Cryptanalysis of Loiss Stream Cipher-Revisited

Abstract

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.