Welcome to the resource topic for 2022/693
Title:
Unified View for Notions of Bit Security
Authors: Shun Watanabe and Kenji Yasunaga
Abstract:We study the framework of Watanabe and Yasunaga (Asiacrypt 2021) that enables us to evaluate the bit security of cryptographic primitives/games with an operational meaning. First, we observe that their quantitative results preserve even if adversaries are allowed to output the failure symbol in games. With this slight modification, we show that their framework evaluates the advantage of adversaries more pessimistically than that of Micciancio and Walter (Eurocrypt 2018). Also, we prove the optimality of the Goldreich-Levin hard-core predicate by employing the reduction algorithm of Hast (J. Cryptology, 2004). These two results resolve open problems that remained. We demonstrate that all games we need to care about in their framework are decision games. Namely, we show that for every search game G, there is the corresponding decision game G' such that G has \lambda-bit security if and only if G' has \lambda-bit security. The game G' consists of the real and the ideal games, where attacks in the ideal game are never approved. Such games often appear in game-hopping security proofs. The result justifies such security proofs because they lose no security. Finally, we provide a distribution replacing theorem. Suppose that a game using distribution Q in a black-box manner is \lambda-bit secure, and two distributions P and Q are computationally \lambda-bit secure indistinguishable. In that case, the game where Q is replaced by P is also \lambda-bit secure.
ePrint: https://eprint.iacr.org/2022/693
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