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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.  ...  By proving many new properties and equivalence classes for circulant matrices, we greatly reduce the search space for finding lightweight maximum distance separable (MDS) circulant matrices.  ...  Therefore, this paper is devoted to tackle these problems and reduce the search space for finding generic lightweight MDS circulant matrices through analyzing the circulant structure. Contributions.  ... 
doi:10.1007/978-3-662-52993-5_6 fatcat:gdkgxfau45edxhhyalkqmgojeu

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

Yongqiang Li, Mingsheng Wang
2016 Lecture Notes in Computer Science  
Keywords: MDS matrix, circulant involutory matrix, Hadamard matrix, lightweight c IACR 2016. This paper is an extended version in FSE 2016.  ...  More examples of circulant involutory MDS matrices are given in the appendix.  ...  Lightweight circulant MDS matrices In this section, we investigate the construction of lightweight circulant involutory, non-involutory and orthogonal MDS matrices respectively.  ... 
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  ...  For the purpose of verifying the existence of such matrices, we found 4 × 4 Hadamard generalized-involutory MDS matrix over GF(2 4 ) consuming as little as 38 XOR gates with 4 additional XOR gates for  ...  [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

On The Construction Of Lightweight Circulant Maximum Distance Separable Matrices

Qinyi Mei, Li-Ping Wang
2017 Zenodo  
We propose a new method of constructing lightweight MDS matrices using circulant matrices which can be implemented efficiently in hardware.  ...  In the present paper, we investigate the problem of constructing MDS matrices which are both lightweight and low-latency.  ...  CONSTRUCTION OF LIGHTWEIGHT CIRCULANT MDS MATRICES In this section, we investigate the problem of constructing lightweight circulant MDS matrices.  ... 
doi:10.5281/zenodo.1131221 fatcat:vsx6zcfin5fdlfffrep563mf4y

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.  ...  Secondly, the implementation cost of instantiations of the generic near-MDS matrices is examined.  ...  Conclusion This paper presents new designs of lightweight linear diffusion layer from lightweight near-MDS matrices. For 5 ≤ n ≤ 9, some generic n × n near-MDS circulant matrices are found.  ... 
doi:10.13154/tosc.v2017.i1.129-155 dblp:journals/tosc/LiW17 fatcat:gdg5ior3t5dqrnslbmrgtkmzc4

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.  ...  Secondly, the implementation cost of instantiations of the generic near-MDS matrices is examined.  ...  Conclusion This paper presents new designs of lightweight linear diffusion layer from lightweight near-MDS matrices. For 5 ≤ n ≤ 9, some generic n × n near-MDS circulant matrices are found.  ... 
doi:10.46586/tosc.v2017.i1.129-155 fatcat:vttzixkrvrdxhbmqzonfjjovhu

Lightweight MDS Involution Matrices [chapter]

Siang Meng Sim, Khoongming Khoo, Frédérique Oggier, Thomas Peyrin
2015 Lecture Notes in Computer Science  
the search space and make lightweight MDS matrices of rather high dimension possible to find.  ...  In this article, we provide new methods to look for lightweight MDS matrices, and in particular involutory ones.  ...  In this section, we first recall a few properties of MDS matrices and we then explain various constructions of (involutory) MDS matrices that were used to generate lightweight candidates.  ... 
doi:10.1007/978-3-662-48116-5_23 fatcat:sm3rhkizyrg2hd7qppicvnflcy

Lightweight MDS Serial-Type Matrices with Minimal Fixed XOR Count [chapter]

Dylan Toh, Jacob Teo, Khoongming Khoo, Siang Meng Sim
2018 Lecture Notes in Computer Science  
We obtain MDS matrices which outperform existing lightweight (involutory) matrices.  ...  Serial matrices with the MDS property obtain a trade-off between area requirement and clock cycle performance to meet the needs of lightweight cryptography.  ...  We presented new lightweight sparse DSI and LFS k-MDS matrices that outperform existing lightweight matrices.  ... 
doi:10.1007/978-3-319-89339-6_4 fatcat:hycmckyll5gdxip74sgpu6rvdy

