Browse > Article
http://dx.doi.org/10.3837/tiis.2022.04.012

An Improved Pseudorandom Sequence Generator and its Application to Image Encryption  

Sinha, Keshav (Birla Institute of Technology)
Paul, Partha (Sarala Birla University)
Amritanjali, Amritanjali (Birla Institute of Technology)
Publication Information
KSII Transactions on Internet and Information Systems (TIIS) / v.16, no.4, 2022 , pp. 1307-1329 More about this Journal
Abstract
This paper proposes an improved Pseudorandom Sequence Generator (PRSG) based on the concept of modular arithmetic systems with non-integral numbers. The generated random sequence use in various cryptographic applications due to its unpredictability. Here the mathematical model is designed to solve the problem of the non-uniform distribution of the sequences. In addition, PRSG has passed the standard statistical and empirical tests, which shows that the proposed generator has good statistical characteristics. Finally, image encryption has been performed based on the sort-index method and diffusion processing to obtain the encrypted image. After a thorough evaluation of encryption performance, there has been no direct association between the original and encrypted images. The results show that the proposed PRSG has good statistical characteristics and security performance in cryptographic applications.
Keywords
Pseudorandom sequence generator; Image security; Probability distribution; Non-integral numbers; Modular arithmetic system; Differential attack;
Citations & Related Records
Times Cited By KSCI : 2  (Citation Analysis)
연도 인용수 순위
1 Benlashram, M. Al-Ghamdi, R. AlTalhi, and P. Kaouther Laabidi, "A novel approach of image encryption using pixel shuffling and 3D chaotic map," J. Phys. Conf. Ser., vol. 1447, p. 012009, Jan. 2020.   DOI
2 A. Hasnat, D. Barman, and S. Sarkar, "Color image share cryptography: a novel approach," J. Intell. Fuzzy Syst., vol. 36, no. 5, pp. 4491-4506, May 2019.   DOI
3 A. Lavasani, and T. Eghlidos, "Practical next bit test for evaluating pseudorandom sequences," Sci. Iran., vol. 16, pp. 19-33, June 2009.
4 A. Rukhin, J. Sota, J. Nechvatal, M. Smid, E. Barker, S. Leigh, M. Levenson, M. Vangel, D. Banks, A. Heckert, J. Dray, and S. Vo, "A statistical test suite for random and pseudorandom number generators for cryptographic applications," NIST, 2000.
5 H. Luo and B. Ge, "Image encryption based on Henon chaotic system with nonlinear term," Multimed. Tools. Appl., vol. 78, no. 24, pp. 34323-34352, Aug. 2019.   DOI
6 D. H. Bailey, "A Pseudorandom Number Generator Based on Normal Numbers," Office of Scientific and Technical Information (OSTI), Berkeley, CA, USA, Tech. Rep. LBNL-57489, Dec. 2004.
7 D. Shanks and J. W. Wrench, "Calculation of e to 100,000 Decimals," Math. Comput., vol. 23, no. 107, pp. 679-680, Jul. 1969.
8 H. Huang, S. Yang, and R. Ye, "Efficient symmetric image encryption by using a novel 2D chaotic system," IET Image Process., vol. 14, no. 6, pp. 1157-1163, Apr. 2020.   DOI
9 H. Huang and S. Yang, "Image Encryption Technique Combining Compressive Sensing with Double Random-Phase Encoding," Math. Probl. Eng., vol. 2018, pp. 1-10, 2018.
