Some cryptanalytic results on Lizard

Lizard is a lightweight stream cipher proposed by Hamann, Krause and Meier in IACR ToSC 2017. It has a Grain-like structure with two state registers of size 90 and 31 bits. The cipher uses a 120 bit secret key and a 64 bit IV. The authors claim that Lizard provides 80-bit security against key recovery attacks and a 60-bit security against distinguishing attacks. In this paper, we present an assortment of results and observations on Lizard. First, we show that by doing $2^58$ random trials it is possible to find a set of 2 64 triplets (K, IV 0 , IV 1 ) such that the Key-IV pairs (K, IV 0 ) and (K, IV 1 ) produce identical keystream bits. Second, we show that by performing only around 2 28 random trials it is possible to obtain $2^64$ Key-IV pairs (K 0 , IV 0 ) and (K 1 , IV 1 ) that produce identical keystream bits. Thereafter, we show that one can construct a distinguisher for Lizard based on IVs that produce shifted keystream sequences. The process takes around $2^{51.5}$ random IV encryptions (with encryption required to produce $2^{18}$ keystream bits) and around $2^{76.6}$ bits of memory. Next, we propose a key recovery attack on a version of Lizard with the number of initialization rounds reduced to 223 (out of 256) based on IV collisions. We then outline a method to extend our attack to 226 rounds. Our results do not affect the security claims of the designers.