Using Indistinguishability Obfuscation via UCEs

Abstract

Abstract. We provide the first standard model construction for a powerful class of Universal Computational Extractors (UCEs; Bellare et al. Crypto 2013) based on indistinguishability obfuscation. Our construction suffices to instantiate q-query correlation-secure hash functions and to extract polynomially many hardcore bits from any one-way function.For many cryptographic primitives and in particular for correlation-secure hash functions all known constructions are in the random-oracle model. Indeed, recent negative results by Wichs (ITCS 2013) rule out a large class of techniques to prove the security of correlation-secure hash functions in the standard model. Our construction is based on puncturable PRFs (Sahai und Waters; STOC 2014) and indistinguishability obfuscation. However, our proof also relies on point obfuscation under auxiliary inputs (AIPO). This is crucial in light of Wichs' impossibility result. Namely, Wichs proves that it is often hard to reduce two-stage games (such as UCEs) to a "one-stage assumption" such as DDH. In contrast, AIPOs and their underlying assumptions are inherently two-stage and, thus, allow us to circumvent Wichs' impossibility result.Our positive result is also noteworthy insofar as Brzuska, Farshim and Mittelbach (Crypto 2014) have shown recently, that iO and some variants of UCEs are mutually exclusive. Our results, hence, validate some of the new UCE notions that emerged as a response to the iO-attack.

Instantiating Random Oracles via UCEs

“…In an important advance, Brzuska and Mittelback [51] bring the first non-trivial positive results, showing that certain forms of UCE are achievable assuming iO and AIPO. BHK14 [19] provide domain-extension methods for UCE in answer to the question above and also show that UCE can overcome some of the limitations of indifferentiability [103] in multi-stage games pointed out by [109].…”

Indistinguishability Obfuscation versus Multi-bit Point Obfuscation with Auxiliary Input

“…We call this notion strong unpredictability and, indeed, give a construction based on AIPO and indistinguishability obfuscation. An analogous notion of unpredictability has recently been introduced by Brzuska and Mittelbach in the context of UCE security [BM14].…”

“…We weaken the original MB-AIPO definition (Definition 2.9) by requiring that an obfuscation must only be secure for unpredictable distributions that hide the point address even given the the point value m. We call this notion of unpredictability strong unpredictability and note that an analogous notion has recently been introduced in the context of UCE security [BM14]. If we restrict adversaries to strong unpredictability we yield an MB-AIPO notion that we call weak MB-AIPO.…”

“…For our positive result, a construction of weak MB-AIPO and subsequently a construction of a leakage resilient PKE scheme, we combine AIPOs and indistinguishability obfuscation. In a recent work Brzuska and Mittelbach (BM, [BM14]) show that combining these techniques allows to build powerful primitives and they give the first construction of a standard model hash function which is UCE secure for a non-trivial UCE notion which implies universal hardcore-functions and q-query correlated input secure hash functions. Furthermore, we note that our notion of weak MB-AIPO is inspired by the UCE notion introduced by BM: UCE security with respect to strongly unpredictable sources.…”

“…Statistical unpredictability has already proved useful for the construction of q-query secure correlation-secure hash functions [BM14] and CCA secure PKE schemes [MH14].…”