Fast Algebraic Immunity of <inline-formula> <tex-math notation="LaTeX">$2^m+2$ </tex-math></inline-formula> &#x0026; <inline-formula> <tex-math notation="LaTeX">$2^m+3$ </tex-math></inline-formula> Variables Majority Function

• Main Authors: Yindong Chen, Liu Zhang, Fei Guo, Weihong Cai
• Format: Article
• Language: English
• Published: IEEE 2019-01-01
• Series: IEEE Access
• Subjects: fast algebraic immunity; majority function; algebraic immunity; Boolean function
• Online Access: https://ieeexplore.ieee.org/document/8737939/
• ISSN: 2169-3536

Boolean functions should possess high fast algebraic immunity (FAI) when it is used in stream ciphers in order to stand up to fast algebraic attacks. However, in previous research, the FAI of Boolean functions was usually calculated by computer. But, as everyone knows, it is very difficult to calculate the FAI of a given Boolean function with high algebraic degree when the variable number is greater than 18. In 2016, Tang et al. gave that the exact value of FAI of the majority function on 2^m and 2^m + 1 (m &#x2265; 2) variables is 2^m-1 + 2. This paper proves that the FAI of 2^m + 2 and 2^m + 3 (m &#x2265; 2) variables majority function equals 2^m-1 + 4.