Exact Formula for RX-Differential Probability Through Modular Addition for All Rotations

Abstract: This work presents an exact and compact formula for the probability of rotation-xor differentials (RX-differentials) through modular addition, for arbitrary rotation amounts, which has been a long-standing open problem. The formula comes with a rigorous proof and is also verified by extensive experiments. Our formula uncovers error in a recent work from 2022 proposing a formula for rotation amounts bigger than 1. Surprisingly, it also affects correctness of the more studied and used formula for the rotation amount equal to 1 (from TOSC 2016). Specifically, it uncovers rare cases where the assumptions of this formula do not hold. Correct formula for arbitrary rotations now opens up a larger search space where one can often find better trails. For applications, we propose automated mixed integer linear programming (MILP) modeling techniques for searching optimal RX-trails based on our exact formula. They are consequently applied to several ARX designs, including Salsa, Alzette and a .... https://tosc.iacr.org/index.php/ToSC/article/view/12087

Angaben zum Objekt

• Standort: Deutsche Nationalbibliothek Frankfurt am Main
• Umfang: Online-Ressource
• Sprache: Englisch

Verweise und Beziehungen

• Erschienen in: Exact Formula for RX-Differential Probability Through Modular Addition for All Rotations ; volume:2025 ; number:1 ; year:2025 ; IACR transactions on symmetric cryptology ; 2025, Heft 1 (2025)

Beteiligte, Orts- und Zeitangaben

• Urheber: Biryukov, Alex ; Lambin, Baptiste ; Udovenko, Aleksei

Weitere Informationen

• DOI: 10.46586/tosc.v2025.i1.542-591
• URN: urn:nbn:de:101:1-2503121754308.156126610206
• Rechteinformation: Open Access; Der Zugriff auf das Objekt ist unbeschränkt möglich.
• Letzte Aktualisierung: 15.08.2025, 07:24 MESZ