International Association for Cryptologic Research

International Association
for Cryptologic Research

CryptoDB

Nicky Mouha

Publications

Year
Venue
Title
2021
TOSC
Maximums of the Additive Differential Probability of Exclusive-Or
At FSE 2004, Lipmaa et al. studied the additive differential probability adp⊕(α,β → γ) of exclusive-or where differences α,β,γ ∈ Fn2 are expressed using addition modulo 2n. This probability is used in the analysis of symmetric-key primitives that combine XOR and modular addition, such as the increasingly popular Addition-Rotation-XOR (ARX) constructions. The focus of this paper is on maximal differentials, which are helpful when constructing differential trails. We provide the missing proof for Theorem 3 of the FSE 2004 paper, which states that maxα,βadp⊕(α,β → γ) = adp⊕(0,γ → γ) for all γ. Furthermore, we prove that there always exist either two or eight distinct pairs α,β such that adp⊕( α,β → γ) = adp⊕(0,γ → γ), and we obtain recurrence formulas for calculating adp⊕. To gain insight into the range of possible differential probabilities, we also study other properties such as the minimum value of adp⊕(0,γ → γ), and we find all γ that satisfy this minimum value.
2017
ASIACRYPT
2016
ASIACRYPT
2015
EPRINT
2015
EPRINT
2015
EPRINT
2015
CRYPTO
2014
EPRINT
2014
EPRINT
2014
ASIACRYPT
2014
FSE
2012
FSE
2011
FSE

Program Committees

FSE 2020
FSE 2019