A note on MDS property of circulant matrices
*Tapas ChatterjeeCorresponding authortapasc@iitrpr.ac.inDepartment of MathematicsIndian Institute of Technology RoparRopar, Punjab, India0000-0002-6956-2322View full profile → , Ayantika Lahaayantikalaha@iitpkd.ac.inDepartment of Computer Science and EngineeringIndian Institute of Technology PalakkadPalakkad, Kerala, India0000-0001-8406-3006View full profile →
* Corresponding author · click or hover a name for details
- Received:
- 09 Oct 2024
- Published Online:
- 11 Sep 2025
- Article type:
- Research Article
- Language:
- EN
- Article no.:
- JDMSC-2315
- Pages:
- 1595–1608
Abstract
Keywords
Subject Classifications
References
[1] P. S. L. M. Barreto and V. Rijmen, The Whirlpool hashing function (2003).
[2] V. Cauchois and P. Loidreau, On circulant involutory MDS matrices, Design, Codes and Cryptography, vol. 87, pp. 249-260 (2019).
[3] T. Chatterjee and A. Laha, A note on Semi-Orthogonal (G-matrix) and Semi-Involutory MDS Matrices, Finite Fields and Their Applications, vol. 92, Paper No. 102279, 27 (2023).
[4] T. Chatterjee and A. Laha. A note on cyclic MDS and non-MDS matrices. Cryptography and Communications, vol. 17, pp. 1109–1124 (2025).
[5] T. Chatterjee and A. Laha, A Characterization of Semi-Involutory MDS Matrices, arxiv.org/pdf/2406.12842 (2024).
[6] T. Chatterjee and A. Laha, On MDS Property of g-Circulant Matrices, arxiv.org/pdf/2406.15872 (2024).
[7] T. Chatterjee, A. Laha and S. K. Sanadhya, On the Structure of Format Preserving Sets in the Diffusion Layer of Block Ciphers, IEEE Transactions on Information Theory, vol. 68, no. 12, pp. 8268-8279 (2022).
[8] G. Cheon, B. Curtis and H. Kim, Semi-involutory matrices and signed self-inverse, Linear Algebra and its Applications, vol. 622, pp. 294-315 (2021).
[9] J. Daemen, L. R. Knudsen and V. Rijmen, The block cipher SQUARE, Fast Software Encryption Workshop, LNCS, vol. 1267, pp. 149-165 (1997).
[10] J. Daemen and V. Rijmen, The Design of Rijndael: AES - The Advanced Encryption Standard, Springer-Verlag (2002).
[11] X. D. Dong, B. S. Cheong, and E. Gunawan, Matrix characterization of MDS linear codes over modules, Linear Algebra and its Application, vol. 277, pp. 57-61 (1998).
[12] M. Fiedler and F. J. Hall, G-matrices, Linear Algebra and its Applications, pp. 731-741 (2012).
[13] J. Guo, T. Peyrin and A. Poschmann, The PHOTON family of lightweight hash functions, CRYPTO 2011, Lecture Notes in Computer Science, vol. 6841, pp. 222-239 (2011).
[14] J. Guo, T. Peyrin, A. Poschmann, and M. J. B. Robshaw, The LED Block Cipher, CHES 2011, LNCS, vol. 6917, pp. 326-341 (2011).
[15] K. C. Gupta and I. G. Ray, On Constructions of Involutory MDS Matrices, Progress in Cryptology -- AFRICACRYPT 2013, vol. 7918, pp. 43-60, 2013).
[16] K. C. Gupta and I. G. Ray, On constructions of circulant MDS matrices for lightweight cryptography, ISPEC 2014, Springer, pp. 564-576 (2014).
[17] K. C. Gupta and I. G. Ray, Cryptographically significant MDS matrices based on circulant and circulant-like matrices for lightweight applications, Cryptography and Communications, vol. 7, pp. 257-287 (2015).
[18] K. C. Gupta, S. K. Pandey, I. G. Ray and S. Samanta, Cryptographically significant mds matrices over finite fields: A brief survey and some generalized results, Advances in Mathematics of Communications, pp. 779-843 (2019).
[19] K. C. Gupta, S. K. Pandey and A. Venkateswarlu, On the direct construction of recursive MDS matrices, Design Codes and Cryptography, vol. 82, pp. 77-94 (2017).
[20] J. Lacan and J. Fimes, Systematic MDS erasure codes based on Vandermonde matrices, IEEE Trans. Commun. Lett., vol. 8, pp. 570-572 (2004).
[21] M. Liu and S. M. Sim, Lightweight MDS generalized circulant matrices, Fast Software Encryption, LNCS, vol. 9783, pp. 101-120 (2016).
[22] T. Luong, On the direct building of 8×8 self-reciprocal recursive MDS Matrices effective for implementation over GF(q) using Reed-Solomon codes, Journal of Discrete Mathematical Sciences and Cryptography, vol. 26, no. 4, pp. 1237-1248 (2023).
[23] F. J. MacWilliams and N. J. A. Sloane, The Theory of Error Correcting Codes, North-Holland Publishing Co., Amsterdam-New York-Oxford (1977).
[24] V. Rijmen, J. Daemen, B. Preneel, A. Bosselaers and E.D. Win, The cipher SHARK, Fast Software Encryption Workshop, LNCS,vol. 1039, pp. 99-112 (1996).
[25] S. Sarkar and H. Syed, Lightweight diffusion layer: Importance of Toeplitz matrices, IACR Trans. Symmetric Cryptol., 2016, 95-113 (2016).
[26] S. Sarkar and H. Syed, Analysis of Toeplitz MDS matrices, ACISP 2017, LNCS, vol. 10343, pp. 3-18 (2017).
[27] M. Sajadieh, M. Dakhilalian, H. Mala and B. Omoomi, On construction of involutory MDS matrices from Vandermonde Matrices in GF(2q)., Design, Codes Cryptography, vol. 64, pp. 287-308 (2012).
[28] B. Schneier, J. Kelsey, D. Whiting, D. Wagner, C. Hall and N. Ferguson, Twofish: A 128-bit block cipher, In the first AES Candidate Conference. National Institute for Standards and Technology (1998).
[29] M. R. M. Shamsabad and S. M. Dehnavi, Nonlinear 4×4 MDS diffusion layers, Journal of Information and Optimization Sciences, vol. 43, no. 4, pp. 663-676 (2022).
[30] A. M. Youssef, S. Mister and S. E. Tavares, On the Design of Linear Transformations for Substitution Permutation Encryption Networks, In Workshop On Selected Areas in Cryptography, SAC, vol. 97, pp. 40-48 (1997).
[31] A. A. Zain and B. S. Rajan, Algebraic characterization of MDS group codes over cyclic groups, IEEE Transactions on Information Theory, vol. 41, pp. 2052-2056 (1995).
