6,264 research outputs found
Cryptographic Hashing From Strong One-Way Functions
Constructing collision-resistant hash families (CRHFs) from one-way functions is a long-standing open problem and source of frustration in theoretical cryptography. In fact, there are strong negative results: black-box separations from one-way functions that are -secure against polynomial time adversaries (Simon, EUROCRYPT \u2798) and even from indistinguishability obfuscation (Asharov and Segev, FOCS \u2715).
In this work, we formulate a mild strengthening of exponentially secure one-way functions, and we construct CRHFs from such functions. Specifically, our security notion requires that every polynomial time algorithm has at most probability of inverting two independent challenges.
More generally, we consider the problem of simultaneously inverting functions , which we say constitute a ``one-way product function\u27\u27 (OWPF). We show that sufficiently hard OWPFs yield hash families that are multi-input correlation intractable (Canetti, Goldreich, and Halevi, STOC \u2798) with respect to all sparse (bounded arity) output relations. Additionally assuming indistinguishability obfuscation, we construct hash families that achieve a broader notion of correlation intractability, extending the recent work of Kalai, Rothblum, and Rothblum (CRYPTO \u2717). In particular, these families are sufficient to instantiate the Fiat-Shamir heuristic in the plain model for a natural class of interactive proofs.
An interesting consequence of our results is a potential new avenue for bypassing black-box separations. In particular, proving (with necessarily non-black-box techniques) that parallel repetition amplifies the hardness of specific one-way functions -- for example, all one-way permutations -- suffices to directly bypass Simon\u27s impossibility result
Regular and almost universal hashing: an efficient implementation
Random hashing can provide guarantees regarding the performance of data
structures such as hash tables---even in an adversarial setting. Many existing
families of hash functions are universal: given two data objects, the
probability that they have the same hash value is low given that we pick hash
functions at random. However, universality fails to ensure that all hash
functions are well behaved. We further require regularity: when picking data
objects at random they should have a low probability of having the same hash
value, for any fixed hash function. We present the efficient implementation of
a family of non-cryptographic hash functions (PM+) offering good running times,
good memory usage as well as distinguishing theoretical guarantees: almost
universality and component-wise regularity. On a variety of platforms, our
implementations are comparable to the state of the art in performance. On
recent Intel processors, PM+ achieves a speed of 4.7 bytes per cycle for 32-bit
outputs and 3.3 bytes per cycle for 64-bit outputs. We review vectorization
through SIMD instructions (e.g., AVX2) and optimizations for superscalar
execution.Comment: accepted for publication in Software: Practice and Experience in
September 201
Commitment and Oblivious Transfer in the Bounded Storage Model with Errors
The bounded storage model restricts the memory of an adversary in a
cryptographic protocol, rather than restricting its computational power, making
information theoretically secure protocols feasible. We present the first
protocols for commitment and oblivious transfer in the bounded storage model
with errors, i.e., the model where the public random sources available to the
two parties are not exactly the same, but instead are only required to have a
small Hamming distance between themselves. Commitment and oblivious transfer
protocols were known previously only for the error-free variant of the bounded
storage model, which is harder to realize
Postprocessing for quantum random number generators: entropy evaluation and randomness extraction
Quantum random-number generators (QRNGs) can offer a means to generate
information-theoretically provable random numbers, in principle. In practice,
unfortunately, the quantum randomness is inevitably mixed with classical
randomness due to classical noises. To distill this quantum randomness, one
needs to quantify the randomness of the source and apply a randomness
extractor. Here, we propose a generic framework for evaluating quantum
randomness of real-life QRNGs by min-entropy, and apply it to two different
existing quantum random-number systems in the literature. Moreover, we provide
a guideline of QRNG data postprocessing for which we implement two
information-theoretically provable randomness extractors: Toeplitz-hashing
extractor and Trevisan's extractor.Comment: 13 pages, 2 figure
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