Revisiting the Security Proof of QUAD Stream Cipher: Some Corrections and Tighter Bounds

摘要

In EUROCRYPT 2006, Berbain et al. proposed a provably secure stream cipher named QUAD based on the hardness of solving multivariate quadratic equations. The authors also mentioned that whether the security bound can be made tighter or not is an open problem. Through the last decade, there have been some works on the analysis of QUAD as well as design extensions of QUAD, but to our knowledge no work has addressed the existence of tighter bounds. In this paper, we revisit the proof technique by the authors and correct some bugs in their proof. Further, we derive tighter security bounds using two approaches.