Investigating Additive Differential Probabilities of Bitwise XOR and Bit Rotation Composition

Core Concepts

Properties and symmetries of additive differential probabilities are explored for bitwise XOR and bit rotation compositions.

Abstract

The study delves into the properties of the additive differential probability adpXR, focusing on compositions of bitwise XOR and bit rotations. It investigates maximums of adpXR, particularly when rotations are one bit left or right with fixed arguments. Symmetries of adpXR are identified, allowing for the construction of distinct differentials with equal probabilities. The research also provides impossible differentials in terms of regular expression patterns, highlighting the reduction in impossible differentials due to rotation. The paper offers insights into ARX constructions and their vulnerability to differential cryptanalysis.

Stats

Properties of ARX constructions: fast performance, compactness, resistance to timing attacks.
Additive differential probability formulas for XOR and rotations studied.
Maximums of adpXR analyzed for one-bit left/right rotations.
Number estimates for impossible differentials provided.
Comparison between impossible differentials in XOR versus rotation operations.

Quotes

"There is an efficient way to calculate this probability."
"Rotation significantly reduces the number of impossible differentials."
"Symmetries allow us to construct distinct differentials with equal probabilities."

Key Insights Distilled From

On additive differential probabilities of the composition of bitwise exclusive-or and a bit rotation

by Nikolay Kolo... at arxiv.org 03-19-2024

https://arxiv.org/pdf/2303.04097.pdf

Deeper Inquiries

How do these findings impact the security analysis of ARX constructions

The findings regarding the symmetries of adpXR have significant implications for the security analysis of ARX constructions in cryptography. Understanding these symmetries allows cryptanalysts to identify patterns and relationships between differentials, which can aid in the detection of vulnerabilities or weaknesses in cryptographic algorithms. By leveraging these symmetries, researchers can potentially uncover new attack vectors or strengthen existing defense mechanisms against differential cryptanalysis.

What implications do the symmetries of adpXR have on cryptographic algorithms

The symmetries observed in adpXR play a crucial role in cryptographic algorithms by influencing their design and evaluation. These symmetries provide insights into how input differences transform into output differences through XOR operations and bit rotations. Cryptographers can utilize this knowledge to create more robust encryption schemes that are resistant to differential attacks. Additionally, understanding these symmetries helps developers optimize algorithm performance while maintaining security standards.

How can the concept of impossible differentials be applied in other areas beyond cryptography

The concept of impossible differentials, as explored within the context of cryptography, can be applied beyond traditional encryption methods. In other areas such as data processing, error correction codes, and machine learning models, identifying impossible paths or outcomes can enhance system reliability and efficiency. By leveraging the principles behind impossible differentials, practitioners across various fields can improve data integrity, fault tolerance mechanisms, and decision-making processes based on improbable scenarios that should not occur under normal circumstances.