DIVERSITY AES IN MIXCOLUMNS STEP WITH 8X8 CIRCULANT MATRIX

Yan-Wen Chen,Chong-Dao Lee,Yan-Haw Chen,Jeng-Jung Wang

doi:10.29121/ijetmr.v8.i9.2021.1037

Abstract

In AES MixColumns operation, the branch number of circulant matrix is raised from 5 to 9 with 8´8 circulant matrices that can be enhancing the diffusion power. An efficient method to compute the circulant matrices in AES MixColumns transformation for speeding encryption is presented. Utilizing 8´8 involutory matrix multiplication is required 64 multiplications and 56 additions in in AES Mix-Columns transformation. We proposed the method with diversity 8´8 circulant matrices is only needed 19 multiplications and 57 additions. It is not only to encryption operations but also to decryption operations. Therefore, 8´8 circlant matrix operation with AES key sizes of 128bits, 192bits, and 256 bits are above 29.1%, 29.3%, and 29.8% faster than using 4´4 involutory matrix operation (16 multiplications, 12 additions), respectively. 8´8 circulant matrix encryption/decryption speed is above 78% faster than 8´8 involutory matrix operation. Ultimately, the proposed method for evaluating matrix multiplication can be made regular, simple and suitable for software implementations on embedded systems.

Highlights

In AES MixColumns operation, the branch number of circulant matrix is raised from 5 to 9 with 8×8 circulant matrices that can be enhancing the diffusion power
8×8 circlant matrix operation with AES key sizes of 128bits, 192bits, and 256 bits are above 33.5%, 33.7%, and 33.9% faster than using 4×4 involutory matrix operation (16 multiplications, 12 additions), respectively. 8×8 circulant matrix
The reducing encryption time is above 79% faster than the 8×8 involutory matrix multiplication

Summary

INTRODUTION

Network security techniques and algorithms are introducing protecting data transmission that is more important than ever. In AES (Daemen and Rijmen (1999); National Institute of Standards and Technology (NIST) (2001) of the MixColumns-InvMixColumns transformation is one of the functions in the Cipher-InvCipher; it needs large amounts of CPUs time for operating during the encryption and decryption. × Diversity Aes in Mixcolumns Step with 8 8 Circulant Matrix (Daemen and Rijmen (1999); National Institute of Standards and Technology (NIST) (2001). We propose an enhancement security method for AES encryption/decryption transformations with the Elliptic Curve Diffie–Hellman key exchange (ECDH) using elliptic curve in ANSI X9.62. The AES key and first rows of the matrix can use ECDH method for exchanging both. The paper is in combining diversity AES and ECDH methods for security enhancement approaches to protect against new threats.

FINITE FIELD MULTIPLICATION:

REDUCING MULTIPLICATIONS BY MULTIPLY 2

RESULT

Findings

CONCLUSIONS AND RECOMMENDATIONS