International Association for Cryptologic Research

International Association
for Cryptologic Research


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

Christof Beierle , Ruhr University Bochum
Alex Biryukov , Snt, University of Luxembourg
Luan Cardoso dos Santos , Snt, University of Luxembourg
Johann Großschädl , Snt, University of Luxembourg
Léo Perrin , Inria
Aleksei Udovenko , CryptoExperts
Vesselin Velichkov , University of Edinburgh
Qingju Wang , Snt, University of Luxembourg
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Conference: CRYPTO 2020
Abstract: S-boxes are the only source of non-linearity in many symmetric cryptographic 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. In this paper, 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, while two iterations are at least as secure as the AES super S-box. Since 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 outerperforms 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).
Video from CRYPTO 2020
  title={Alzette: a 64-bit ARX-box (feat. CRAX and TRAX)},
  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},