Subhadeep Banik, Hailun Yan
ePrint Report
Fruit-F is a lightweight short-state stream cipher designed by Ghafari et al. The authors designed this version of the cipher, after earlier versions of the cipher viz. Fruit 80/v2 succumbed to correlation attacks. The primary motivation behind this design seemed to be preventing correlation attacks. Fruit-F has a Grain-like structure with two state registers of size 50 bits each. In addition, the cipher uses an 80-bit secret key and an 80-bit IV. The authors use a complex key-derivation function to update the non-linear register which prevents the same key-bit alignment across fixed-length window of keystream bits, which is essentially what stops the correlation attacks.
In this paper, we first present two attacks against Fruit-F. The first attack stems from the fact that the key-derivation can be rewritten as the Boolean xor of two key-dependent terms one of which is the Boolean OR of two bits of the key. Using this we show that the cipher does not offer 80-bit security: the effective key space of Fruit-F is slightly less than $2^{80}$, i.e. a simple brute force attack costs around $2^{80}-2^{49}$ time. The second is a differential attack using the cipher’s complex initialization process. We show that under some given conditions, it is possible to have two initial vectors $V_1$ and $V_2$ that produce identical keystream vectors with any given key. Using this as a distinguisher, it is possible to collect enough linear and quadratic equations of the secret key to find it in practical time with very few keystream bits.
