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**2015/636**

**Title:**

On Stream Ciphers with Provable Beyond-the-Birthday-Bound Security against Time-Memory-Data Tradeoff Attacks

**Authors:**
Matthias Hamann, Matthias Krause

**Abstract:**

We propose and analyze the LIZARD-construction, a way to construct keystream generator (KSG) based stream ciphers with provable \frac{2}{3} n-security with respect to generic time-memory-data tradeoff attacks. Note that for the vast majority of known practical KSG-based stream ciphers such attacks reduce the effective key length to the birthday bound n/2, where n denotes the inner state length of the underlying KSG. This implies that practical stream ciphers have to have a comparatively large inner state length (e.g., n=288 bit for Trivium and n=160 bit for Grain v1). The LIZARD-construction proposes a state initialization algorithm for stream ciphers working in packet mode (like the GSM cipher A5/1 or the Bluetooth cipher E_0). The proposal is that for each packet i the packet initial state q^i_{init} is computed from the secret session key k and the packet initial value IV^{i} via q^i_{init}=P(k\oplus IV^{i})\oplus k, where P denotes a state mixing algorithm. Note that the recently published cipher LIZARD (see ePrint 2016/926), a stream cipher having inner state length of only 121 bit, is a lightweight practical instantiation of our proposal, which is competitive w.r.t. the usual hardware and power consumption metrics. The main technical contribution of this paper is to introduce a formal ideal primitive model for KSG-based stream ciphers and to show the sharp \frac{2}{3} n-bound for the security of the LIZARD-construction against generic time-memory-data tradeoff attacks.

**ePrint:**
https://eprint.iacr.org/2015/636

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