Matrix Encryption Standard

Yıl 2020, Cilt: 11 Sayı: 3, 999 - 1010, 30.09.2020

Orhan Dişkaya Erdinç Avaroğlu Hamza Menken

https://doi.org/10.24012/dumf.733498

Öz

AES (Advanced Encryption Standard) is a standard for encrypting electronic data. AES operates on a column-major order array of bytes. The operations in the matrix are also performed on the polynomials in a special finite field and using S-box. We firstly recall necessary information about matrix algebra. In the present work, we examine the AES encryption method. We create a new encryption algorithm called matrix encryption standard (MES). MES is performed by similar steps to the AES algorithm over 16x16 matrices with elements {0,1} without using polynomials operations and S-box in the AES algorithm. So, we provide 256-bits plain text to be encrypted by passing it through certain rounds with the 16x16 matrix key. In order to decrypt the cipher text, we take the reverse of the 16x16 key matrix through the computer and perform the decryption process by performing a certain number of reverse rounds.

Anahtar Kelimeler

Cryptology, Encryption, AES, Matrix

Matrix Encryption Standard

Öz

AES (Advanced Encryption Standard) is a standard for encrypting electronic data. AES operates on a column-major order array of bytes. The operations in the matrix are also performed on the polynomials in a special finite field and using S-box. We firstly recall necessary information about matrix algebra. In the present work, we examine the AES encryption method. We create a new encryption algorithm called matrix encryption standard (MES). MES is performed by similar steps to the AES algorithm over 16x16 matrices with elements {0,1} without using polynomials operations and S-box in the AES algorithm. So, we provide 256-bits plain text to be encrypted by passing it through certain rounds with the 16x16 matrix key. In order to decrypt the cipher text, we take the reverse of the 16x16 key matrix through the computer and perform the decryption process by performing a certain number of reverse rounds.

Anahtar Kelimeler

Cryptology, Encryption, AES, Matrix

Kaynakça

• [1] Avaroğlu, E., Dişkaya, O., and Menken, H. “The classıcal aes-lıke cryptology vıa the Fıbonaccı polynomıal matrıx”. Turkish journal of engineering, 4(3), 123-128, 2020.
• [2] Ayres, F., and Jaisingh, L. R. “Schaum's outline of theory and problems of abstract algebra”. McGraw-Hill, 2004.
• [3] Kak, Avi. "Lecture 8: AES: The advanced encryption standard." Lecture Notes on’Computer and Network Security’, Purdue University, URL: https://engineering. purdue. edu/kak/compsec/NewLectures/Lecture8. pdf . 2016.
• [4] Koc, C. K. "About cryptographic engineering." Cryptographic engineering. Springer, Boston, MA, 1-4, 2009.
• [5] Paar, C., and Pelzl, J. “Understanding cryptography: a textbook for students and practitioners”. Springer Science & Business Media, 2009.
• [6] Stinson, D. R., and Paterson, M. “Cryptography: theory and practice”. CRC press, 2018.