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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Is $f(x)=g(x)||g(\bar{x})$ a one-way function where $g(x)$ is a OWF?

Given that $g$ is a OWF, is $f(x)=g(x)||g(\bar{x})$ necessarily also a OWF?
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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?
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Trapdoor One Way Functions [closed]

If y = F(x) is a relatively practical One Way Function. How can you construct a Trapdoor One Way Function using F?
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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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One way text→text function

I need a way to map some printable text to other printable text. E.g.: Ian BoydKcp Zbas Notice some of the important ...
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Security of Hash Functions

Given a Hash Function H, how are the properties such as collision resistance, target collision resistance, one wayness, and non-malleability proved? I have read about hash function and stating that it ...
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I'm having trouble understanding this [duplicate]

Let $x=(x_1,x_2,...x_n)∈\{0,1\}^n$ for $n∈\mathbb N$. Prove that if one-way functions (OWFs) exist, then there exists a one-way function f such that for every bit $i∈[1, n]$ there exists an algorithm $...
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One way function existence

Let $x = (x_1, x_2,...,x_n)\in\{0,1\}^n$ for $n\in\mathbb{N}$. Prove that if one-way functions (OWFs) exist, then there exists a one-way function $f$ such that for every bit $i\in[1,n]$ there exists ...
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Rigorous practical pseudorandom generators

It is known that existence of pseudorandom generators (PRGs) is equivalent to the existence of one-way functions. In turn, the latter is an open problem. I am curious if someone developed kind of &...
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Do I understand $P = NP$ correctly in relation to one-way functions?

If I understand this relation correctly is, that any function whose inverse can be found in polynomial time is not a one way function. The $P = NP$ proved would cause that any candidate for a one-way ...
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How can one-way hash functions in the signatures help by using same algorithm for encryption and signature verification?

I read some documents about digital signatures and one way hash functions, etc., but everything was too complicated and I don't have much experience in cryptography. Can anyone explain to me in a ...
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A function $H(x)$ is given. If there is an algorithm $B(H(x))$ that get part of $x$, is $H(x)$ a one-way function?

I came up with this question while I was reading this paper: Pilaram, Hossein, and Taraneh Eghlidos. "An efficient lattice based multi-stage secret sharing scheme." IEEE Transactions on ...
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In the reduction proof below, where OWF exists only if is a PRG. I am not able to understand the highlighted part

I am able to understand how G(x) id generated. But then what is the use of variable z. Also if the probability is >1/2 + e then the distinguisher wins! Then how is this still a OWF
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Single-block hash construction based on a block cipher with two fixed keys

Let k1, k2 be two arbitrary fixed keys (nothing-up-my-sleeve values like "foo" and "bar") and ...
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Is this a One Way Function?

$f_{p,g,h}(x_1,x_2)=g^{x_1}h^{x_2}\bmod p$ where $g$ is a generator of $\mathbb Z_p^*$; $h\in\mathbb Z_p^*$; $x_1,x_2\in\mathbb Z_{p-1}$ Is this a One Way Function? (Assuming DL is hard) Anyone has an ...
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Does Rabin function lose its one-way property if squaring mod a prime?

I am looking into various one way functions and I stumbled upon a Rabin function, which is squaring modulo an RSA modulus $N=pq$, where $p,q$ are prime: $R_N(x) = x^2 \mod N$. Would it lose the one-...
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Does this break the pre-image resistance of the hash function?

Supposing a secure hash function $f(\cdot): \{0,1\}^* \rightarrow \{0,1\}^n$ satisfies pre-image resistance. That is, given a hash value $y$ it should be difficult to find any message $x$ such that $y ...
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If $H(x)$ is a one-way function, is $f(x)=H(x)\cdot x^{-1}$ a one-way function?

Assume $S$ is a domain. $S' \subseteq S$ and all elements in $S'$ are invertible. $H:S'\rightarrow S$. If $H(x)$ is a one-way function, is $f(x)=H(x)\cdot x^{-1}$ a one-way function?
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Is it hard to determine an automorphism when the mapped value by several compositions of the automorphism is given

Generalization of the Discrete logarithm problem to non-abelian groups is discussed by many authors. One of the generalizations is shown in MOR cryptosystem as in the below link, by considering the ...
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Provable Lower Bounds for some Algorithmic Problems?

Are there any problems for which we have known lower bounds? For example, for comparison based sorting, we know you need $\Omega(n \log n)$ comparisons. Edit: I'm aware that this requires restricting ...
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Generator of one-way functions

Please pardon my question if it seems silly, but I am very keen on knowing: in applied cryptography, there is such a thing as a one-way function, which given an input would generate an output that is ...
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Does this qualify as a one-way function?

First, we observe that the expression X*Y mod P (where X and Y are secret and P is a large public prime) reveals no useful information. Next we define an extending function E(U, M) which "somehow&...
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Are there any public-key encryption schemes based on DLog?

There are public-key encryption schemes based on many different mathematical hardness assumptions, like the hardness of Decisional Diffie-Hellman problem, the hardness of the Factoring problem, the ...
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Length Regular and Length Preserving

What does it mean to say a function is length regular and Length preserving? Does any one of them implies the other? Example if any could be useful
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Do probabilistic one-way functions imply deterministic one-way functions?

Suppose $f$ is a probabilistic one-way function. Then my question is, does there exist a construction of a deterministic one-way function $g$ based on $f$? Or is it possible that probabilistic one-...
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What one-way functions are there based on the Diffie-Hellman problem?

