Cryptanalysis of Loiss Stream Cipher-Revisited

Loiss is a novel byte-oriented stream cipher proposed in 2011. In this paper, based on solving systems of linear equations, we propose an improved Guess and Determine attack on Loiss with a time complexity of 2231 and a data complexity of 268, which reduces the time complexity of the Guess and Determine attack proposed by the designers by a factor of 216. Furthermore, a related key chosen IV attack on a scaled-down version of Loiss is presented. The attack recovers the 128-bit secret key of the scaled-down Loiss with a time complexity of 280, requiring 264 chosen IVs. The related key attack is minimal in the sense that it only requires one related key. The result shows that our key recovery attack on the scaled-down Loiss is much better than an exhaustive key search in the related key setting.