Linear and differential cryptanalysis of small-sized random (n, m)-S-boxes

S-boxes are used in cryptography in order to provide non-linearity in the design of cryptographic primitives such as block ciphers and hash functions. Some cryptographic primitives use bijective S-boxes as in the Advanced Encryption Standard (AES), and others use surjective S-boxes as in the Data En...

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Published in2016 11th International Conference for Internet Technology and Secured Transactions (ICITST) pp. 447 - 454
Main Authors Alsalami, Y., Yeun, C. Y., Martin, T., Khonji, M.
Format Conference Proceeding
LanguageEnglish
Published Infonomics Society 01.12.2016
Subjects
Block Ciphers
Cryptography
Differential Cryptanalysis
Encryption
Linear Cryptanalysis
Substitution Boxes
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Summary:S-boxes are used in cryptography in order to provide non-linearity in the design of cryptographic primitives such as block ciphers and hash functions. Some cryptographic primitives use bijective S-boxes as in the Advanced Encryption Standard (AES), and others use surjective S-boxes as in the Data Encryption Standard (DES). That is, S-boxes can have inputs and outputs of the same length as in the (8,8)-S-box of AES, or alternatively the input length can be larger than the output as in the (6, 4)-S-boxes of DES. In this paper, we perform a statistical study of linear and differential properties of randomly generated (n, m)-S-boxes, where m ≤ n. We show that certain S-boxes with well-behaved linear and differential properties can be feasibly obtained via random search. We show further that certain types of S-boxes with specific desirable linear and differential properties are improbable.
DOI:10.1109/ICITST.2016.7856751