A Novel Dynamic Mathematical Model Applied in Hash Function Based on DNA Algorithm and Chaotic Maps

Nada E. El-Meligy, Tamer O. Diab, Ashraf S. Mohra, Ashraf Y. Hassan and Wageda I. El-Sobky
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Nada E. El-Meligy: Electrical Engineering Department, Benha Faculty of Engineering, Benha University, Benha 13511, Egypt
Tamer O. Diab: Electrical Engineering Department, Benha Faculty of Engineering, Benha University, Benha 13511, Egypt
Ashraf S. Mohra: Electrical Engineering Department, Benha Faculty of Engineering, Benha University, Benha 13511, Egypt
Ashraf Y. Hassan: Electrical Engineering Department, Benha Faculty of Engineering, Benha University, Benha 13511, Egypt
Wageda I. El-Sobky: Department of Basic Engineering Sciences, Canadian International College (CIC), New Cairo 11865, Egypt

Mathematics, 2022, vol. 10, issue 8, 1-21

Abstract: This paper aims to improve SHA-512 security without increasing complexity; therefore, we focused on hash functions depending on DNA sequences and chaotic maps. After analysis of 45 various chaotic map types, only 5 types are selected in this proposal—namely, improved logistic, cosine logistic map, logistic sine system, tent sine system, and hybrid. Using DNA features and binary coding technology with complementary rules to hide information is a key challenge. This article proposes improving SHA-512 in two aspects: the modification of original hash buffer values, and the modification of additive constants K t . This proposal is to make hash buffer values (a, b, c, d, e, f, g, and h) and K t dependent on one-dimensional discrete chaotic maps and DNA sequences instead of constant. This modification complicates the relationship between the original message and hash value, making it unexpected. The performance of the proposed hash function is tested and analyzed the confusion, diffusion, and distributive and compared with the original SHA-512. The performance of security is analyzed by collision analysis, for which the maximum number of hits is only three, showing that the proposed hash function enhances the security and robustness of SHA-512. The statistical data and experimental analysis indicate that the proposed scheme has good properties and satisfies high-performance requirements for secure hash functions.

Keywords: hash function; chaotic map; improved logistic; cosine logistic map; logistic sine system; tent sine system; DNA sequence; DNA complementary rules (search for similar items in EconPapers)
JEL-codes: C (search for similar items in EconPapers)
Date: 2022
References: View references in EconPapers View complete reference list from CitEc
Citations: View citations in EconPapers (1)

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