On properties of translation groups in the affine general linear group with applications to cryptography

DOI10.1016/j.jalgebra.2020.10.034zbMath1473.20006arXiv1702.00581OpenAlexW3109187247MaRDI QIDQ2216563

Marco Calderini, Roberto Civino, Massimiliano Sala

Publication date: 16 December 2020

Published in: Journal of Algebra (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1702.00581

zbMATH Keywords

block cipherscryptanalysisaffine grouptranslation group

Mathematics Subject Classification ID

Cryptography (94A60) Matrices over special rings (quaternions, finite fields, etc.) (15B33) Subgroups of symmetric groups (20B35) Characterization theorems for permutation groups (20B10) Other groups of matrices (20H99)

Related Items (6)

Unrefinable partitions into distinct parts in a normalizer chain ⋮ Элементарные регулярные абелевы подгруппы аффинной группы векторного пространства в связи с анализом криптографических примитивов;Elementary Abelian regular subgroups of vector space affine group related to cryptanalysis ⋮ Differential experiments using parallel alternative operations ⋮ Rigid commutators and a normalizer chain ⋮ On invariant subspaces in the Lai-Massey scheme and a primitivity reduction ⋮ A chain of normalizers in the Sylow 2-subgroups of the symmetric group on \({\mathbf{2}}^n\) letters

Uses Software

• Magma
• PRESENT

Cites Work

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• More on regular subgroups of the affine group
• The group generated by the round functions of a GOST-like cipher
• Regular subgroups of the affine group with no translations
• The design of Rijndael. The Advanced Encryption Standard (AES)
• Differential cryptanalysis of DES-like cryptosystems
• On some block ciphers and imprimitive groups
• Group theoretic properties of Rijndael-like ciphers
• The Magma algebra system. I: The user language
• On hidden sums compatible with a given block cipher diffusion layer
• Wave-shaped round functions and primitive groups
• Differential attacks: using alternative operations
• Regular subgroups of the affine group
• Regular subgroups with large intersection
• Type-preserving matrices and security of block ciphers
• On Differential Uniformity of Maps that May Hide an Algebraic Trapdoor
• The Round Functions of RIJNDAEL Generate the Alternating Group
• PRESENT: An Ultra-Lightweight Block Cipher
• REGULAR SUBGROUPS OF THE AFFINE GROUP AND RADICAL CIRCLE ALGEBRAS
• Differential Cryptanalysis of Feal and N-Hash
• Generators for Certain Alternating Groups with Applications to Cryptography
• Primitivity of PRESENT and other lightweight ciphers
• ON REGULAR SUBGROUPS OF THE AFFINE GROUP
• Maximal Abelian Subgroups of the Symmetric Groups

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