Quantum Guess and Determine Attack on Stream Ciphers

Abstract

Abstract To guarantee the security of symmetric key schemes against quantum adversary, developing quantum cryptanalytic techniques becomes a major worldwide challenge in the post-quantum world. In this paper, we present a general framework of classical guess and determine attack on stream ciphers, and then convert it into quantum guess and determine attack. It shows that, for a given stream cipher with a key size of $k$ bits and an internal state size of $n$ bits, if a basic guess and determine attack with a time complexity below $O ( {{{2}^{{3k}/{2}}}}/{n} )$ is available, there is a quantum guess and determine attack with multiple data that can recover all $n$ internal state bits of the cipher with complexity below $O ( {{2^{k / 2}}} )$. As applications, we present quantum guess and determine attacks on the SNOW-like stream ciphers. The results show that all of SNOW 1.0 with 128-bit key, SNOW 2.0 with 128-bit key and SOSEMANUK are insecure against quantum guess and determine attack. The resource requirements for implementing a quantum guess and determine attack on SNOW 3G are evaluated as a case study. To the best of our knowledge, this is the first time that the general quantum guess and determine attack is formally proposed and applied to the SNOW-like stream ciphers.