Loiss is a byte-oriented stream cipher designed by Dengguo Feng et al. Its design builds upon the design of the SNOW family of ciphers. The algorithm consists of a linear feedback shift register (LFSR) and a non-linear finite state machine (FSM). Loiss utilizes a structure called Byte-Oriented Mixer with Memory (BOMM) in its filter generator, which aims to improve resistance against algebraic attacks, linear distinguishing attacks and fast correlation attacks. In this paper, by exploiting some differential properties of the BOMM structure during the cipher initialization phase, we provide an attack of a practical complexity on Loiss in the related-key model. As confirmed by our experimental results, our attack recovers 92 bits of the 128-bit key in less than one hour on a PC with 3 GHz Intel Pentium 4 processor. The possibility of extending the attack to a resynchronization attack in a single-key model is discussed. We also show that Loiss is not resistant to slide attacks.
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