Serpent Algorithm: An Improvement by $4\times 4$ S-Box from Finite Chain Ring

Serpent Algorithm, one of the most important proposed Algorithm for AES (Advanced encryption standard) which haven't been paid attention like Rijndael Algorithm but still it is considered as a secured Algorithm in different applications. The only reason that Serpent paid less attention is the lack in its speed. In this paper, we improved the Serpent Algorithm computationally and algebraically in order to make it compatible in different usages like Rijndael Algorithm. The method uses 4 by 4 S-box (consists of bytes instead of nibbles) constructed through the multiplicative group of finite commutative chain ring. Furthermore, all the operations in this work coincides with the operations of commutative chain ring. Results clearly show that improved serpent algorithm is computationally efficient than standard serpent algorithm. In addition, asymptotic lower bound and asymptotic upper bound of the improved serpent algorithm is less than standard serpent algorithm. Moreover, time Execution Performance Efficiency is better than standard serpent algorithm.