Cryptography often considers the strongest yet plausible attacks in the real world. Preprocessing (a.k.a. non-uniform attack) plays an important role in both theory and practice: an efficient online attacker can take advantage of advice prepared by a time-consuming preprocessing stage. Salting is a heuristic strategy to counter preprocessing attacks by feeding a small amount of randomness to the cryptographic primitive. We present general and tight characterizations of preprocessing against cryptographic salting, with upper bounds matching the advantages of the most intuitive attack. Our result quantitatively strengthens the previous work by Coretti, Dodis, Guo, and Steinberger (EUROCRYPT'18). Our proof exploits a novel connection between the non-uniform security of salted games and direct product theorems for memoryless algorithms. For quantum adversaries, we give similar characterizations for property finding games, resolving an open problem of the quantum non-uniform security of salted collision resistant hash by Chung, Guo, Liu, and Qian (FOCS'20). Our proof extends the compressed oracle framework of Zhandry (CRYPTO'19) to prove quantum strong direct product theorems for property finding games in the average-case hardness.

翻译：密码学通常考虑现实世界中最强且合理的攻击。预处理（又称非均匀攻击）在理论和实践中均扮演重要角色：高效的在线攻击者可以利用耗时预处理阶段准备的建议信息。加盐是一种通过向密码原语注入少量随机性来抵抗预处理攻击的启发式策略。本文提出了针对密码学加盐的预处理攻击的通用且紧致的刻画，其上界与最直观攻击的优势度相匹配。我们的结果从定量角度强化了Coretti、Dodis、Guo和Steinberger（EUROCRYPT'18）的前期工作。证明过程揭示了加盐游戏的非均匀安全性与无记忆算法的直积定理之间的新颖联系。针对量子敌手，我们对属性寻找游戏给出了类似刻画，解决了Chung、Guo、Liu和Qian（FOCS'20）提出的加盐抗碰撞哈希函数的量子非均匀安全性这一开放问题。我们的证明将Zhandry（CRYPTO'19）的压缩预言机框架扩展至平均情况硬度下的属性寻找游戏，从而证明了量子强直积定理。