UCL Discovery
UCL home » Library Services » Electronic resources » UCL Discovery

Construction of a polynomial invariant annihilation attack of degree 7 for T-310

Courtois, NT; Patrick, A; Abbondati, M; (2020) Construction of a polynomial invariant annihilation attack of degree 7 for T-310. Cryptologia , 44 (4) pp. 289-314. 10.1080/01611194.2019.1706062. Green open access

[thumbnail of nt_unique_inv2_ucry.pdf]
Preview
Text
nt_unique_inv2_ucry.pdf - Accepted version

Download (855kB) | Preview

Abstract

Cryptographic attacks are typically constructed by black-box methods and combinations of simpler properties, for example in [Generalised] Linear Cryptanalysis. In this article, we work with a more recent white-box algebraic-constructive methodology. Polynomial invariant attacks on a block cipher are constructed explicitly through the study of the space of Boolean polynomials which does not have a unique factorisation and solving the so-called Fundamental Equation (FE). Some recent invariant attacks are quite symmetric and exhibit some sort of clear structure, or work only when the Boolean function is degenerate. As a proof of concept, we construct an attack where a highly irregular product of seven polynomials is an invariant for any number of rounds for T-310 under certain conditions on the long term key and for any key and any IV. A key feature of our attack is that it works for any Boolean function which satisfies a specific annihilation property. We evaluate very precisely the probability that our attack works when the Boolean function is chosen uniformly at random.

Type: Article
Title: Construction of a polynomial invariant annihilation attack of degree 7 for T-310
Open access status: An open access version is available from UCL Discovery
DOI: 10.1080/01611194.2019.1706062
Publisher version: https://doi.org/10.1080/01611194.2019.1706062
Language: English
Additional information: This version is the author accepted manuscript. For information on re-use, please refer to the publisher's terms and conditions.
Keywords: algebraic cryptanalysis; ANF; annihilator space; backdoors; Boolean functions; Cold War; Feistel ciphers; Generalised Linear Cryptanalysis; modern block ciphers; multivariate polynomials; polynomial invariants; polynomial ringsT-310; unique factorisation; weak keys
UCL classification: UCL
UCL > Provost and Vice Provost Offices
UCL > Provost and Vice Provost Offices > UCL BEAMS
UCL > Provost and Vice Provost Offices > UCL BEAMS > Faculty of Engineering Science
UCL > Provost and Vice Provost Offices > UCL BEAMS > Faculty of Engineering Science > Dept of Computer Science
URI: https://discovery.ucl.ac.uk/id/eprint/10133690
Downloads since deposit
13Downloads
Download activity - last month
Download activity - last 12 months
Downloads by country - last 12 months

Archive Staff Only

View Item View Item