On additive differential probabilities of the composition of bitwise exclusive-or and a bit rotation
arXiv (Cornell University)(2023)
摘要
Properties of the additive differential probability
adp^XR of the composition of bitwise XOR and a bit
rotation are investigated, where the differences are expressed using addition
modulo 2^n. This composition is widely used in ARX constructions consisting
of additions modulo 2^n, bit rotations and bitwise XORs. Differential
cryptanalysis of such primitives may involve maximums of
adp^XR, where some of its input or output differences are
fixed. Although there is an efficient way to calculate this probability
(Velichkov et al, 2011), many of its properties are still unknown. In this
work, we find maximums of adp^XR, where the rotation is
one bit left/right and one of its input differences is fixed. Some symmetries
of adp^XR are obtained as well. We provide all its
impossible differentials in terms of regular expression patterns and estimate
the number of them. This number turns out to be maximal for the one bit left
rotation and noticeably less than the number of impossible differentials of
bitwise XOR.
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关键词
additive differential probabilities,bitwise
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