Elliptic curve cryptography has received great attention in recent years due to its high resistance against modern cryptanalysis. The aim of this article is to present efficient generators to generate substitution boxes (S-boxes) and pseudo random numbers which are essential for many well-known cryptosystems. These generators are based on a special class of ordered Mordell elliptic curves. Rigorous analyses are performed to test the security strength of the proposed generators. For a given prime, the experimental results reveal that the proposed generators are capable of generating a large number of distinct, mutually uncorrelated, cryptographically strong S-boxes and sequences of random numbers in low time and space complexity. Furthermore, it is evident from the comparison that the proposed schemes can efficiently generate secure S-boxes and random numbers as compared to some of the well-known existing schemes over different mathematical structures.

椭圆曲线密码学由于其对现代密码分析的高度抵抗力，近年来受到了极大的关注。本文的目的是提出一种高效的生成器，以生成替换框（S-box）和伪随机数，这对于许多众所周知的密码系统而言都是必不可少的。这些生成器基于一类特殊的有序Mordell椭圆曲线。进行了严格的分析，以测试提出的发电机的安全强度。对于给定的素数，实验结果表明，所提出的生成器能够以低时间和空间复杂性生成大量不同的，互不相关的，密码学强的S盒和随机数序列。此外，