Limits of Extractability Assumptions with Distributional Auxiliary Input

Extractability, or “knowledge,” assumptions have recently gained popularity in the cryptographic community, leading to the study of primitives such as extractable one-way functions, extractable hash functions, succinct non-interactive arguments of knowledge (SNARKs), and (public-coin) differing-inputs obfuscation ((PC-)diO), and spurring the development of a wide spectrum of new applications relying on these primitives. For most of these applications, it is required that the extractability assumption holds even in the presence of attackers receiving some auxiliary information that is sampled from some fixed efficiently computable distribution Z. We show that, assuming the existence of public-coin collision-resistant hash functions, there exists an efficient distributions Z such that either • PC-diO for Turing machines does not exist, or • extractable one-way functions w.r.t. auxiliary input Z do not exist. A corollary of this result shows that additionally assuming existence...

• Type: Journal
• Year: 2015
• Where: ASIACRYPT
• Authors: Elette Boyle, Rafael Pass
• Keywords: ASIACRYPT 2015, Cryptology