DeepAI
Log In Sign Up

Inaccessible Entropy II: IE Functions and Universal One-Way Hashing

05/04/2021
by   Iftach Haitner, et al.
0

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 One-Way Hash Functions (UOWHFs) can be based on any one-way functions. We observe that a small tweak of any one-way function f is already a weak form of a UOWHF: consider the function F(x,i) that returns the i-bit-long 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 one-way 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 well-established notion of pseudoentropy, whereas Statistically Hiding Commitments and UOWHFs rely on the newer notion of inaccessible entropy.

READ FULL TEXT

page 1

page 2

page 3

page 4

02/28/2019

Unifying computational entropies via Kullback-Leibler divergence

We introduce KL-hardness, a new notion of hardness for search problems w...
05/03/2021

Distributional Collision Resistance Beyond One-Way Functions

Distributional collision resistance is a relaxation of collision resista...
12/18/2021

Cryptography from Pseudorandom Quantum States

Pseudorandom states, introduced by Ji, Liu and Song (Crypto'18), are eff...
11/02/2017

Improved Lower Bounds for the Fourier Entropy/Influence Conjecture via Lexicographic Functions

Every Boolean function can be uniquely represented as a multilinear poly...
07/08/2019

Santha-Vazirani sources, deterministic condensers and very strong extractors

The notion of semi-random sources, also known as Santha-Vazirani (SV) so...