Questions tagged [one-way-function]

A function which is easy to compute but hard to invert (i.e. find preimages for). The existence of one-way functions implies the possibility of many useful cryptographic schemes. No one-way functions have so far been proven to exist, but many likely candidates exist.

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Can I generalize trapdoor information to trapdoor functions for one-way function?

We know that, for one-way function $y=f(x)$, it's hard to compute $x=f^{-1}(y)$, but there exists an efficient algorithm $A(y,t)=f^{-1}(x)$ once we know the trapdoor information $t$. I'm wondering, ...
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On Constructing Universal One-Way Hash Functions from Arbitrary One-Way Functions | Claim 9 Proof Clarification

I'm reading Katz and Koo's paper that constructs UOWHFs from OWFs. I'm trying to rigorously understand every proof, and I'm having a hard time understanding an equality. This lemma is trying to prove ...
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Public one-way bijection [duplicate]

What methods do we know to construct a function $f:D\to D$ with domain $D=[0,n)\cap\mathbb N$ (thus $n\in\mathbb N$ elements); demonstrably surjective (thus bijective since $D$ is finite); with ...
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About Levin's constructure of universal OWF, why $\log n$ bits TM can work?

In Pass's lecture notes 2.13 section, a universal OWF is constructed. But I have some confusion about: Let $M_g$ be the smallest machine which computes function $g$. Since $M_g$ is a uniform ...
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Are there examples of XOR of OWF still being OWF?

I am trying to prove that given two OWF $f$ and $g$ the function $h$ given as: $$\text{h}(x)=(\text{f}(x),\text{g}(x))$$ is not always OWF. As a counter example I am considering $\text{f}(x) = \text{g}...
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Impossibility of uniform generation in random world

I was reading Limits on the provable consequences of one way permutations by Impagliazzo and Rudich when I got stuck on a sentence. First of all, they define a polynomial relation that is any relation ...
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What is the AEGIS design rationale for one way rounds and slow diffusion?

The AEGIS reference document doesn't specify why the authors chose a slow diffusion process and a one way round transformation. As you can see the previous state is XORed with AES applied to itself ...
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What is a non-OWF?

We know that A function $f:\Bbb Z_2^n \longrightarrow\Bbb Z_2^m$ is a (strong) one-way function (OWF), if: $f$ can be computed by a PT algorithm. Equivalently, there exists a PPT algorithm that on ...
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On the construction and notation of a certain OWF

I am studying a little bit about one-way functions from Dr Goyal's notes. He constructs the following OWF: Let $D=\Bbb Z_2^{n^3}$ and $R=\Bbb Z_2^{2 n}$. Given $x \in D$, $f$ interprets $x$ as a set $...
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Worst-case one-way permutations under P different from NP

This is probably obvious, but I cannot find it anywhere, since all textbooks define OWFs for average-case hardness. Do we known if worst-case one-way permutations exist assuming $\mathbf{P} \neq \...
Noel Arteche's user avatar
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Does removing just last bit from output of one way function change its one wayness?

If $g(x)$ if length preserving one way function, is there a scenario where $h(x) := g(x)_{1\ldots |x|−1}$ . I.e., $h$ returns all bits that g returns, except for the last bit., is not a one way ...
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Post-quantum EU-CMA security from OWF-only

In the paper: "Universal One-Way Hash Functions and their Cryptographic Applications". The following is proven: "If 1-1 one-way functions exist, then the one-way based signature scheme ...
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Deterministically secure PRG from deterministically secure OWF

Consider the construction of "A Pseudorandom Generator from any One-way Function" [HILL99] in Hastad et al. One way to proof pseudorandomness of this construction is by contradiction. That ...
Nicholas Brandt's user avatar
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Is it One Way Function?

I am currently studying a course in cryptography, and I have this exercise about OWF. I'm failing to prove that this is an inverter to f. Am I in the right direction at all? Thank you!
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Technical feasibility of a theoritical compression mechanism

Considering that quantum computers (in theory) can break\reverse some of one-way-hashes a lot faster than conventional-computers. Is it technically feasible in any theoritical (but realistic) senarion,...
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Existence of PRGs satisfying the following weaker definition

Consider the following definition. Let $p(n) > n$ be a polynomial, and $G_n: \{0, 1\}^n \rightarrow \{0, 1\}^{p(n)}$ a PRG. Moreover, given $x \leftarrow \{0, 1\}^n$, we say $S$ is a length $n-1$ ...
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Given the existence of provably-hard-to-solve problems, why do we routinely rely on conjectured-to-be-hard problems for encryption?

