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

DOI10.1007/978-3-662-53018-4_23zbMath1378.94022OpenAlexW2500084106MaRDI QIDQ2835604

Thorsten Kranz, Gregor Leander, Christof Beierle

Publication date: 30 November 2016

Published in: Advances in Cryptology – CRYPTO 2016 (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1007/978-3-662-53018-4_23

zbMATH Keywords

finite fieldsblock ciphermultiplicationlightweight cryptographyMDS matricesXOR-count

Mathematics Subject Classification ID

Cryptography (94A60) Mathematical problems of computer architecture (68M07)

Related Items (17)

Provable one-XOR matrices for construction of 4 × 4 hardware-oriented MDS diffusion layers ⋮ Involutory-multiple-lightweight MDS matrices based on Cauchy-type matrices ⋮ A framework to optimize implementations of matrices ⋮ A new matrix form to generate all \(3\times 3\) involutory MDS matrices over \(\mathbb{F}_{2^m}\) ⋮ Improved heuristics for low-latency implementations of linear layers ⋮ Construction of recursive MDS matrices using DLS matrices ⋮ Optimizing the depth of quantum implementations of linear layers ⋮ Four by four MDS matrices with the fewest XOR gates based on words ⋮ Twin column parity mixers and Gaston. A new mixing layer and permutation ⋮ On the construction of involutory MDS matrices over \(\mathbb{F}_{2^m}\) ⋮ Almost involutory recursive MDS diffusion layers ⋮ Recursive MDS matrices over finite commutative rings ⋮ Cryptographic properties of cyclic binary matrices ⋮ A proof of the Beierle-Kranz-Leander conjecture related to lightweight multiplication in \(\mathbb{F}_{2^n} \) ⋮ Construction of MDS matrices from generalized Feistel structures ⋮ Construction of lightweight involutory MDS matrices ⋮ On the construction of \(4 \times 4\) lightweight involutory MDS matrices over \(\mathbb{F}_{2^8}\)

Uses Software

• Whirlwind
• Keccak
• LED
• Serpent
• Square

Cites Work

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• Cryptographically significant MDS matrices based on circulant and circulant-like matrices for lightweight applications
• Factorization of polynomials over finite fields
• Whirlwind: a new cryptographic hash function
• A Deeper Understanding of the XOR Count Distribution in the Context of Lightweight Cryptography
• Block Ciphers – Focus on the Linear Layer (feat. PRIDE)
• Direct Construction of Recursive MDS Diffusion Layers Using Shortened BCH Codes
• LS-Designs: Bitslice Encryption for Efficient Masked Software Implementations
• Lightweight MDS Involution Matrices
• The LED Block Cipher
• Recursive Diffusion Layers for (Lightweight) Block Ciphers and Hash Functions
• The block cipher Square
• Serpent: A New Block Cipher Proposal
• Lightweight MDS Generalized Circulant Matrices
• On the Construction of Lightweight Circulant Involutory MDS Matrices
• Matrix Representation of Finite Fields
• Recursive Diffusion Layers for Block Ciphers and Hash Functions
• Keccak
• The PHOTON Family of Lightweight Hash Functions
• FOAM: Searching for Hardware-Optimal SPN Structures and Components with a Fair Comparison

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