Dasta - Alternative Linear Layer for Rasta

Progress in the areas of multi-party computation (MPC) and fully homomorphic encryption (FHE) caused the demand of new design strategies, that minimize the number of multiplications in symmetric primitives. Rasta is an approach for a family of stream ciphers with an exceptional low AND depth, which equals the number of ANDs per encrypted bit. This is achieved in particular by randomizing parts of the computation with the help of a PRNG, implying that the security arguments rely on the provided randomness and the encryption/ decryption is potentially slowed down by this generation. In this paper we propose a variant of Rasta that achieves the same performance with respect to the AND depth and the number of ANDs per encrypted bit, but does not rely on a PRNG, i.e. is based on fixed linear layers.

[1]  Jason Smith,et al.  The SIMON and SPECK Families of Lightweight Block Ciphers , 2013, IACR Cryptol. ePrint Arch..

[2]  Joan Daemen,et al.  Cipher and hash function design strategies based on linear and differential cryptanalysis , 1995 .

[3]  Masahiro Yagisawa,et al.  Fully Homomorphic Encryption without bootstrapping , 2015, IACR Cryptol. ePrint Arch..

[4]  Don Coppersmith,et al.  Matrix multiplication via arithmetic progressions , 1987, STOC.

[5]  Dana Randall Efficient Generation of Random Nonsingular Matrices , 1993, Random Struct. Algorithms.

[6]  Alex Biryukov,et al.  Cryptographic Schemes Based on the ASASA Structure: Black-Box, White-Box, and Public-Key (Extended Abstract) , 2014, ASIACRYPT.

[7]  Anne Canteaut,et al.  Stream Ciphers: A Practical Solution for Efficient Homomorphic-Ciphertext Compression , 2016, Journal of Cryptology.

[8]  Claude Carlet,et al.  Towards Stream Ciphers for Efficient FHE with Low-Noise Ciphertexts , 2016, EUROCRYPT.

[9]  Stefan Kölbl,et al.  Observations on the SIMON Block Cipher Family , 2015, CRYPTO.

[10]  Guido Bertoni,et al.  Keccak , 2013, EUROCRYPT.

[11]  O. Antoine,et al.  Theory of Error-correcting Codes , 2022 .

[12]  Gregor Leander,et al.  Searching for Subspace Trails and Truncated Differentials , 2018, IACR Trans. Symmetric Cryptol..

[13]  François Le Gall,et al.  Powers of tensors and fast matrix multiplication , 2014, ISSAC.

[14]  Martin R. Albrecht,et al.  Ciphers for MPC and FHE , 2015, IACR Cryptol. ePrint Arch..

[15]  Sebastian Ramacher,et al.  Improvements to the Linear Layer of LowMC: A Faster Picnic , 2017, IACR Cryptol. ePrint Arch..

[16]  Christian Rechberger,et al.  Subspace Trail Cryptanalysis and its Applications to AES , 2017, IACR Trans. Symmetric Cryptol..

[17]  Itai Dinur,et al.  Linear Equivalence of Block Ciphers with Partial Non-Linear Layers: Application to LowMC , 2019, IACR Cryptol. ePrint Arch..

[18]  Florian Mendel,et al.  Rasta: A cipher with low ANDdepth and few ANDs per bit , 2018, IACR Cryptol. ePrint Arch..

[19]  Morris J. Dworkin,et al.  SHA-3 Standard: Permutation-Based Hash and Extendable-Output Functions , 2015 .

[20]  Vincent Rijmen,et al.  The Wide Trail Design Strategy , 2001, IMACC.