Paper 2015/433

A New Classification of 4-bit Optimal S-boxes and its Application to PRESENT, RECTANGLE and SPONGENT

Wentao Zhang, Zhenzhen Bao, Vincent Rijmen, and Meicheng Liu


In this paper, we present a new classification of 4-bit optimal S-boxes. All optimal 4-bit S-boxes can be classified into 183 different categories, among which we specify 3 platinum categories. Under the design criteria of the PRESENT (or SPONGENT) S-box, there are 8064 different S-boxes up to adding constants before and after an S-box. The 8064 S-boxes belong to 3 different categories, we show that the S-box should be chosen from one out of the 3 categories or other categories for better resistance against linear cryptanalysis. Furthermore, we study in detail how the S-boxes in the 3 platinum categories influence the security of PRESENT, RECTANGLE and SPONGENT88 against differential and linear cryptanalysis. Our results show that the S-box selection has a great influence on the security of the schemes. For block ciphers or hash functions with 4-bit S-boxes as confusion layers and bit permutations as diffusion layers, designers can extend the range of S-box selection to the 3 platinum categories and select their S-box very carefully. For PRESENT, RECTANGLE and SPONGENT88 respectively, we get a set of potentially best/better S-box candidates from the 3 platinum categories. These potentially best/better S-boxes can be further investigated to see if they can be used to improve the security-performance tradeoff of the 3 cryptographic algorithms.

Note: A footnote is added as per the IACR copyright agreement.

Available format(s)
Secret-key cryptography
Publication info
A minor revision of an IACR publication in FSE 2015
4-bit S-boxclassificationblock cipherhash functiondifferential cryptanalysislinear cryptanalysisPRESENTRECTANGLESPONGENT
Contact author(s)
zhangwentao @ iie ac cn
vincent rijmen @ esat kuleuven be
2015-05-07: revised
2015-05-06: received
See all versions
Short URL
Creative Commons Attribution


      author = {Wentao Zhang and Zhenzhen Bao and Vincent Rijmen and Meicheng Liu},
      title = {A New Classification of 4-bit Optimal S-boxes and its Application to PRESENT, RECTANGLE and SPONGENT},
      howpublished = {Cryptology ePrint Archive, Paper 2015/433},
      year = {2015},
      note = {\url{}},
      url = {}
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