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Lightweight Iterative MDS Matrices: How Small Can We Go?

Shun Li, Siwei Sun, Danping Shi, Chaoyun Li, Lei Hu
2020 IACR Transactions on Symmetric Cryptology  
Guided by these bounds and based on the ideas employed to identify them, we explore the design space of lightweight iterative MDS matrices with other dimensions and report on improved results.  ...  Since the circuit latency is another important factor, we also consider the lower bound of the number of iterations for certain iterative MDS matrices.  ...  In this section, we derive some bounds on the MDS orders of certain iterative MDS matrices, and try to find lightweight iterative MDS matrices with minimal MDS orders.  ... 
doi:10.46586/tosc.v2019.i4.147-170 fatcat:hgf6jospzfcy3atr4imrsr63fy

Lightweight Iterative MDS Matrices: How Small Can We Go?

Shun Li, Siwei Sun, Danping Shi, Chaoyun Li, Lei Hu
2020 IACR Transactions on Symmetric Cryptology  
Guided by these bounds and based on the ideas employed to identify them, we explore the design space of lightweight iterative MDS matrices with other dimensions and report on improved results.  ...  Since the circuit latency is another important factor, we also consider the lower bound of the number of iterations for certain iterative MDS matrices.  ...  In this section, we derive some bounds on the MDS orders of certain iterative MDS matrices, and try to find lightweight iterative MDS matrices with minimal MDS orders.  ... 
doi:10.13154/tosc.v2019.i4.147-170 dblp:journals/tosc/LiSSLH19 fatcat:scp6d7jkfbb53fudychgemwpa4

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.  ...  Even though we focused our studies on involutory MDS matrices, we also obtained results for non-involutory MDS matrices.  ...  We also wish to thank Wang HuaXiong for providing useful and valuable suggestions.  ... 
doi:10.1007/978-3-662-48116-5_23 fatcat:sm3rhkizyrg2hd7qppicvnflcy

Constructing Low-latency Involutory MDS Matrices with Lightweight Circuits

Shun Li, Siwei Sun, Chaoyun Li, Zihao Wei, Lei Hu
2019 IACR Transactions on Symmetric Cryptology  
In recent years, continuous efforts are made on the construction of MDS matrices with small area footprints in the context of lightweight cryptography.  ...  We apply the new SLP heuristic to a large set of lightweight involutory MDS matrices, and we identify a depth 3 involutory MDS matrix whose implementation costs 88 XOR gates, which is superior to the AES  ...  When using MDS matrices as the diffusion layers in iterative block ciphers, it is possible to achieve a desired number of differentially or linearly active non-linear elements with a relatively small number  ... 
doi:10.46586/tosc.v2019.i1.84-117 fatcat:oyldkokh65gw7j3tnja63br3ji

Constructing Low-latency Involutory MDS Matrices with Lightweight Circuits

Shun Li, Siwei Sun, Chaoyun Li, Zihao Wei, Lei Hu
2019 IACR Transactions on Symmetric Cryptology  
In this article, we focus on the construction of lightweight involutory MDS matrices, which are even more desirable than ordinary MDS matrices, since the same circuit can be reused when the inverse is  ...  In recent years, continuous efforts are made on the construction of MDS matrices with small area footprints in the context of lightweight cryptography.  ...  When using MDS matrices as the diffusion layers in iterative block ciphers, it is possible to achieve a desired number of differentially or linearly active non-linear elements with a relatively small number  ... 
doi:10.13154/tosc.v2019.i1.84-117 dblp:journals/tosc/LiSLWH19 fatcat:6xypskh3ardm3dotw662sy6aai

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

Lightweight Multiplication in $$GF(2^n)$$ with Applications to MDS Matrices [chapter]

Christof Beierle, Thorsten Kranz, Gregor Leander
2016 Lecture Notes in Computer Science  
Here we construct new MDS matrices which outperform all previous results when focusing on a round-based hardware implementation.  ...  We investigate which field representation, that is which choice of basis, allows for an optimal implementation.  ...  Acknowledgements We would like to thank Thomas Peyrin for some valuable discussions on the notion of the XOR-count. We would also like to thank Gottfried Herold.  ... 
doi:10.1007/978-3-662-53018-4_23 fatcat:26zxfkx7snewloxmwkehdxhbau

