Variable elimination strategies and construction of nonlinear polynomial invariant attacks on T-310

One of the major open problems in symmetric cryptanalysis is to discover new specific types of invariant properties for block ciphers. In this article, we study nonlinear polynomial invariant attacks. The number of such attacks grows as and systematic exploration is not possible. The main question i...

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Published in:Cryptologia Vol. 44; no. 1; pp. 20 - 38
Main Authors: Courtois, Nicolas T., Georgiou, Marios
Format: Journal Article
Language:English
Published: West Point Taylor & Francis 02.01.2020
Taylor & Francis Inc
Subjects:
algebraic cryptanalysis
Algorithms
ANF
backdoors
Boolean functions
ciphertext-only attacks
Circuits
Cold War
Complexity
Cryptography
Encryption
Feistel ciphers
generalized linear cryptanalysis
higher-order correlation attacks
history
I/O sums
Invariants
Mathematical analysis
modern block ciphers
multivariate polynomials
partitioning cryptanalysis
polynomial invariants
Polynomials
T-310
weak keys
ISSN:0161-1194, 1558-1586
Online Access:Get full text
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Summary:One of the major open problems in symmetric cryptanalysis is to discover new specific types of invariant properties for block ciphers. In this article, we study nonlinear polynomial invariant attacks. The number of such attacks grows as and systematic exploration is not possible. The main question is HOW do we find such attacks? We have developed a constructive algebraic approach that is about making sure that a certain combination of polynomial equations is zero. We work by progressive elimination of specific variables in polynomial spaces and we show that one can totally eliminate big chunks of the cipher circuit. As an application, we present several new attacks on the historical T-310 block cipher that has particularly large hardware complexity and a very large number of rounds compared with modern ciphers, e.g., AES. However, all this complexity is not that useful if we are able to construct new types of polynomial invariant attacks that work for any number of rounds.
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ISSN:0161-1194
1558-1586
DOI:10.1080/01611194.2019.1650845