Let $(X, Y, Z)$ be a set of binary strings of length $n$. Let random $X$ be the private key for encoding (or decoding) message random $Y$ as $Z$. Let the encryption algorithm $m$ be a matching ...
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Is sha3 a one-way funtion

If i store sensitive stuff (e.g passwords, salted passwords, Internet protacel adresss(so i know its not tamperd with), private keys(the keys are using a portion of the key on multiple disks in ...
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Is every pseudorandom generator a one-way function, even if the output length has no extra restrictions?

Intuitively, if we can invert a PRG, then we can easily distinguish it with random distribution by checking g(inverse(y)) = y. So every PRG is a OWF? Unlike the problem "Is every pseudorandom ...
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Is $g(x_1||x_2) = f(x_1 \wedge x_2)$ a one way function assuming f is a one way function

Intuitively I think not because assuming the bit string $x_1,x_2 \sim \{0,1\}^{n/2}$, $x_1 \wedge x_2$ is not uniformly random so if $g$ were still a one-way function then the fact that the definition ...
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Proving that the length-preserving OWF does not have polynomially bounded cycle

Here a cycle is the smallest positive integer such that $f^i(x) = x$. Formally we want to prove that if $f$ is OWF then $\forall p(.)$ and sufficiently large $n$, $Exp(cyc_f(U_n))>p(n)$ where $n$ ...
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A random access machine with lots of random data on its tape is a stronger assumption than the existence of OWFs

Suppose we have a random access machine with $(n+1)2^n$ random bits on its tape. This assumption is weaker than assuming the existence of a random oracle, but using this assumption we can construct a ...
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Construct a OWF using two functions $f : X \rightarrow Y$ and $g: X \rightarrow Y$

Given two functions f,g we have to construct h; such that h is one way function. Either f or g is a one way function. We don't know which one is a one way function. Both f and g are defined over X->...
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How to understand the argument “if the adversary outputs x then it queries (a, x) to oracle”?

When I read the work of Dodis et al. ref1, it looks as if I have encountered a simple logical bug. (I'm not concerned with the details of secure proof techniques, but with the logic of reasoning.) In ...
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Existence of universal one-way function

I have some troubles with this proof from Foundations of Cryptography by Oded Goldreich p.52. Why exactly does the parsing of x to x'x'' take quadratic time in length x'x''? If I have |x'x''|=p(|x'|), ...
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Cryptographic functions as feature map/kernel function?

Has there been any use of cryptographic function as a kernel function with support vector machine? There are several standard kernels to be used with SVMs each with its own scenario. I was not able to ...
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Is there a notion of information theoretic one-way function?

This is not a formal but intuitive concept of one-wayness. The intuition is that if you have a combinatorial object that requires $n$ bits to describe. A one way operation introduces noise in random ...
Mohammad Al-Turkistany's user avatar
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Where is the definition of one-way trap-door function used in public key cryptography

This is a rather simple question but I've been unable to find a proper answer for this online. When defining an asymmetric (public key) algorithm is the one-way trap-door function usage referring to ...
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Composition of one-way functions and private keys

Are there any functions f, g and h, such that: f is one-way and is used to generate an encrypted message c when applied to message m with a public key (c = f(m, N)) Original message m can only be ...
lanzalibre's user avatar
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Cryptographic hash function to map interval onto itself

Is there any existing approach to construct perfect hash function that map [0, M) to [0, M)? It should be one to one mapping and ...
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Suppose there exists a one-way function, show that there exists a one-way function with none of its input bit is a hardcore bit

I just learnt the definition of hardcore bit, and I have no intuition about this. I want to know what are the possible approaches to this problem.
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Are pseudorandom generators, pseudorandom permutations and hash functions all keyless?

In Katz's Introduction to Modern Cryptography, Chapter 7 Practical Constructions of Symmetric-Key Primitives In previous chapters we have demonstrated how secure encryption schemes and message ...
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Is the concatenation of two one-way functions a one-way function when each function takes different inputs?

