2023/11/02 by Huan‐Xiang Zhou, Zhou, Huan, Xiaoni Du +5
Computer Science · Social Sciences · #Coding theory and cryptography #Cryptography and Residue Arithmetic #FOS: Computer and information sciences #Information Theory (cs.IT) #Islamic Finance and Communication
paper · pdf · doi:10.48550/arxiv.2311.00982
openalex publication_date 2023/11/02 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
Power functions with low c-differential uniformity have been widely studied not only because of their strong resistance to multiplicative differential attacks, but also low implementation cost in hardware. Furthermore, the c-differential spectrum of a function gives a more precise characterization of its c-differential properties. Let f(x)=x(pn+3)/(2) be a power function over the finite field \mathbbFpn, where p≠3 is an odd prime and n is a positive integer. In this paper, for all primes p≠3, by investigating certain character sums with regard to elliptic curves and computing the number of solutions of a system of equations over \mathbbFpn, we determine explicitly the (-1)-differential spectrum of f with a unified approach. We show that if pn ≡ 3 \pmod 4, then f is a differentially (-1,3)-uniform function except for pn∈\7,19,23\ where f is an APcN function, and if pn ≡ 1 \pmod 4, the (-1)-differential uniformity of f is equal to 4. In addition, an upper bound of the c-differential uniformity of f is also given.