# Questions tagged [one-way-function]

Questions regarding easy-to-compute, but hard-to-invert functions.

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### is the set of all numbers that sum up a subset sum problem a one way function?

I have difficulties checking whether $f^{-1}(x)$ is a one way function. $x \leq 2^n$ is the sum that we want the set of numbers $a_1,...,a_m$ to be. $m \leq 2^n$. There are $4^n$ different ways to sum ...
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### Why are one way functions and pseudorandom number generators considered necessary or essential for derandomization?

If strong pseudorandom number generator exists then $BPP=P$ holds and if one way functions exists then $BPP\subseteq SUBEXP$ holds. What are the best statements we have proved that come close to ...
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### Does Wikipedia assume a solution to the halting problem in their description of universal one way functions?

(As for the question in the title: the answer must be no, but then I don't understand what is intended.) The Wikipedia page on one way functions states: Goldreich gives one construction of a ...
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### What's known about basing one-way function on the $P \neq NP$ assumption?

Is there a conditional impossibility result or the question is completely open?
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### Understanding the weak-OWF exists -> OWF exists proof

This is a proof that I've gone back to many times over the last few years and while I can read it and easily verify the steps, it seems like it's a proof, where I will always essentially forget the ...
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### Candidates for One-Way Function

Why are the candidates for one-way functions so few? Today, almost all candidates are based on elementary mathematics, except Goldreich's candidate 2000 and ... (?!). Why one can not generate ...
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### "Partial" invert a one-way permutation

First of all, to my best understanding, traditionally, if $f$ is a one-way function that maps a length $l$ bit string to another length $l$ bit string (i.e., $f:\{0,1\}^l\rightarrow\{0,1\}^l$), then ...
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### one-way functions vs. secret-coin CRHFs

Is there any paper which can be used to show that there can be no relativizing construction of a secret-coin Collision-Resistant Hash Family from a one-way function and unlike this paper, does not ...
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### One-way functions with respect to various resource bounds

Informally, one-way functions are defined with respect to PTIME algorithms. They are computable in polynomial time but not invertible in average-case polynomial time. The existence of such functions ...
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### Consequences of OWFs for Complexity

It it well-known that the existence of one-way functions is necessary and sufficient for much of cryptography (digital signatures, pseudorandom generators, private-key encryption, etc.). My question ...
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### One Way Boolean Function [closed]

If one way functions exist, what would the truth table of a one way boolean function look like?
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### One-Way Functions vs. perfectly binding commitments

If OWFs exist, then statistically binding bit commitment is possible.[1] Is it known that if OWFs exist then perfectly binding bit commitment is possible? If no, is there a known black-box ...
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### Arguments for existence of one-way functions

I have read in several papers that the existence of one-way functions is widely believed. Can someone shed light on why this is the case? What arguments do we have for supporting the existence of one-...
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### How is it proven that Key Exchange implies OWFs?

Page 38 says that Key Exchange implies the existence of one-way functions. When I try to work out the proof myself, I get that in the hypothetical case where there is Key Exchange but no one-way ...
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### VNP = VP versus complexity classes in Arithmetic Geometry

What is the implication of $VNP = VP$ to cryptography schemes such as Elliptic curve/Abelian Variety/Arithmetic Geometry based cryptography? Are there any papers or books that talk about sophisticated ...
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### One-Way Permutations without Trapdoor

In Short: Assuming one-way permutations exist, can we construct one that has no trapdoor? More info: A one-way permutation is a permutation $\pi$ which is easy to compute, but hard to invert (see the ...
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### A generalisation of one-wayness

$\mathbf{NP}$-complete problems are worst-case hard. Their average-case counterpart are one-way functions. Is there an analogous one-wayness notion for $\mathbf{coNP}$-complete problems? More ...
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### NP-Complete Hard-on-Average Problems

This question considers a special class of problems in (NP,P-samplable). The question is: Do there exists a problem $(L,\mu) \in \mbox{(NP,P-samplable)}$ such that: $L$ is $\rm{NP}$-complete, and $L$...
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### Hardness of approximation assuming the existence of one-way functions

This question is inspired by a question posed by Shiva Kintali, Hardness of approximation assuming NP != coNP . Multiplication of two prime numbers of equal size is strong candidate for one-way ...
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### What are the different notions of one-way functions?

For instance, A function that is computable but not invertable in log space, Is it one-way function? What are the known definitions of one-way functions? (especially the ones that do not invoke ...