A Novel Cryptographic Substitution Box Design Using Gaussian Distribution

• Published in: IEEE access Vol. 7; pp. 15999 - 16007
• Main Authors: Khan, Muhammad Fahad, Ahmed, Adeel, Saleem, Khalid
• Format: Journal Article
• Language: English
• Published: Piscataway IEEE 2019; The Institute of Electrical and Electronics Engineers, Inc. (IEEE)
• Subjects: Algorithms; Approximation; block cipher; Boolean algebra; Boolean functions; Ciphers; Criteria; cryptographic confusion; Cryptography; Distribution functions; Encryption; Gaussian distribution; Histograms; linear fractional transform; Mathematical analysis; Normal distribution; random number generation; S-box; Statistical analysis; Substitutes; Substitution permutation networks; Transforms
• ISSN: 2169-3536; 2169-3536
• DOI: 10.1109/ACCESS.2019.2893176

In this paper, a novel method is being proposed to construct a substitution box or Boolean function for block ciphers using Gaussian distribution and linear fractional transform. The substitution box is constructed by employing a linear fractional transform based on Box-Muller transform, polarization decision, and central limit algorithm. The cryptographic strength of the proposed S-boxes is evaluated with standardized tests such as linear approximation probability, unified averaged changed intensity, bit independent criterion, histogram analysis, nonlinearity score, strict avalanche criterion, and differential approximation probability. The results show that the proposed substitution box achieves better cryptographic strength as compared with the state-of-the-art techniques.