On Efficient Constructions of Lightweight MDS Matrices

Lijing Zhou, Licheng Wang, Yiru Sun
2018 IACR Transactions on Symmetric Cryptology  
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  ...  We obtain many new involutory Hadamard MDS matrices with much fewer XOR counts than optimal results reported before.  ...  [12] investigated lightweight Circulant MDS matrices and proved that Circulant involutory MDS matrices do not exist over GF (2 m ). At IACR Transactions on Symmetric Cryptology 2016, Sarkar et al.  ... 
doi:10.13154/tosc.v2018.i1.180-200 dblp:journals/tosc/ZhouWS18 fatcat:z3nqzvryqfhmdl4gezqn6pydpi

On Efficient Constructions of Lightweight MDS Matrices

Lijing Zhou, Licheng Wang, Yiru Sun
2018 IACR Transactions on Symmetric Cryptology  
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  ...  We obtain many new involutory Hadamard MDS matrices with much fewer XOR counts than optimal results reported before.  ...  [12] investigated lightweight Circulant MDS matrices and proved that Circulant involutory MDS matrices do not exist over GF (2 m ). At IACR Transactions on Symmetric Cryptology 2016, Sarkar et al.  ... 
doi:10.46586/tosc.v2018.i1.180-200 fatcat:lvrexxiopzebjb3o3bootfe5xm

Optimizing Implementations of Lightweight Building Blocks

Jérémy Jean, Thomas Peyrin, Siang Meng Sim, Jade Tourteaux
2017 IACR Transactions on Symmetric Cryptology  
For linear permutations, we exhibit several new MDS diffusion matrices lighter than the state-of-the-art, and we also decrease the implementation cost of several already known MDS matrices.  ...  We study the synthesis of small functions used as building blocks in lightweight cryptographic designs in terms of hardware implementations.  ...  We also thank Meicheng Liu for his help in the search for lightweight linear layer.  ... 
doi:10.46586/tosc.v2017.i4.130-168 fatcat:t7hywlbkfrazpkcrcn634rspiy

Optimizing Implementations of Lightweight Building Blocks

Jérémy Jean, Thomas Peyrin, Siang Meng Sim, Jade Tourteaux
2017 IACR Transactions on Symmetric Cryptology  
For linear permutations, we exhibit several new MDS diffusion matrices lighter than the state-of-the-art, and we also decrease the implementation cost of several already known MDS matrices.  ...  We study the synthesis of small functions used as building blocks in lightweight cryptographic designs in terms of hardware implementations.  ...  We also thank Meicheng Liu for his help in the search for lightweight linear layer.  ... 
doi:10.13154/tosc.v2017.i4.130-168 dblp:journals/tosc/JeanPST17 fatcat:gwpxqbtsdzflnkuq4wvd23b3ru

Applying Horner's Rule to Optimize Lightweight MDS Matrices

Jian Bai, Yao Sun, Ting Li, Dingkang Wang
2019 International Journal of Digital Crime and Forensics  
This article is concerned with the problem of constructing lightweight MDS matrices. The authors present a new construction of 4 × 4 MDS matrices over GL(F2, m) for any integer m.  ...  They give sufficient and necessary conditions to determine whether the construction is an MDS matrix. Further, for any even number m ≥ 4, they construct lightweight MDS matrices in this structure.  ...  Another way for constructing lightweight MDS matrices is by recursive construction.  ... 
doi:10.4018/ijdcf.2019100106 fatcat:4o243wf36ngq7cwdiafxnniqga

Towards Lightweight Error Detection Schemes for Implementations of MixColumns in Lightweight Cryptography [article]

Anita Aghaie, Mehran Mozaffari Kermani, Reza Azarderakhsh
2018 arXiv   pre-print
In this paper, through considering lightweight cryptography, we present a comparative realization of MDS matrices used in the VLSI implementations of lightweight cryptography.  ...  We verify the MixColumn/MixNibble transformation using MDS matrices and propose reliability approaches for thwarting natural and malicious faults.  ...  One of the common methods to construct lightweight MDS matrices, e.g., circulant, is sparing and compacting in implementation, and then composing it several times in which it provides similar rows in matrices  ... 
arXiv:1804.06480v1 fatcat:36r3vfcbrzcpxa5bps6zp366kq

Lightweight Diffusion Layer: Importance of Toeplitz Matrices

Sumanta Sarkar, Habeeb Syed
2016 IACR Transactions on Symmetric Cryptology  
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.  ...  In this paper we report the minimum value of XOR counts of 4 × 4 MDS matrices over F24 and F28 , respectively.  ...  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
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