An Injective S-Box Design Scheme over an Ordered Isomorphic Elliptic Curve and Its Characterization

Algorithm 1

Efficient generation of the proposed S-boxes.

Input: Two integers , a prime , two non-negative integers and ,

  a positive integer such that and (mod ), and a total

  order on the EC .

Output: The proposed injective S-box .

  (1) Calculate the multiplicative inverse of in .

  (2) Sort all integers in the interval as: is a predecessor of , if

  , for any two integers .

  (3) output by selecting first integers from the sorted integers in .