Paper 2019/1378

Alzette: a 64-bit ARX-box (feat. CRAX and TRAX)

Christof Beierle, Alex Biryukov, Luan Cardoso dos Santos, Johann Großschädl, Léo Perrin, Aleksei Udovenko, Vesselin Velichkov, and Qingju Wang

Abstract

S-boxes are the only source of non-linearity in many symmetric primitives. While they are often defined as being functions operating on a small space, some recent designs propose the use of much larger ones (e.g., 32 bits). In this context, an S-box is then defined as a subfunction whose cryptographic properties can be estimated precisely. We present a 64-bit ARX-based S-box called Alzette, which can be evaluated in constant time using only 12 instructions on modern CPUs. Its parallel application can also leverage vector (SIMD) instructions. One iteration of Alzette has differential and linear properties comparable to those of the AES S-box, and two are at least as secure as the AES super S-box. As the state size is much larger than the typical 4 or 8 bits, the study of the relevant cryptographic properties of Alzette is not trivial. We further discuss how such wide S-boxes could be used to construct round functions of 64-, 128- and 256-bit (tweakable) block ciphers with good cryptographic properties that are guaranteed even in the related-tweak setting. We use these structures to design a very lightweight 64-bit block cipher (CRAX) which outperforms SPECK-64/128 for short messages on micro-controllers, and a 256-bit tweakable block cipher (TRAX) which can be used to obtain strong security guarantees against powerful adversaries (nonce misuse, quantum attacks).

Metadata
Available format(s)
PDF
Category
Secret-key cryptography
Publication info
A major revision of an IACR publication in Crypto 2020
DOI
10.1007/978-3-030-56877-1_15
Keywords
(tweakable) block cipherrelated-tweak settinglong trail strategyAlzetteMEDCPMELCC
Contact author(s)
sparklegrupp @ googlegroups com
History
2020-08-20: last of 2 revisions
2019-12-01: received
See all versions
Short URL
https://ia.cr/2019/1378
License
Creative Commons Attribution
CC BY

BibTeX

@misc{cryptoeprint:2019/1378,
      author = {Christof Beierle and Alex Biryukov and Luan Cardoso dos Santos and Johann Großschädl and Léo Perrin and Aleksei Udovenko and Vesselin Velichkov and Qingju Wang},
      title = {Alzette: a 64-bit ARX-box (feat. CRAX and TRAX)},
      howpublished = {Cryptology ePrint Archive, Paper 2019/1378},
      year = {2019},
      doi = {10.1007/978-3-030-56877-1_15},
      note = {\url{https://eprint.iacr.org/2019/1378}},
      url = {https://eprint.iacr.org/2019/1378}
}
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