Mathematical hardness assumptions like that of the factoring problem, the RSA problem, and the discrete log problem all straightforwardly lead to one-way functions. But what about the computational ...
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Is this really a universal one-way function?

This PDF supposedly gives a construction of a universal one-way function, i.e. a function which is one-way as long as there exists a one-way function: Recall that there are only countably many Turing ...
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Does there exist a universal one-way permutation?

Leonid Levin constructed a universal one-way function, i.e. a function which is one-way as long as there exists at least one one-way function. But my question is, does there exist a universal one-way ...
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Are there any universal PRG’s or PRF’s?

Leonid Levin constructed a universal one-way function, i.e. a function $f$ such that if any one-way functions exist, then $f$ is a one-way function. My question is, what universal pseudorandom ...
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Questions regarding the one-wayness and collision-resistance of a hash function based on RSA-like problem

Problem statement: "Bob is a paranoid cryptographer who does not trust dedicated hash functions such as SHA1 and SHA-2. Bob decided to build his own hash function based on some ideas from number ...
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Has anyone implemented a public-key encryption scheme using a universal one-way function?

There exists a function $f$ such that if one-way functions exist then $f$ is a one-way function. Such a function is called a universal one-way function. Now the public-key encryption schemes that I’...
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When is a OWF practically insecure?

Let's say we got a one way function (OWF). Such a function takes 512-bit input and gives 256-bit output. And let's say we can easly invert some specific inputs. There is exactly $2^{256}$ such blocks ...
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One way permutation and its inverse

Is the following statement correct? Let $F$ be a OWP. Then the inverse $F^{-1}$ of $F$ is also a OWP.
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Is it easy to crack a hashed phone number?

I want to SHA256 hash phone numbers in order to hide them. Is this a good idea? Are there any other ways I could make this safe?
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If OWF were to exist, do we know for sure that one of the candidate OWF would indeed be a OWF?

We have several candidates for OWF, like multiplication/factoring and discrete exponencial/logarithm. What I am asking is: Does the existence of one way functions imply that our candidate functions ...
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Is $f(g)$ a PRG if $f$ is a OWF and $g$ a PRG?

If we have a PRG $g$ and a OWF $f$, can we say that $g' = f(g)$ is a PRG? And what if $g$ stretches its input by a factor of 2?
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What is the probability that a random function is invertible?

Having a random function - $R\in{}\mathcal{R}$ s.t. $R:\{0,1\}^n\rightarrow{}\{0,1\}^n$. What is the probability that $R$ is invertible? I know calculating it suppose to be straight forward, but I'...
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(updated) Utilizing a non-computable function to create a one-way function

Why can't uncomputable functions be adapted to serve as theoretically perfect one-way functions? This has been bugging me for years, and I've never been able to track down an explanation of why it ...
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Composition of an injective/surjective function and a one-way function remains a one-way function?

I recently read about OWFs and realized that the composition of two OWFs (called, say, $g$ and $f$) are not necessarily an OWF. However, if I modify the question a little bit and fix $g$ to be an ...
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Are all public-key encryption protocols based on one-way functions? [duplicate]

Are there any public-key cryptography protocols which don't rely on one-way (or trapdoor) functions? RSA and Diffie-Hellman cryptographic protocols both rely on one-way functions (prime factorization ...
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How can I show, that RSA with OWP is IND-CPA secure by using H function?

How can I show, that RSA with OWP is IND-CPA secure by using H function , a random oracle model. The Encryption goes like: $\text{Encryption_H_PK}(M)\gets(C_1,C_2)\gets(f(x),H(x)\oplus M)$ ...
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Can one-way permutations be constructed from one-way functions?

We can construct various symmetric key primitives like PRGs, PRFs, SPRPs etc., assuming the existence of either one-way permutations or one-way functions with the former assumption allowing simpler ...
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A hash functin based on XOR and matrix multiplication

Imagine an $n$ bit to $n$ bit hash function defined as follows: Let $K$ and $K'$ be two random predetermined $n\times n$ matrices. Then the hash function $h$ of an $n$ bit number $a$ would be: $$h(a)=...
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Can the input to a one way function be pseudorandom?

I know that normally a one-way function takes in a completely random input, but can a one-way function take in something pseudorandom instead of completely random? Will it still be a one-way function? ...
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Why does the one-time pad not imply $P \not= NP$?

I apologize that this is a rather trivial question, but I haven't been able to find an answer anywhere. If the one-time pad is unconditionally secure and impossible to crack (with just ciphertext), ...
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Permutation of first $k$ prime powers as a one-way function?

Let $a_1$ through $a_k$ be some permutation of the first $k$ primes. Let $n \in [1,k!]$ be a parameter specifying the exact ordering by taking the $n$th permutation in a sorted list or by some other ...
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Are bijective polynomials of degree $2 \bmod 2^m$ efficiently inverted?

Take a bijective polynomial of degree $2 \bmod 2^{64}$ like: $m = (n(n+1)/2)\ \bmod 2^{64}$ It is bijective and can trivially be inverted for numbers up to $2^{32}$ by calculating $\lfloor\sqrt{2m}\...
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Does adding OWF of the private key to encryption scheme hurts security?

Suppose I have a symmetric semantic-secure encryption system $\Pi = (Enc, Dec)$ and an OWF $f$. Now, define the following encryption scheme $\Pi^{'} = (Enc^{'}, Dec^{'})$ where , $Dec^{'} = Dec$ and $...

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