Fine-Grained Complexity in a World Without Cryptography
Abstract: The study of fine-grained cryptography has proliferated in recent years due to its allure of potentially relying on weaker assumptions compared to standard cryptography. As fine-grained cryptography only requires polynomial gaps between the adversary and honest parties, it seems plausible to build primitives relying upon popular hardness assumptions about problems in \(\textbf{P}\) such as \(k\text {-}\textsf{SUM}\) or \(\textsf{Zero}\text {-}k\text {-}\textsf{Clique}\). The ultimate hope is that fine-grained cryptography could still be viable even if all current cryptographic assumptions are false, such as if \(\textbf{P} = \textbf{NP}\) or if we live in Pessiland where one-way functions do not exist.
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