10 F. Ozkaynak and S. Yavuz, "Security problems for a pseudorandom sequence generator based on the Chen chaotic system," Comput. Phys. Commun., vol. 184, no. 9, pp. 2178-2181, Sep. 2013.   DOI
11 I. Ozturk and R. Kilic, "A novel method for producing pseudo random numbers from differential equation-based chaotic systems," Nonlinear Dyn., vol. 80, no. 3, pp. 1147-1157, Feb. 2015.   DOI
12 I. Peterson, "Pi Wars: Dueling Supercomputers," Science News, Wiley, vol. 131, no. 8, p. 118, Feb. 1987.   DOI
13 J. Dutka, "The Square Root of 2 to 1,000,000 Decimals," Math. Comput., vol. 25, no. 116, pp. 927-930, Oct. 1971.   DOI
14 J. Ferreiros, "Gauss and the Mathematical Background to Standardisation," HoST - Journal of History of Science and Technology, vol. 14, no. 1, pp. 32-51, Jun. 2020.   DOI
15 J. Peng, W. Yang, S. Jin, S. Pang, D. Tang, J. Bai, D. Zhang, "Image Encryption Based on Fractional-order Chen Hyperchaotic System," in Proc. of 15th IEEE Conference on Industrial Electronics and Applications (ICIEA), Kristiansand, Norway, pp. 213-217, Nov 2020.
16 L. Milinkovic, M. Antic, and Z. Cica, "Pseudorandom number generator based on irrational numbers," in Proc. of 10th International Conference on Telecommunication in Modern Satellite Cable and Broadcasting Services (TELSIKS), Nis, Serbia, pp. 719-722, Oct. 2011.
17 M. A. Ivanov, I. G. Konnova, E. A. Salikov, and M. A. Stepanova, "Obfuscation of logic schemes of pseudorandom number generators based on linear and non-linear feedback shift registers," Bezopasnost informacionnyh tehnology, vol. 28, no. 1, pp. 74-83, Jan. 2021.
18 M. Bellare, R. Guerin, and P. Rogaway, "XOR MACs: New Methods for Message Authentication Using Finite Pseudorandom Functions," in Proc. of CRYPTO 1995: Advances in Cryptology - CRYPT0' 95, pp. 15-28, 1995.
19 O. Laia, E. M. Zamzami, and Sutarman, "Analysis of Combination Algorithm Data Encryption Standard (DES) and Blum-Blum-Shub (BBS)," J. Phys. Conf. Ser., vol. 1898, no. 1, p. 012017, Jun. 2021.   DOI
20 P. G. Anderson, "A Fibonacci-Based Pseudorandom Number Generator," Applications of Fibonacci Numbers, vol. 4, pp. 1-8, July 30 - Aug 3, 1991.
21 M. Bullynck, "Modular arithmetic before C.F. Gauss: Systematizations and discussions on remainder problems in 18th-century Germany," Hist. Math., vol. 36, no. 1, pp. 48-72, Feb. 2009.   DOI
22 R. P. Agarwal and H. Agarwal, "Origin of Irrational Numbers and Their Approximations," Comput., vol. 9, no. 3, p. 29, Mar. 2021.
23 S. Chakraborty, "On Why and What of Randomness," arXiv:0902.1232 [cs], February 2009.
24 S. Zhu, C. Zhu, and W. Wang, "A New Image Encryption Algorithm Based on Chaos and Secure Hash SHA-256," Entropy, vol. 20, no. 9, p. 716, Sep. 2018.   DOI
25 T. W. Judson, Abstract Algebra: Theory And Applications, USA: Orthogonal Publishing, 2020.
26 V. Kapur, S. Teja Paladi, and N. Dubbakula, "Two Level Image Encryption using Pseudo Random Number Generators," Int. J. Comput. Appl., vol. 115, no. 12, pp. 1-4, Apr. 2015.   DOI
27 W. A. Beyer, N. Metropolis, and J. R. Neergaard, "Square Roots of Integers 2 to 15 in Various Bases 2 to 10: 88062 Binary Digits or Equivalent," Math. Comput., vol. 23, no. 107, p. 679, Jul. 1969.
28 W. Hao-Xiang, C. Guo-Liang, M. Sheng, T. Li-Xin, "Nonlinear feedback control of a novel hyperchaotic system and its circuit implementation," Chin. Phys. B, vol. 19, no. 3, p. 030509, Mar 2010.   DOI
29 W. Sen, C. Li, L. Qin, W. Gang, "Chaotic phenomena in Josephson circuits coupled quantum cellular neural networks," Chin. Phys., vol. 16, no. 9, pp. 2631-4, Sep 2007.   DOI
30 X. Chen, S. Qian, F. Yu, Z. Zhang, H. Shen, Y. Huang, S. Cai, Z. Deng, Y. Li, and S. Du, "Pseudorandom Number Generator Based on Three Kinds of Four-Wing Memristive Hyperchaotic System and Its Application in Image Encryption," Complexity, vol. 2020, pp. 1-17, Dec. 2020.
