Mordell Elliptic Curve Based Design of Nonlinear Component of Block Cipher

作     者：Hafeez ur Rehman Tariq Shah Mohammad Mazyad Hazzazi Ali Alshehri Bassfar Zaid 

作者机构：Department of MathematicsQuaid-i-Azam UniversityIslamabadPakistan Department of MathematicsCollege of ScienceKing Khalid UniversityAbhaSaudi Arabia Department of Computer ScienceUniversity of TabukTabuk71491Saudi Arabia Department of Information TechnologyUniversity of TabukTabuk71491Saudi Arabia 

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

年 卷 期：2022年第73卷第11期

页      面：2913-2930页

核心收录：

学科分类：0831[工学-生物医学工程（可授工学、理学、医学学位）] 0808[工学-电气工程] 0809[工学-电子科学与技术（可授工学、理学学位）] 07[理学] 0805[工学-材料科学与工程（可授工学、理学学位）] 0701[理学-数学] 0812[工学-计算机科学与技术（可授工学、理学学位）] 0801[工学-力学（可授工学、理学学位）] 070101[理学-基础数学] 

基　　金：The authors extend their gratitude to the Deanship of Scientific Research at King Khalid University for funding this work through the research groups program under grant number R.G.P.2/109/43 

主　　题：Galois field Mordell elliptic curve nonlinearity substitution box 

摘      要：Elliptic curves(ECs)are deemed one of the most solid structures against modern computational attacks because of their small key size and high *** many well-known cryptosystems,the substitution box(Sbox)is used as the only nonlinear portion of a security ***,it has been shown that using dynamic S-boxes rather than static S-boxes increases the security of a *** conferred study also extends the practical application of ECs in designing the nonlinear components of block ciphers in symmetric key *** this study,instead of the Mordell elliptic curve(MEC)over the prime field,the Galois field has been engaged in constructing the S-boxes,the main nonlinear component of the block ***,the proposed scheme uses the coordinates of MEC and the operation of the Galois field to generate a higher number of S-boxes with optimal nonlinearity,which increases the security of *** proposed S-boxes resilience against prominent algebraic and statistical attacks is evaluated to determine its potential to induce confusion and produce acceptable results compared to other ***,the majority logic criteria(MLC)are used to assess the new S-boxes usage in the image encryption application,and the outcomes indicate that they have significant cryptographic strength.