Construction of CCZ transform for quadratic APN functions |
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| Institution: | 1. Department of EIE, Dr. Mahalingam College of Engineering and Technology, Pollachi, Coimbatore, India;2. Department of EEE, Dr. Mahalingam College of Engineering and Technology, Pollachi, Coimbatore, India;1. School of Information Engineering, Zhengzhou University, Zhengzhou 450001, China;2. National Institute of Telecommunications (Inatel), Santa Rita do Sapucaí, MG, Brazil;3. Instituto de Telecommunicações, Portugal;4. University of Fortaleza (UNIFOR), Fortaleza, CE, Brazil;5. School of Computer Science and Engineering, Beihang University, Beijing 100191, China;6. School of Computer Science, Xidian University, Xi''an 710071, China;1. School of Information Engineering, Zhengzhou University, Zhengzhou 450001, China;2. National Institute of Telecommunications (Inatel), Santa Rita do Sapucaí, MG, Brazil;3. Instituto de Telecommunicações, Portugal;4. University of Fortaleza (UNIFOR), Fortaleza, CE, Brazil;5. School of Computer Science and Engineering, Beihang University, Beijing 100191, China;1. Department of Electronics and Communication Engineering, Sethu Institute of Technology, Madurai 625019, India;2. Department of Electronics and Communication Engineering, VMKV Engineering College, Vinayaka Mission''s Research Foundation, Salem 636308, India;3. Ciddse Technologies Pvt Ltd, Chennai 600087, India;1. EEE Dept, Kamaraj College of Engineering and Technology, Virudhunagar, Tamil Nadu, India;2. EEE Dept, Mepco Schlenk Engineering College, Sivakasi, Tamil Nadu, India |
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| Abstract: | Almost perfect nonlinear (APN) function is an important type of function in cryptography, especially quadratic APN function. Since the notion of CCZ-equivalence developed, the construction of CCZ transform for APN functions to obtain new APN functions became a critical issue in cryptography. Inspired by the result of Budaghyan who used Gold functions, this article gives the construction of CCZ transform for all quadratic vectorial Boolean functions and proves that for quadratic APN functions, the functions transformed have algebraic degree 3, thus EA-inequivalent to all quadratic functions, and have minimum algebraic degree 2, thus EA-inequivalent to all power functions. |
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| Keywords: | APN function CCZ transform Quadratic function Power function EA-equivalence |
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