A Mathematical Approach for Generating a Highly Non-Linear Substitution Box Using Quadratic Fractional Transformation

作     者：Abid Mahboob Muhammad Asif Rana Muhammad Zulqarnain Imran Saddique Hijaz Ahmad Sameh Askar 

作者机构：Department of MathematicsDivision of Science and TechnologyUniversity of EducationLahorePakistan Department of MathematicsUniversity of Management and TechnologySialkot Campus51310Pakistan School of Mathematical SciencesZhejiang Normal UniversityJinhua321004China Department of MathematicsUniversity of Management and TechnologyLahore54770Pakistan Section of MathematicsInternational Telematic University UninettunoCorso Vittorio Emanuele IIRoma39-00186Italy Department of Statistics and Operations ResearchCollege of ScienceKing Saud UniversityP.O.Box 2455Riyadh11451Saudi Arabia 

出 版 物：《Computers, Materials & Continua》 (计算机、材料和连续体（英文）)

年 卷 期：2023年第77卷第11期

页      面：2565-2578页

核心收录：

学科分类：07[理学] 0701[理学-数学] 070101[理学-基础数学] 

基　　金：The authors received the funding for this study from King Saud University Riyadh Saudi Arabia under the research supporting project Number RSP 2023R167.Sameh Askar received this grant from King Saud University 

主　　题：Block cipher S-box data security fractional transformation 

摘      要：Nowadays,one of the most important difficulties is the protection and privacy of confidential *** address these problems,numerous organizations rely on the use of cryptographic techniques to secure data from illegal activities and *** cryptographic ciphers use the non-linear component of block cipher to ensure the robust encryption process and lawful decoding of plain data during the decryption *** the designing of a secure substitution box(S-box),non-linearity(NL)which is an algebraic property of the S-box has great ***,the main focus of cryptographers is to achieve the S-box with a high value of *** this suggested study,an algebraic approach for the construction of 16×16 S-boxes is provided which is based on the fractional transformation Q(z)=1/α(z)^(m)+β(mod257)and finite *** technique is only applicable for the even number exponent in the range(2-254)that are not multiples of ***,we choose a quadratic fractional transformation,swap each missing element with repeating elements,and acquire the initial *** the second stage,a special permutation of the symmetric group S256 is utilized to construct the final S-box,which has a higher NL score of 112.75 than the Advanced Encryption Standard(AES)S-box and a lower linear probability score of *** addition,a tabular and graphical comparison of various algebraic features of the created S-box with many other S-boxes from the literature is provided which verifies that the created S-box has the ability and is good enough to withstand linear and differential *** different analyses,it is ensured that the proposed S-boxes are better than as compared to the existing *** these S-boxes can be utilized in the security of the image data and the text data.