# 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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### 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 ...
91 views

### 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 ...
122 views

### 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 is still a one way function

recently I have been reading about OWF and realized that composition of two OWFs g,f are not necessarily a OWF. However if I modify the question a little bit and fix g to be a injective function, and ...
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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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### Does weak hardcore bit(s) implies strong hardcore bit(s)?

It is well known that weak OWF implies strong OWF by concatenating several evaluations of weak OWF (see e.g. here), where weak OWF is defined as $\exists$ poly $Q$, $\forall$ PPT $\mathcal A$ such ...
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### How simple hash provide message authentication?

This structure provides message authentication. My question is if someone finds the key he can simply change the message and compute new hash according new message and send it to the receiver. If so, ...
Let's say I tell you $G: \mathbb{F} \rightarrow \mathbb{F}$ is a random permutation (some finite field). Does that mean: $G$ is one-way, so that if I give you $G(x)$, it is infeasible to determine ...