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Questions tagged [one-way-function]

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

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6 votes
0 answers
119 views

Is there a known correlation between the Strong Exponential Time Hypothesis (SETH) and the existence of one-way functions?

It is known that (one-way functions exist $\implies$ $\textbf{P}\neq \textbf{NP}$) and as far as my knowledge goes, the converse is not known to be true. Are there any known results correlating $\...
5 votes
0 answers
92 views

Does there exist a cryptographic associative hash function?

Does there exist a function $f(x,y)$ with these properties: Computing $f(x,y)$ is in P. $f$ is associative: $f(x, f(y, z)) = f(f(x, y), z)$. $f$ is one-way (assuming P $\neq$ NP): Given the value ...
2 votes
0 answers
31 views

Impossibility of uniform generation in random world

I specify that this is a cross-post from crypto.stackexchange but I didn't get satisfactory answers. I was reading Limits on the provable consequences of one way permutations by Impagliazzo and Rudich ...
0 votes
0 answers
109 views

Assume `P != NP`, does it imply that one-way functions exist?

I define a function f to be one-way iff for any sufficiently large x computing f(x) bounded ...
0 votes
1 answer
155 views

What is the simplest one-way function (in terms of boolean circuit complexity)?

What is the simplest known one-way function? By simplest, I mean, when implemented as boolean logic, the number of AND/OR/NOT gates needed is minimal (smallest circuit complexity). (I'm trying to find ...
1 vote
0 answers
74 views

One way analogues of Logspace

When we say a function is one-way we typically mean a function is encodable in $P$ but its decryption is not in $P$ but in $UP$. Likewise we say a function is logspace one-way if the function is ...
1 vote
0 answers
72 views

Describe Levins 'Tile Expansion' one way functon in layman terms

I'd like some explanation on the details of the 'Complete OWF' presented on this paper in 'layman terms'. See page 13 of https://arxiv.org/pdf/cs/0012023.pdf I'd prefer that the answerer had '...
10 votes
2 answers
364 views

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 ...
14 votes
1 answer
387 views

Function that is guaranteed to be one-way if one-way functions exist?

There is an old trick for writing down an algorithm that, if P = NP, solves SAT in polynomial time. Essentially, one lists all polynomial time machines and multi-tasks over them. Is there an ...
18 votes
2 answers
539 views

Is it possible to encrypt a CNF?

Is it possible to convert a CNF $\mathcal C$ into another CNF $\Psi(\mathcal C)$ such that The function $\Psi$ can be computed in polynomial time from some secret random parameter $r$. $\Psi(\mathcal ...
8 votes
3 answers
604 views

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 ...
3 votes
0 answers
277 views

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 ...
3 votes
1 answer
194 views

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 ...
9 votes
2 answers
540 views

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?
10 votes
2 answers
497 views

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 ...
5 votes
0 answers
80 views

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 ...
25 votes
4 answers
4k views

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-...
0 votes
0 answers
111 views

"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 ...
8 votes
0 answers
637 views

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 ...
3 votes
0 answers
68 views

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 ...
13 votes
1 answer
293 views

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 ...
16 votes
5 answers
1k views

Do "One Way Functions" have any applications outside crypto ?

A function $f \colon \{0, 1\}^* \to \{0, 1\}^*$ is one-way if $f$ can be computed by a polynomial time algorithm, but for every randomized polynomial time algorithm $A$, $\Pr[f(A(f(x))) = f(x)] < ...
4 votes
2 answers
338 views

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 ...
-3 votes
1 answer
396 views

One Way Boolean Function [closed]

If one way functions exist, what would the truth table of a one way boolean function look like?
6 votes
1 answer
448 views

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 ...
10 votes
1 answer
379 views

Reducing factoring prime products to factoring integer products (in average-case)

My question is about the equivalence of the security of various candidate one-way functions that can be constructed based on the hardness of factoring. Assuming the problem of FACTORING:[Given $N ...
9 votes
0 answers
564 views

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 ...
8 votes
1 answer
284 views

One-way functions with polynomial inverting complexity

Is there a trap-door-like function whose encoding complexity is polynomial time $n^{k_{1}}$ and inverting complexity(without secret key) is also a polynomial function in input length $n^{k_{2}}$ with $...
4 votes
0 answers
321 views

A approximation version of the Goldreich-Levin Theorem

A little introduction The Goldreich-Levin Theorem says that let $f$ a one-way function and set $f'(x,r)=(f(x),r)$ where $|r|=|x|$ then $\langle x, r \rangle = \sum_{i}x_ir_i \mod 2$ is an hard-core ...
9 votes
2 answers
982 views

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 ...
10 votes
1 answer
504 views

Finite One-Way Permutation with Infinite Domain

Let $\pi \colon \{0,1\}^* \to \{0,1\}^*$ be a permutation. Note that while $\pi$ acts on an infinite domain, its description might be finite. By description, I mean a program that describes $\pi$'s ...
8 votes
1 answer
1k views

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 $L$...
5 votes
2 answers
260 views

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 ...