A Real-time Inversion Attack on the GMR-2 Cipher Used in the Satellite Phones

The GMR-2 cipher is a type of stream cipher currently being used in some Inmarsat satellite phones. It has been proven that such a cipher can be cracked using only one single-frame (15 bytes) known keystream but with a moderate executing times. In this paper, we present a new thorough security analysis of the GMR-2 cipher. We first study the inverse properties of the cipher\u27s components to reveal a bad one-way character of the cipher. By then introducing a new concept called ``valid key chain according to the cipher\u27s key schedule, we propose an unprecedented real-time inversion attack using a single-frame keystream. This attack comprises three phases: (1) table generation; (2) dynamic table look-up, filtration and combination; and (3) verification. Our analysis shows that, using the proposed attack, the size of the exhaustive search space for the 64-bit encryption key can be reduced to approximately $2^{13}$ when a single-frame keystream is available. Compared with previous known attacks, this inversion attack is much more efficient. Finally, the proposed attack is carried out on a 3.3-GHz PC, and the experimental results thus obtained demonstrate that the 64-bit encryption-key could be recovered in approximately 0.02 s on average