On the Complexity of Collision Resistant Hash Functions: New and Old Black-Box Separations

Bitansky, Nir; Degwekar, Akshay

doi:10.1007/978-3-030-36030-6_17

Cited by 8 publications

(1 citation statement)

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“…Bitansky and Degwekar [BD19], based on the coupling-based approach presented in this work, showed that collision-resistant hash functions do not imply hardness in \sansS \sansZ \sansK , and also gave a new proof of the separation of IO and collision-resistant hash functions previously shown by Asharov and Segev [AS15].…”

Section: Theorem 13 (Informal)mentioning

confidence: 68%

Structure Versus Hardness Through the Obfuscation Lens

Bitansky¹,

Degwekar²,

Vaikuntanathan³

2021

SIAM J. Comput.

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Much of modern cryptography, starting from public-key encryption and going beyond, is based on the hardness of structured (mostly algebraic) problems like factoring, discrete log, or finding short lattice vectors. While structure is perhaps what enables advanced applications, it also puts the hardness of these problems in question. In particular, this structure often puts them in low (and so-called structured) complexity classes such as \sansN \sansP \cap \sansc \sanso \sansN \sansP or statistical zero-knowledge (\sansS \sansZ \sansK ). Is this structure really necessary? For some cryptographic primitives, such as one-way permutations and homomorphic encryption, we know that the answer is yes---they imply hard problems in \sansN \sansP \cap \sansc \sanso \sansN \sansP and \sansS \sansZ \sansK , respectively. In contrast, one-way functions do not imply such hard problems, at least not by black-box reductions. Yet, for many basic primitives such as public-key encryption, oblivious transfer, and functional encryption, we do not have any answer. We show that the above primitives, and many others, do not imply hard problems in \sansN \sansP \cap \sansc \sanso \sansN \sansP or \sansS \sansZ \sansK via black-box reductions. In fact, we first show that even the very powerful notion of indistinguishability obfuscation (IO) does not imply such hard problems, and then deduce the same for a large class of primitives that can be constructed from IO.

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Section: Theorem 13 (Informal)mentioning

confidence: 68%