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

Direct construction of quasi-involutory recursive-like MDS matrices from 2-cyclic codes

Victor Cauchois, Pierre Loidreau, Nabil Merkiche
2017 IACR Transactions on Symmetric Cryptology  
In this paper, we propose a direct construction for new recursive-like MDS matrices.  ...  However, as a new type of construction, it offers alternatives for MDS matrices design.  ...  In [SKOP15] , the authors presented a good survey of lightweight MDS matrices with such properties. • Serial or recursive matrices.  ... 
doi:10.13154/tosc.v2016.i2.80-98 dblp:journals/tosc/CauchoisLM16 fatcat:oq2f7wmah5hfjcbjib64d36ika

Direct construction of quasi-involutory recursive-like MDS matrices from 2-cyclic codes

Victor Cauchois, Pierre Loidreau, Nabil Merkiche
2017 IACR Transactions on Symmetric Cryptology  
In this paper, we propose a direct construction for new recursive-like MDS matrices.  ...  However, as a new type of construction, it offers alternatives for MDS matrices design.  ...  Hardware Architecture In the previous sections, we demonstrated how to directly construct MDS matrices with quasi-involutory property.  ... 
doi:10.46586/tosc.v2016.i2.80-98 fatcat:le5xtesp5ja4lgt75bbsqxj6qy

The QARMA Block Cipher Family. Almost MDS Matrices Over Rings With Zero Divisors, Nearly Symmetric Even-Mansour Constructions With Non-Involutory Central Rounds, and Search Heuristics for Low-Latency S-Boxes

Roberto Avanzi
2017 IACR Transactions on Symmetric Cryptology  
We introduce and analyse a family of Almost MDS matrices defined over a ring with zero divisors that allows us to encode rotations in its operation while maintaining the minimal latency associated to {  ...  0, 1}-matrices.  ...  We acknowledge many interesting discussions with Can Acar, Satish Anand, Christina Boura, Antonio Cardoso Costa, Xiaoyang Dong, Orr Dunkelman, Richard Grisenthwaite, Rene Peralta, Meltem Sönmez Turan,  ... 
doi:10.46586/tosc.v2017.i1.4-44 fatcat:iaiczp4lhzh5pgz4quzhjcj3jm

The QARMA Block Cipher Family. Almost MDS Matrices Over Rings With Zero Divisors, Nearly Symmetric Even-Mansour Constructions With Non-Involutory Central Rounds, and Search Heuristics for Low-Latency S-Boxes

Roberto Avanzi
2017 IACR Transactions on Symmetric Cryptology  
We introduce and analyse a family of Almost MDS matrices defined over a ring with zero divisors that allows us to encode rotations in its operation while maintaining the minimal latency associated to {  ...  0, 1}-matrices.  ...  We acknowledge many interesting discussions with Can Acar, Satish Anand, Christina Boura, Antonio Cardoso Costa, Xiaoyang Dong, Orr Dunkelman, Richard Grisenthwaite, Rene Peralta, Meltem Sönmez Turan,  ... 
doi:10.13154/tosc.v2017.i1.4-44 dblp:journals/tosc/Avanzi17 fatcat:l5zgiqa3lzedpdajqqomixpabe

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

Towards Low-Latency Implementation of Linear Layers

Qun Liu, Weijia Wang, Yanhong Fan, Lixuan Wu, Ling Sun, Meiqin Wang
2022 IACR Transactions on Symmetric Cryptology  
Besides, we obtain better implementations in XOR gates for 54.3% of 4256 Maximum Distance Separable (MDS) matrices proposed by Li et al. at FSE 2019.  ...  Lightweight cryptography features a small footprint and/or low computational complexity. Low-cost implementations of linear layers usually play an important role in lightweight cryptography.  ...  In addition, our research provides a new tool for the construction of lightweight MDS matrices.  ... 
doi:10.46586/tosc.v2022.i1.158-182 fatcat:y57fgnqe5bgz3hat5isn4stbym
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