Similar to this question, but having two seperate inputs for each length preserving one way function $f$ and $g$, i.e. $h: \lbrace 0,1 \rbrace^{2\kappa} \to \lbrace 0,1 \rbrace^{2\kappa}, h(x) = f(x_1)...
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Why is RSA not a hashfunction?

The RSA-Assumption says that $(GenSP,F,SampleX)$ is one-way. So if we initialize an instance of RSA $(n,e), (n,d)$ and fairly forget the secret-key and SampleX uniformly distributed over $X, F = x^e \...
killertoge's user avatar
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Is a mapping of a k bit string to another k bit string containing 1's a one way function?

I'm new to cryptanalysis and I saw in another answer to a question that $f: \lbrace0, 1\rbrace^{\kappa}\to \lbrace0, 1\rbrace^{\kappa}, f(x) = 1^{\kappa} $ is a one way function. Why is this the case? ...
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Deterministically produce an array of indexes based on input number

Please see the Reference section below for terms. Is there a known one-way method to produce an array of indexes, based only on two input elements: length of the resulting array number, used as a key ...
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OWF from PRG and OWF

Let $f : \mathcal{U}_{2\lambda} \to \mathcal{U}_{2\lambda}$ be a OWF, and $G : \mathcal{U}_{\lambda} \to \mathcal{U}_{2\lambda}$ be a PRG with $\lambda$-bit stretch. Establish whether the following ...
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The existence of OWFs vs $\mathbf{EXP} \neq \mathbf{BPP}$

In CRYPTO 2021, Liu and Pass published a paper with title "On the Possibility of Basing Cryptography on $\mathbf{EXP} \neq \mathbf{BPP}$. One of the main results of this work can be interpreted ...
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Is this construction a OWF?

Given the OWF function $f: \{0,1\}^{2\lambda} \rightarrow \{0,1\}^{2\lambda}$ and the PRG $G: \{0,1\}^{\lambda} \rightarrow \{0,1\}^{2\lambda}$, is the following function $f^*$ a OWF? \begin{align} f^...
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One way function with fixed point

As part of an exercise in a cryptography course, I want to come up with a one way function for which it is "easy" to find a collision from a given OWF. To achieve this, I tried the following:...
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Prove: If there exist strong OWFs then there exist weak OWFs that aren't strong

Please help me to understand the proof of the following claim: Assume there exist strong OWFs, then there exist functions that are weak $\frac{2}{3}$-one-way functions, but not strong one-way ones ...
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What are security reductions of symmetric-key algorithms?

I was reading Wikipedia page of post-quantum cryptography. It says that it is desirable for cryptographic algorithms to be reducible to some particular mathematical problem, that is intractability of ...
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I am confused on how to solve this question about one way hashing

I know that I have to use decryption, but I am confused about how it breaks one-way (preimage resistance)
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PRG implies OWF Proof

I got the idea of this proof, that since PRG expands from n to 2n, it cannot project to all {0,1}^{2n}, only to a neglible part which we can abuse to make a good distinguisher just by telling if A ...
killertoge's user avatar
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What's an algorithm for laypeople to make personal passwords

I'm going to be teaching an audience about algorithms. I'd like to give them one to create unique personal passwords for websites. They could start with the domain name of the site and their own ...
DocWriter's user avatar
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OWF and iO Correlation

What is the relationship between one way functions(OWF) and indistinguishable obfuscation(iO)? I know that iO exists even when P=NP and OWF don't exist. But does the existence of OWF imply iO?
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Deciphering input from known output using SHA512?

Basic question. I'm doing self-study on hash functions. If I insert hello as input in a SHA512 hash function (e.g. using this) I get the following hash: ...
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It is possible to verify the computation of a hash function without actually proving it in zero knowledge?

Let me first introduce the context: Let's say that we have a hash function evaluation: $$h = H(x, y),$$ where $x$ and $y$ are the public and the private input of the hash function $H$, respectively. ...
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XOR of all bits of $f(x)$ a hard-core bit

Why consider a random $r$ in building a hardcore predicate in Goldreich Levin theorem? Why not consider just the XOR of all bits of the input?
Zoey's user avatar
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Why is a fixed permutation not oneway?

This may not be a good question, but I am just start to learn cryptography. I would like to ask why a fix permutation is not one way. An adversary is given y=f(x) and try to invert y, x and y are n ...
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