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On the Construction of Lightweight Circulant Involutory MDS Matrices [chapter]

Yongqiang Li, Mingsheng Wang
2016 Lecture Notes in Computer Science  
To the best of our knowledge, it is the first time that circulant involutory MDS matrices have been constructed.  ...  More examples of circulant involutory MDS matrices are given in the appendix.  ...  This work was supported by the 973 project under Grant (2013CB834203), by the National Science Foundation of China (No.61303255, No.61379142).  ... 
doi:10.1007/978-3-662-52993-5_7 fatcat:bmeaynvmenc2tabb2lijevp3qa

Construction of generalized-involutory MDS matrices [article]

Xuting Zhou, Tianshuo Cong
2022 IACR Cryptology ePrint Archive  
In this paper, we present a new type of MDS matrices called generalized-involutory MDS matrices, implementation of whose inverse matrix-vector products in decryption is the combination of the matrix-vector  ...  The main advantage of involutory MDS matrices lies in that both encryption and decryption share the same matrix-vector product.  ...  [6] also relaxed circulancy to θ-circulancy to construct θ-circulant involutory MDS matrices for fields of characteristic 2.  ... 
dblp:journals/iacr/ZhouC22 fatcat:qyeqjtxhebffdbgvgar4f3occ4

Lightweight MDS Involution Matrices [chapter]

Siang Meng Sim, Khoongming Khoo, Frédérique Oggier, Thomas Peyrin
2015 Lecture Notes in Computer Science  
In this article, we provide new methods to look for lightweight MDS matrices, and in particular involutory ones.  ...  the search space and make lightweight MDS matrices of rather high dimension possible to find.  ...  Acknowledgments The authors would like to thank the anonymous referees for their helpful comments. We also wish to thank Wang HuaXiong for providing useful and valuable suggestions.  ... 
doi:10.1007/978-3-662-48116-5_23 fatcat:sm3rhkizyrg2hd7qppicvnflcy

On Efficient Constructions of Lightweight MDS Matrices

Lijing Zhou, Licheng Wang, Yiru Sun
2018 IACR Transactions on Symmetric Cryptology  
Secondly, we discuss the existence of several types of involutory MDS matrices and propose an efficient necessary-and-sufficient condition for identifying a Hadamard matrix being involutory.  ...  Firstly, by analyzing the minimal polynomials of binary matrices with 1 XOR count and element-matrices with few XOR counts, we present an efficient method for constructing MDS matrices with as few XOR  ...  Acknowledgments We want to give our thanks to the anonymous reviews of FSE 2018 and to Dr. Bing Sun for his effort to improving the quality of our manuscript.  ... 
doi:10.46586/tosc.v2018.i1.180-200 fatcat:lvrexxiopzebjb3o3bootfe5xm

On Efficient Constructions of Lightweight MDS Matrices

Lijing Zhou, Licheng Wang, Yiru Sun
2018 IACR Transactions on Symmetric Cryptology  
Secondly, we discuss the existence of several types of involutory MDS matrices and propose an efficient necessary-and-sufficient condition for identifying a Hadamard matrix being involutory.  ...  Firstly, by analyzing the minimal polynomials of binary matrices with 1 XOR count and element-matrices with few XOR counts, we present an efficient method for constructing MDS matrices with as few XOR  ...  Acknowledgments We want to give our thanks to the anonymous reviews of FSE 2018 and to Dr. Bing Sun for his effort to improving the quality of our manuscript.  ... 
doi:10.13154/tosc.v2018.i1.180-200 dblp:journals/tosc/ZhouWS18 fatcat:z3nqzvryqfhmdl4gezqn6pydpi

Design of Lightweight Linear Diffusion Layers from Near-MDS Matrices

Chaoyun Li, Qingju Wang
2017 IACR Transactions on Symmetric Cryptology  
We present new designs of lightweight linear diffusion layers by constructing lightweight near-MDS matrices. Firstly generic n×n near-MDS circulant matrices are found for 5 ≤ n ≤9.  ...  Moreover, we present some involutory near-MDS matrices of order 8 constructed from Hadamard matrices.  ...  Acknowledgements The authors would like to thank Bart Preneel and the anonymous reviewers of FSE for their comments and suggestions.  ... 
doi:10.46586/tosc.v2017.i1.129-155 fatcat:vttzixkrvrdxhbmqzonfjjovhu

Design of Lightweight Linear Diffusion Layers from Near-MDS Matrices

Chaoyun Li, Qingju Wang
2017 IACR Transactions on Symmetric Cryptology  
We present new designs of lightweight linear diffusion layers by constructing lightweight near-MDS matrices. Firstly generic n×n near-MDS circulant matrices are found for 5 ≤ n ≤9.  ...  Moreover, we present some involutory near-MDS matrices of order 8 constructed from Hadamard matrices.  ...  Acknowledgements The authors would like to thank Bart Preneel and the anonymous reviewers of FSE for their comments and suggestions.  ... 
doi:10.13154/tosc.v2017.i1.129-155 dblp:journals/tosc/LiW17 fatcat:gdg5ior3t5dqrnslbmrgtkmzc4

Lightweight Diffusion Layer: Importance of Toeplitz Matrices

Sumanta Sarkar, Habeeb Syed
2016 IACR Transactions on Symmetric Cryptology  
Further we give theoretical constructions of 4 × 4 involutory MDS matrices over F24 and F28 that have the best known XOR counts so far: for F24 our construction gives an involutory MDS matrix that actually  ...  We give theoretical constructions of Toeplitz MDS matrices and show that they achieve the minimum XOR count. We also prove that Toeplitz matrices cannot be both MDS and involutory.  ...  One may refer to [10] for the construction of circulant MDS matrices, where they also proved that an MDS circulant matrix cannot be involutory.  ... 
doi:10.13154/tosc.v2016.i1.95-113 dblp:journals/tosc/SarkarS16 fatcat:xgpbl4c6avhdrinkexbaqyx27a

