
Inaccessible Entropy I: Inaccessible Entropy Generators and Statistically Hiding Commitments from OneWay Functions
We put forth a new computational notion of entropy, measuring the (in)fe...
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Unifying computational entropies via KullbackLeibler divergence
We introduce KLhardness, a new notion of hardness for search problems w...
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Distributional Collision Resistance Beyond OneWay Functions
Distributional collision resistance is a relaxation of collision resista...
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Quantum security of hash functions and propertypreservation of iterated hashing
This work contains two major parts: comprehensively studying the securit...
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Improved Lower Bounds for the Fourier Entropy/Influence Conjecture via Lexicographic Functions
Every Boolean function can be uniquely represented as a multilinear poly...
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Crooked Indifferentiability Revisited
In CRYPTO 2018, Russell et al introduced the notion of crooked indiffere...
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Companions, Causality and Codensity
In the context of abstract coinduction in complete lattices, the notion ...
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Inaccessible Entropy II: IE Functions and Universal OneWay Hashing
This paper uses a variant of the notion of inaccessible entropy (Haitner, Reingold, Vadhan and Wee, STOC 2009), to give an alternative construction and proof for the fundamental result, first proved by Rompel (STOC 1990), that Universal OneWay Hash Functions (UOWHFs) can be based on any oneway functions. We observe that a small tweak of any oneway function f is already a weak form of a UOWHF: consider the function F(x,i) that returns the ibitlong prefix of f(x). If F were a UOWHF then given a random x and i it would be hard to come up with x'≠ x such that F(x,i)=F(x',i). While this may not be the case, we show (rather easily) that it is hard to sample x' with almost full entropy among all the possible such values of x'. The rest of our construction simply amplifies and exploits this basic property.Combined with other recent work, the construction of three fundamental cryptographic primitives (Pseudorandom Generators, Statistically Hiding Commitments and UOWHFs) out of oneway functions is now to a large extent unified. In particular, all three constructions rely on and manipulate computational notions of entropy in similar ways. Pseudorandom Generators rely on the wellestablished notion of pseudoentropy, whereas Statistically Hiding Commitments and UOWHFs rely on the newer notion of inaccessible entropy.
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