A, Frasca M. A true random bit generator based on a memristive chaotic circuit: analysis, design and FPGA implementation. Chaos, Solitons & Fractals, 2019, 119: 143–149

[13] Teh J S, Samsudin A, Al-Mazrooie M, Akhavan A. GPUs and chaos: a new true random number generator. Nonlinear Dynamics, 2015, 82(4): 1913–1922

[14] Davis D, Ihaka R, Fenstermacher P. Cryptographic randomness from air turbulence in disk drives. In: Proceedings of Annual International Cryptology Conference. 1994, 114–120

[15] Hu Y, Liao X, wo Wong K, Zhou Q. A true random number generator based on mouse movement and chaotic cryptography. Chaos, Solitons & Fractals, 2009, 40(5): 2286–2293

[16] Xingyuan W, Xue Q, Lin T. A novel true random number generator based on mouse movement and a one-dimensional chaotic map. Mathematical Problems in Engineering, 2012

[17] Yeoh W Z, Teh J S, Chern H R. A parallelizable chaos-based true random number generator based on mobile device cameras for the android platform. Multimedia Tools and Applications, 2019, 78(12): 15929–15949

[18] Nikolic S, Veinovic M. Advancement of true random number generators based on sound cards through utilization of a new post-processing method. Wireless Personal Communications, 2016, 91(2): 603–622

[19] Davies R B. Exclusive OR (XOR) and hardware random number generators. see Wikipedia, 2002

[20] Von Neumann J. Various techniques used in connection with random digits. National Bureau of Standards Applied Mathematical Series, 1951, 12(36–38): 5

[21] Lacharme P. Post-processing functions for a biased physical random number generator. In: Proceedings of International Workshop on Fast Software Encryption. 2008, 334–342

[22] Avaroğlu E, Tuncer T, Őzer A, Ergen B, Tűrk M. A novel chaos-based post-processing for TRNG. Nonlinear Dynamics, 2015, 81(1–2): 189–199

[23] Schindler W, Killmann W. Evaluation criteria for true (physical) random number generators used in cryptographic applications. In: Proceedings of International Workshop on Cryptographic Hardware and Embedded Systems. 2002, 431–449

[24] Sunar B, Martin W J, Stinson D R. A provably secure true random number generator with built-in tolerance to active attacks. IEEE Transactions on Computers, 2007, 56(1): 109–119

[25] Kwok S H, Ee Y L, Chew G, Zheng K, Khoo K, Tan C H. A comparison of post-processing techniques for biased random number generators. In: Proceedings of IFIP International Workshop on Information Security Theory and Practices. 2011, 175–190

[26] Ahmad M, Khurana S, Singh S, AlSharari H D. A simple secure hash function scheme usingmultiple chaotic maps. 3D Research, 2017, 8(2): 13

[27] Li Y, Ge G. Cryptographic and parallel hash function based on cross coupled map lattices suitable for multimedia communication security. Multimedia Tools and Applications, 2019, 78(13): 17973–17994

[28] ur Rehman A, Liao X. A novel robust dual diffusion/confusion encryption technique for color image based on chaos, DNA and SHA-2. Multimedia Tools and Applications, 2018, 78(2): 2105–2133

[29] Xiong Z, Wu Y, Ye C, Zhang X, Xu F. Color image chaos encryption algorithm combining CRC and nine palace map. Multimedia Tools and Applications, 2019, 78(22): 31035–31055

[30] Garcia-Bosque M, Perez-Resa A, Sanchez-Azqueta C, Aldea C, Celma S. Chaos-based bitwise dynamical pseudorandom number generator on FPGA. IEEE Transactions on Instrumentation and Measurement, 2019, 68(1): 291–293

[31] Rukhin A, Soto J, Nechvatal J. A statistical test suite for random and pseudorandom number generators for cryptographic applications. National Institute of Standards, NIST Special Publication 800-22, 2010

[32] Marsaglia G. DIEHARD: a battery of tests of Randomness. 1996

[33] Walker J. ENT Program. 2008

[34] Teh J S, Teng W, Samsudin A. A true random number generator based on hyperchaos and digital sound. In: Proceedings of the 3rd International Conference on Computer and Information Sciences. 2016, 264–269

[35] Dodis Y, Pointcheval D, Ruhault S, Vergniaud D, Wichs D. Security analysis of pseudo-random number generators with input: /dev/random is not robust. In: Proceedings of the 2013 ACM SIGSAC Conference on Computer & Communications Security. 2013, 647–658

[36] Coron J S. On the security of random sources. In: Proceedings of International Workshop on Public Key Cryptography. 1999, 29–42

[37] Benítez R, Bolós V, Ramírez M. A wavelet-based tool for studying non-periodicity. Computers & Mathematics with Applications, 2010, 60(3): 634–641

[38] Ritter T. The efficient generation of cryptographic confusion sequences. Cryptologia, 1991, 15(2): 81–139

[39] Golomb S W. Shift register sequences. World Scientific. 2014

[40] Massey J. Shift-register synthesis and BCH decoding. IEEE Transactions on Information Theory, 1969, 15(1): 122–127

[41] Menezes A J, van Oorschot P C, Vanstone S A. Handbook of Applied Cryptography. CRC Press, 2018

[42] Bardis N G, Markovskyi A P, Doukas N, Karadimas N V. True random number generation based on environmental noise measurements for military applications. In: Proceedings of the 8th WSEAS International Conference on Signal Processing, Robotics and Automation. 2009, 68–73

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