A combinatorial problem related to sparse systems of equations

Nowadays sparse systems of equations occur frequently in science and engineering. In this contribution we deal with sparse systems common in cryptanalysis. Given a cipher system, one converts it into a system of sparse equations, and then the system is solved to retrieve either a key or a plaintext....

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Bibliographic Details
Published in:Designs, codes, and cryptography Vol. 85; no. 1; pp. 129 - 144
Main Authors: Horak, Peter, Semaev, Igor, Tuza, Zsolt
Format: Journal Article
Language:English
Published: New York Springer US 01.10.2017
Springer Nature B.V
Subjects:
Algebra
Boxes
Circuits
Coding and Information Theory
Combinatorial analysis
Complexity
Computer Science
Cryptography
Cryptology
Data Structures and Information Theory
Discrete Mathematics in Computer Science
Encryption
Information and Communication
Linear algebra
Mathematical analysis
05C65
68Q25
Sparse systems of equations
94A60
MaxMinMax problem
Gluing algorithm
ISSN:0925-1022, 1573-7586
Online Access:Get full text
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Summary:Nowadays sparse systems of equations occur frequently in science and engineering. In this contribution we deal with sparse systems common in cryptanalysis. Given a cipher system, one converts it into a system of sparse equations, and then the system is solved to retrieve either a key or a plaintext. Raddum and Semaev proposed new methods for solving such sparse systems common in modern ciphers which are combinations of linear layers and small S-boxes. It turns out that the solution of a combinatorial MaxMinMax problem provides an upper bound on the average computational complexity of those methods. In this paper we initiate the study of a linear algebra variation of the MaxMinMax problem. The complexity bound proved in this paper significantly overcomes conjectured complexity bounds for Gröbner basis type algorithms.
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ISSN:0925-1022
1573-7586
DOI:10.1007/s10623-016-0294-4