31 X.-Y. Wang, S.-X. Gu, and Y.-Q. Zhang, "Novel image encryption algorithm based on cycle shift and chaotic system," Opt. Lasers Eng., vol. 68, pp. 126-134, May. 2015.   DOI
32 Y. Liu, L. Y. Zhang, J. Wang, Y. Zhang, and K. Wong, "Chosen-plaintext attack of an image encryption scheme based on modified permutation-diffusion structure," Nonlinear Dyn., vol. 84, no. 4, pp. 2241-2250, Feb. 2016.   DOI
33 S. Tariq, M. Khan, A. Alghafis, and M. Amin, "A novel hybrid encryption scheme based on chaotic Lorenz system and logarithmic key generation," Multimed. Tools. Appl., vol. 79, no. 31-32, pp. 23507-23529, Jun. 2020.   DOI
34 Y.-Q. Zhang and X.-Y. Wang, "A symmetric image encryption algorithm based on mixed linear-nonlinear coupled map lattice," Inf. Sci., vol. 273, pp. 329-351, Jul. 2014.   DOI
35 Y.-S. Jeong, K. Oh, C.-K. Cho, and H.-J. Choi, "Pseudo Random Number Generation Using LSTMs and Irrational Numbers," in Proc. of IEEE International Conference on Big Data and Smart Computing (BigComp), Shanghai, China, pp. 541 - 544, Jan. 2018.
36 Z. Man, J. Li, X. Di, X. Liu, J. Zhou, J. Wang, and X. Zhang, "A novel image encryption algorithm based on least squares generative adversarial network random number generator," Multimed. Tools. Appl., vol. 80, no. 18, pp. 27445-27469, May 2021.   DOI
37 T. Sivakumar, R. Venkatesan, "A Novel Image Encryption Using Calligraphy Based Scan Method and Random Number," KSII Transactions on Internet and Information Systems, vol. 9, no. 6, pp. 2317-2337, Jun. 2015.   DOI
38 F. Sun and Z. Lv, "A secure image encryption based on spatial surface chaotic system and AES algorithm," Multimed Tools Appl., vol. 82, pp. 3959-3979, 2022.
39 A. Arab, M. J. Rostami, and B. Ghavami, "An image encryption method based on chaos system and AES algorithm," J of Supercom., vol. 75, no. 10, pp. 6663-6682, May 2019.   DOI
40 K. Kordov and S. Zhelezov, "Steganography in color images with random order of pixel selection and encrypted text message embedding," PeerJ Comput. Sci., vol. 7, p. e380, Jan. 2021.   DOI
41 X. Wang, X. Zhu, X. Wu, and Y. Zhang, "Image encryption algorithm based on multiple mixed hash functions and cyclic shift," Opt. Lasers Eng., vol. 107, pp. 370-379, Aug. 2018.   DOI
42 L. C. Meiser, J. Koch, P. L. Antkowiak, W. J. Stark, R. Heckel, and R. N. Grass, "DNA synthesis for true random number generation," Nat. Commun., vol. 11, no. 1, pp. 1-9, Nov. 2020.   DOI
43 D. Lambic, "Security analysis and improvement of a block cipher with dynamic S-boxes based on tent map," Nonlinear Dyn., vol. 79, no. 4, pp. 2531-2539, 2015.   DOI
44 B. R. Johnson, and D. J. Leeming, "A study of the digits of π, e and certain other irrational numbers," Sankhya: Indian J. Stat., vol. 52, no. 2, 183-189, 1990.
45 J. B. Fraleigh, A First Course in Abstract Algebra, USA, United States: Pearson, 2014.