Cryptology ePrint Archive: Report 2021/336

On Closed-Cycle Loops and Applicability of Nonlinear Product Attacks to DES

Nicolas T. Courtois and Matteo Abbondati and Hamy Ratoanina and Marek Grajek

Abstract: In this article we look at the question of the security of Data Encryption Standard (DES) against non-linear polynomial invariant attacks. Is this sort of attack also possible for DES? We present a simple proof of concept attack on DES where a product of 5 polynomials is an invariant for 2 rounds of DES. Furthermore we present numerous additional examples of invariants with higher degrees. We analyse the success probability when the Boolean functions are chosen at random and compare to DES S-boxes. For more complex higher degree attacks the difficulties disappear progressively and up to 100 % of all Boolean functions in 6 variables are potentially vulnerable. A major limitation for all our attacks, is that they work only for a fraction of the key space. However in some cases, this fraction of the key space is very large for the full 16-round DES.

Category / Keywords: secret-key cryptography / block ciphers, Feistel ciphers, DES, weak keys, history of cryptography, algebraic cryptanalysis, generalized linear cryptanalysis, polynomial invariants, annihilator space, Boolean functions, k-normality

Date: received 15 Mar 2021

Contact author: courtois at minrank org

Available format(s): PDF | BibTeX Citation

Note: A student paper which was considerably revised and improved.

Version: 20210317:143422 (All versions of this report)

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