PRNG Using Primitive Roots of Primes and its Utilization in Chess-based Image Encryption

Recently, number theory has proved its importance in cryptography because of its well-known hard problems. For instance, a primitive root for a prime number shows a special property of uniqueness when raised to different powers mod the prime number. In this paper, a Pseudorandom Number Generator (PRNG) is designed based on this property using a prime number and some of its primitive roots. The PRNG is, first, validated for utilization in cryptography applications using histograms, correlation coefficients, and the National Institute of Standards and Technology (NIST) statistical test suite. Then, the PRNG is utilized in an image encryption system and the system security is tested using statistical measures, differential attack measures, and sensitivity to one-bit change. The results are promising and in the expected good ranges.

[1]  R. Vijay,et al.  Hybrid image compression-encryption scheme based on multilayer stacked autoencoder and logistic map , 2022, China Communications.

[2]  Hanping Hu,et al.  Bit cyclic shift method to reinforce digital chaotic maps and its application in pseudorandom number generator , 2021, Appl. Math. Comput..

[3]  SK Hafizul Islam,et al.  Design of pseudo-random number generator from turbulence padded chaotic map , 2021, Nonlinear Dynamics.

[4]  B Sunandha,et al.  Implementation of modified Dual-CLCG Method for Pseudorandom bit Generation , 2020, 2020 International Conference on Smart Electronics and Communication (ICOSEC).

[5]  Bhaskar Mondal,et al.  A secure image encryption scheme based on genetic operations and a new hybrid pseudo random number generator , 2020, Multimedia Tools and Applications.

[6]  Yong Wang,et al.  A Pseudorandom Number Generator Based on a 4D Piecewise Logistic Map with Coupled Parameters , 2019, Int. J. Bifurc. Chaos.

[7]  Naveed Ahmed Azam,et al.  A novel image encryption scheme based on an elliptic curve , 2019, Signal Process..

[8]  Guang Gong,et al.  Secure simultaneous bit extraction from Koblitz curves , 2018, Designs, Codes and Cryptography.

[9]  Jeaneth Machicao,et al.  Improving the pseudo-randomness properties of chaotic maps using deep-zoom. , 2016, Chaos.

[10]  Salwa K. Abd-El-Hafiz,et al.  Novel permutation measures for image encryption algorithms , 2016 .

[11]  Salwa K. Abd-El-Hafiz,et al.  A fractal-based image encryption system , 2014, IET Image Process..

[12]  James S. Kraft,et al.  An Introduction to Number Theory with Cryptography , 2013 .

[13]  Elaine B. Barker,et al.  SP 800-22 Rev. 1a. A Statistical Test Suite for Random and Pseudorandom Number Generators for Cryptographic Applications , 2010 .

[14]  L. Washington.  Elliptic Curves: Number Theory and Cryptography, Second Edition , 2008 .

[15]  Claude E. Shannon,et al.  Communication theory of secrecy systems , 1949, Bell Syst. Tech. J..

[16]  Mohamed Esmail Karar,et al.  Hash-enhanced elliptic curve bit-string generator for medical image encryption , 2020, J. Intell. Fuzzy Syst..

[17]  S. Agaian,et al.  NPCR and UACI Randomness Tests for Image Encryption , 2011 .