International Association
for Cryptologic Research

Integral attacks belong to the classical attack vectors against any given block ciphers. However, providing arguments that a given cipher is resistant against those attacks is notoriously difficult. In this paper, based solely on the assumption of independent round keys, we develop significantly stronger arguments than what was possible before: our main result is that we show how to argue that the sum of ciphertexts over any possible subset of plaintext is key-dependent, i.e., the non existence of integral distinguishers.

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.

Only the method to estimate the upper bound of the algebraic degree on block ciphers is known so far, but it is not useful for the designer to guarantee the security. In this paper we provide meaningful lower bounds on the algebraic degree of modern block ciphers.