2018/09/28 by Naveed Ahmed Azam, Azam, Naveed Ahmed, Umar Hayat +3
Computer Science · #Coding theory and cryptography #Cryptographic Implementations and Security #Cryptography and Residue Arithmetic #Cryptography and Security (cs.CR) #FOS: Computer and information sciences
paper · pdf · doi:10.48550/arxiv.1809.11057
openalex publication_date 2018/09/28 · openalex created_date 2022/08/02 · openalex updated_date 2026/07/28
Elliptic curve cryptography (ECC) is used in many security systems due to its\nsmall key size and high security as compared to the other cryptosystems. In\nmany well-known security systems substitution box (S-box) is the only\nnon-linear component. Recently, it is shown that the security of a cryptosystem\ncan be improved by using dynamic S-boxes instead of a static S-box. This fact\nnecessitates the construction of new secure S-boxes. In this paper, we propose\nan efficient method for the generation of S-boxes based on a class of Mordell\nelliptic curves (MECs) over prime fields by defining different total orders.\nThe proposed scheme is developed in such a way that for each input it outputs\nan S-box in linear time and constant space. Due to this property, our method\ntakes less time and space as compared to all existing S-box construction\nmethods over elliptic curve. Furthermore, it is shown by the computational\nresults that the proposed method is capable of generating cryptographically\nstrong S-boxes with comparable security to some of the existing S-boxes\nconstructed over different mathematical structures.\n