Cryptanalysis of rabbit

The stream cipher Rabbit is one candidate to the ECRYPT Stream Cipher Project (eSTREAM) on the third evaluation phase. It has a 128-bit key, 64-bit IV and 513-bit internal state. Currently, only one paper [1] studied it besides a series of white papers by the authors of Rabbit. In [1], the bias of the keystream sub-blocks was studied and a distinguishing attack with the estimated complexity 2²⁴⁷ was proposed based on the largest bias computed. In this paper, we first computed the exact bias of the keystream sub-blocks by Fast Fourier Transform (FFT). Our result leads to the best distinguishing attack with the complexity 2¹⁵⁸ so far, in comparison to 2²⁴⁷ in [1]. Meanwhile, our result also indicates that the approximation assumption used in [1] is critical for estimation of the bias and cannot be ignored. Secondly, our distinguishing attack is extended to a multi-frame key-recovery attack, assuming that the relation between part of the internal states of all frames is known. Our attack uses 2^51.5 frames and the first three keystream blocks of each frame. It takes memory O(2³²), precomputation O(2 ³²) and time O(2^97.5) to recover the keys for all frames. This is the first known key-recovery attack on Rabbit, though the attack assumption is unusually strong. Lastly, as an independent result, we introduced the property of Almost-Right-Distributivity of the bit-wise rotation over the modular addition for our algebraic analysis.This allows to solve the nonlinear yet symmetric equation system more efficiently for our problem.