Cryptology ePrint Archive: Report 2018/181

Rasta: A cipher with low ANDdepth and few ANDs per bit

Christoph Dobraunig and Maria Eichlseder and Lorenzo Grassi and Virginie Lallemand and Gregor Leander and Eik List and Florian Mendel and Christian Rechberger

Abstract: Recent developments in multi party computation (MPC) and fully homomorphic encryption (FHE) promoted the design and analysis of symmetric cryptographic schemes that minimize multiplications in one way or another. In this paper, we propose with Rasta a design strategy for symmetric encryption that has ANDdepth d and at the same time only needs d ANDs per encrypted bit. Even for very low values of d between 2 and 6 we can give strong evidence that attacks may not exist. This contributes to a better understanding of the limits of what concrete symmetric-key constructions can theoretically achieve with respect to AND-related metrics, and is to the best of our knowledge the first attempt that minimizes both metrics simultaneously. Furthermore, we can give evidence that for choices of d between 4 and 6 the resulting implementation properties may well be competitive by testing our construction in the use-case of removing the large ciphertext-expansion when using the BGV scheme.

Category / Keywords: secret-key cryptography / Symmetric encryption, ASASA, homomorphic encryption, multiplicative complexity, multiplicative depth

Original Publication (with minor differences): IACR-CRYPTO-2018

Date: received 14 Feb 2018, last revised 21 Jun 2018

Contact author: christoph dobraunig at iaik tugraz at

Available format(s): PDF | BibTeX Citation

Version: 20180621:072504 (All versions of this report)

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