Block Ciphers with Matrices Operating Alternately over Columns and Rows

Pablo Freyre, Oristela Cuellar, Nelson Díaz, Adrián Alfonso


AbstractIn this paper, we present the dynamic cryptographic algorithms for long states named ACDEL-2D and ACDEL-3D. The first one was inspired by Rijndael and the second one was inspired by 3D, a three-dimensional block cipher. In both proposals, MDS matrices are used alternately on rows and columns of the state and all transformations used in the encryption process are randomly selected depending on pseudorandom sequences. In the block cipher ACDEL-3D the state takes the form of a rectangular parallelepiped or cuboid.

Tóm tắtTrong bài báo này, chúng tôi trình bày các thuật toán mật mã động cho các trạng thái dài, có tên là ACDEL-2D và ACDEL-3D. Thuật toán đầu tiên bắt nguồn từ thuật toán Rijndael và thuật toán thứ hai bắt nguồn từ thuật toán 3D, một thuật toán với khối dữ liệu được biểu diễn ở dạng  ba chiều. Cả hai đề xuất đều sử dụng xen kẽ ma trận MDS trong các hàng và cột của trạng thái và tất cả các phép biến đổi được sử dụng trong quá trình mã hóa được chọn ngẫu nhiên tùy thuộc vào chuỗi giả ngẫu nhiên. Trong mật mã khối ACDEL-3D, trạng thái có dạng hình chữ nhật song song hoặc hình khối. 


Block cipher design; Rijndael; Dynamic functions

Full Text:



Daemen J. and Rijmen V. The Rijndael block cipher. AES proposal. 1999. http/∼iran/rijndael.pdf. Accessed on Dec 11, 2020.

Federal Information Processing Standard. Announcing the Advanced Encryption Standard (AES). FIPS Publication 197, 2001.

Daemen J. and Rijmen V. “The design of Rijndael: AES - The Advanced Encryption Standard”. Second Edition. Springer. 2020.

Nakahara J. and Abrahao E. "A New Involutory MDS Matrix for the AES." IJ Network Security 9 (2), 2009.

Elumalai R. and Raji A. "Improving diffusion power of AES Rijndael with 8x8 MDS matrix." International Journal of Scientific & Engineering Research 2 (3), 2011.

Liu Z. and De H. "Dynamic Encryption Algorithm Based on Rijndael." Advanced Materials Research. Vol. 490. Trans Tech Publications Ltd, 2012.

Craig Suzanne. "A Simplified AES with Field Characteristic 7." Proceedings of the NCUR. 2014.

Gowda S., Aravind H. and Usha S. "Design and ASIC Implementation of Modified Rijndael Cipher." (IRJET) International Research Journal of Engineering and Technology. 2016.

Yang M., Xiao B. and Meng Q. "New AES Dual Ciphers Based on Rotation of Columns." Wuhan University Journal of Natural Sciences 24 (2), 2019.

Bossert J, et al. "Pholkos - Efficient Large-state Tweakable Block Ciphers from the AES Round Function." IACR ePrint Archive, Vol. 275, 2020.

Nakahara J. "3D: A three-dimensional block cipher." International Conference on Cryptology and Network Security. Springer, Berlin, Heidelberg, 2008.

Ariffin S., Mahmod R. and Jaafar A.. "Immune systems approaches for cryptographic algorithm." Sixth International Conference on

Bio-Inspired Computing: Theories and Applications. IEEE, 2011.

Jamel S., et al. “The hybrid cubes encryption algorithm (HiSea).” Advances in Wireless, Mobile Networks and Applications. Springer, 2011.

Chugunkov I., et al. “Three - dimensional data stochastic transformation algorithms for hybrid supercomputer implementation.” 17th Mediterranean Electrotechnical Conference. IEEE, 2014.

Federal Information Processing Standard. “SHA-3 standard: Permutation-based hash and extendable-output functions.” FIPS Publication 202, 2015.

Wang Q. and Jin C. “A non-alternate 3D structure and its practical security evaluation against differential and linear cryptanalysis.” Science China Information Sciences 61 (5), 2018.

Rijmen V., Daemen J., Preneel B., Bosselaers A. and De Win E. “The cipher SHARK”. LNCS 1039, pp. 99–111. Springer, 1996.

Federal Agency on Technical Regulation and Metrology. “National Standard of the Russian Federation GOST R34.12-2015”. 2015.

Freyre P, Díaz N and Morgado E. R. “Some algorithms related to matrices with entries in a finite field”. Journal of Discrete Mathematical Sciences & Cryptography. India. Vol. 12, No. 5, pp. 509–519. 2009.

Freyre P and Díaz N. “Generación aleatoria de permutaciones del grupo simétrico o del grupo alternado”. Revista Investigación Operacional. Vol. 36, No. 2, 2015.

Freyre P, Díaz N, Díaz R and Pérez C. “Random generation of MDS matrices”. Proceedings of Current Trends in Cryptology CTCrypt2014. Russia, 2014.

Gupta K. C. and Ray I. G. “On constructions of MDS matrices from companion matrices for lightweight cryptography”. In CD-ARES.2013 Workshop: MOCrySEn, pp. 29-43, Springer. 2013.


  • There are currently no refbacks.