Continuous Diffusion Analysis

• Published in: IEEE access Vol. 8; pp. 123735 - 123745
• Main Authors: Coutinho, Murilo, De Sousa, Rafael Timoteo, Borges, Fabio
• Format: Journal Article
• Language: English
• Published: Piscataway IEEE 2020; The Institute of Electrical and Electronics Engineers, Inc. (IEEE)
• Subjects: AES; Algorithms; Atmospheric measurements; Boolean functions; chacha; Ciphers; Continuity (mathematics); continuous generalization; Cryptography; Diffusion; Mathematical functions; Particle measurements; salsa; Schedules; speck; strict avalanche criterion; symmetric cryptography
• ISSN: 2169-3536; 2169-3536
• DOI: 10.1109/ACCESS.2020.3005504

In this work, we propose a new technique called Continuous Diffusion Analysis (CDA) that can be used to study, design, and compare of cryptographic algorithms. CDA allows us to generalize cryptographic algorithms by transforming the discrete bits into probabilities such that the algorithm is generalized into a continuous mathematical function. We propose three new metrics to measure the diffusion in this generalized continuous space, namely the Continuous Avalanche Factor, the Continuous Neutrality Measure, and the Diffusion Factor. In addition, we show that these measures can be used to analyze the diffusion of cryptographic algorithms, in particular, the Diffusion Factor can be used to compare the diffusion without the need of reducing the number of rounds or considering a small subset of bits. To demonstrate the effectiveness of CDA, we also present a case study with the algorithms Salsa, Chacha, AES, and Speck.