Lightweight Diffusion Layer: Importance of Toeplitz Matrices

Sumanta Sarkar, Habeeb Syed
2016 IACR Transactions on Symmetric Cryptology  
Further we give theoretical constructions of 4 × 4 involutory MDS matrices over F24 and F28 that have the best known XOR counts so far: for F24 our construction gives an involutory MDS matrix that actually  ...  We give theoretical constructions of Toeplitz MDS matrices and show that they achieve the minimum XOR count. We also prove that Toeplitz matrices cannot be both MDS and involutory.  ...  One may refer to [10] for the construction of circulant MDS matrices, where they also proved that an MDS circulant matrix cannot be involutory.  ... 
doi:10.46586/tosc.v2016.i1.95-113 fatcat:oabua5opc5hgrmglxn5bd4geke

Lightweight MDS Generalized Circulant Matrices [chapter]

Meicheng Liu, Siang Meng Sim
2016 Lecture Notes in Computer Science  
In this article, we analyze the circulant structure of generalized circulant matrices to reduce the search space for finding lightweight MDS matrices.  ...  To the best of our knowledge, the latter matrices are the first of its kind, which have a similar matrix structure as circulant matrices and are involutory and MDS simultaneously.  ...  Acknowledgements The authors would like to thank Jian Guo, Thomas Peyrin and Yu Sasaki for their valuable suggestions.  ... 
doi:10.1007/978-3-662-52993-5_6 fatcat:gdkgxfau45edxhhyalkqmgojeu

On the Construction of20×20and24×24Binary Matrices with Good Implementation Properties for Lightweight Block Ciphers and Hash Functions

Muharrem Tolga Sakallı, Sedat Akleylek, Bora Aslan, Ercan Buluş, Fatma Büyüksaraçoğlu Sakallı
2014 Mathematical Problems in Engineering  
The powers of the companion matrix for an irreducible polynomial overGF(2)with degree 5 and 4 are used in finite field Hadamard or circulant manner to construct20×20and24×24binary matrices, respectively  ...  We present an algebraic construction based on state transform matrix (companion matrix) forn×n(wheren≠2k,kbeing a positive integer) binary matrices with high branch number and low number of fixed points  ...  The authors also thank Orhun Kara for his valuable comments on the discussion of Remark 7.  ... 
doi:10.1155/2014/540253 fatcat:vbr5tc7rcjgf3irzrpgr5ufbza

Shorter Linear Straight-Line Programs for MDS Matrices

Thorsten Kranz, Gregor Leander, Ko Stoffelen, Friedrich Wiemer
2017 IACR Transactions on Symmetric Cryptology  
Recently a lot of attention is paid to the search for efficiently implementable MDS matrices for lightweight symmetric primitives.  ...  As a result, we achieve implementations of known, locally optimized, and new MDS matrices that significantly outperform all implementations from the literature.  ...  Acknowledgements We would like to thank Joan Boyar, René Peralta, Chiara Schiavo, and Andrea Visconti for valuable comments on implementations and other practical details of their heuristics.  ... 
doi:10.46586/tosc.v2017.i4.188-211 fatcat:n563zn5iijhddlsfjpl4g56l3e

Shorter Linear Straight-Line Programs for MDS Matrices. Yet another XOR Count Paper

Thorsten Kranz, Gregor Leander, Ko Stoffelen, Friedrich Wiemer
2017 IACR Transactions on Symmetric Cryptology  
Recently a lot of attention is paid to the search for efficiently implementable MDS matrices for lightweight symmetric primitives.  ...  As a result, we achieve implementations of known, locally optimized, and new MDS matrices that significantly outperform all implementations from the literature.  ...  Acknowledgements We would like to thank Joan Boyar, René Peralta, Chiara Schiavo, and Andrea Visconti for valuable comments on implementations and other practical details of their heuristics.  ... 
doi:10.13154/tosc.v2017.i4.188-211 dblp:journals/tosc/KranzLSW17 fatcat:k3gat6oymjfnffndlukjz3b4ay

New Subquadratic Algorithms for Constructing Lightweight Hadamard MDS Matrices (Full Version) [article]

Tianshuo Cong, Ximing Fu, Xuting Zhou, Yuli Zou, Haining Fan
2020 IACR Cryptology ePrint Archive  
To the best of our knowledge, subquadratic multipliers have not been used to construct MDS matrices.  ...  In this paper we mainly talk about constructing lightweight Hadamard MDS matrices based on subquadratic multipliers over GF(2 4 ).  ...  We find 4 × 4 and 8 × 8 lightweight MDS matrices with the fewest XOR counts over GF (2 4 ) until now. In this paper, we focus on the construction of lightweight MDS Hadamard matrices over GF (2 4 ).  ... 
dblp:journals/iacr/CongFZZF20 fatcat:rr3xircr45gsba7ymgnzb5e54a

On circulant involutory MDS matrices

Victor Cauchois, Pierre Loidreau
2018 Designs, Codes and Cryptography  
Finally, we relax further the involutory definition and propose a new direct construction of almost involutory θ-circulant MDS matrices.  ...  We give a new algebraic proof of the non-existence of circulant involutory MDS matrices with coefficients in fields of characteristic 2.  ...  on the size of potential involutory circulant MDS matrices.  ... 
doi:10.1007/s10623-018-0520-3 fatcat:yxg2ofrgw5b5pgvvrbuydmaega
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