### Efficient schemes with diverse of a pair of circulant matrices for AES MixColumns-InvMixcolumns transformation

#### Abstract

Recently, AES is a commonly used encryption-decryption algorithm applied to wireless communication protocols. However, confidentiality and speed both associated with Cipher-InvCipher that are a very important issue in many current communication systems. In this paper, the key idea here is to propose a method with more variations in circulant matrix for enhancing security in AES MixColumns-InvMixColumns step. The paper is also to propose a method minimizes the number of multiplications for matrix multiplication theoretically based on two-point cyclic convolution properties of circulant matrix. The conventional 44 matrix multiplication typically needs 16 multiplications and 12 additions; however, the proposed method, described herein as Scheme 3, can reduce the matrix multiplications into 5 multiplications and 15 additions, which is used for encryption and decryption. Using Scheme 3 and Horner’s rule-based multiplication running on Intel CPU, the computational cost of the matrix multiplication can be reduced by ~63%. Furthermore, experiments using Scheme 3 along with Horner’s rule-based multiplication by means of AES keys lengths with 128, 192, 256 bits were tested by running on STM32L476VG MCU, result leads to the reduction of encryption and decryption time respectively by ~60%. Finally, the proposed procedure enables found many a pair of the circulant matrices for AES Cipher-InvCipher so that diverse of a pair of the circulant matrices can enhance security of the data transmission.

Jeng-Jung Wang, Yan-Haw Chen, Guan-Hsiung Liaw, Jack Chang, Cheng-Chih Lee, "Efficient schemes with diverse of a pair of circulant matrices for AES MixColumns-InvMixcolumns transformation,"

*Communications of the CCISA*, vol. 26, no. 2 , pp. 1-20, May. 2020.

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