Efficient construction of a substitution box based on a Mordell elliptic curve over a finite field

摘要: Elliptic curve cryptography has been used in many security systems due to its small key size and high compared with other cryptosystems. In well-known systems, a substitution box (S-box) is the only non-linear component. Recently, it shown that of cryptosystem can be improved using dynamic S-boxes instead static S-box. This necessitates construction new secure S-boxes. We propose an efficient method generate are based on class Mordell elliptic curves over prime fields achieved by defining different total orders. The proposed scheme developed such way for each input outputs S-box linear time constant space. Due this property, our takes less space than existing methods curves. Computational results show capable generating cryptographically strong comparable some constructed via mathematical structures.