Analysis of SNOW 3G XOR Resynchronization Mechanism

The stream cipher SNOW 3G designed in 2006 by ETSI/SA-GE is a base
algorithm for the second set of 3GPP confidentiality and integrity
algorithms. In this paper, we investigate the resynchronization
security of a close variant of SNOW 3G, in which two modular
additions are replaced by xors and which is called SNOW
3G$^{\oplus}$. It is shown that the feedback from the FSM to the
LFSR is crucial for security. Given a pair of \textit{known} IVs,
the cipher without such a feedback is extremely vulnerable to
differential known IV attacks with practical complexities
($2^{57}$ time and $2^{33}$ keystream). With such a feedback, it
is shown that $16$ out of $33$ initialization rounds can be broken
by a differential \textit{chosen} IV attack. This is the first
public evaluation result for this algorithm.