# 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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### If mac M is defined as M(k,x) = f(k||x) where f is one way function, can M be UNF-CMA secure Mac scheme?

$f$ here can leak inputs that is $f(x_1 \| x_2) = f(x_1) \| x_2$, is still a one way function $(|x_1| = |x_2|)$. I don't think this should be a secure MAC but don't have any way to formulate it.
1 vote
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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 ...
1 vote
101 views

### 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 ...
39 views

### 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 ...
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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,...
1 vote
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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 $n-1$ ...
1 vote
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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 ...
204 views

### 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 ...
1 vote
89 views

### 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 ...
70 views

### 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 ...
1 vote
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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 $n$ ...
48 views

### 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 ...
1 vote
37 views

### 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 ...
1 vote
43 views

### 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'|), ...
87 views

### 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 ...
211 views

### 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 ...
1k views

### 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 ...
1 vote
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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 ...
1 vote
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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 ...
207 views

### 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 ...
1 vote
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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? ...
186 views

### 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 ...
1 vote
173 views

### 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 ...
1 vote
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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 ...
138 views

### 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^...
1 vote
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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:...
113 views

### 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 ...
1 vote
148 views

### 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 ...
136 views

### 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 ...
1 vote
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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?
131 views

### 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. ...
117 views

### 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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### 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 ...
79 views

### 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 ...
56 views

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 $... 1 vote 1 answer 226 views ### One way function existence Let$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]$there exists ... 1 vote 2 answers 136 views ### Rigorous practical pseudorandom generators It is known that existence of pseudorandom generators (PRGs) is equivalent to the existence of one-way functions. In turn, the latter is an open problem. I am curious if someone developed kind of &... 0 votes 0 answers 74 views ### Do I understand$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$proved would cause that any candidate for a one-way ... 2 votes 0 answers 48 views ### How can one-way hash functions in the signatures help by using same algorithm for encryption and signature verification? I read some documents about digital signatures and one way hash functions, etc., but everything was too complicated and I don't have much experience in cryptography. Can anyone explain to me in a ... 2 votes 1 answer 99 views ### A function$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 ...
1 vote