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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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Determining whether functions are one-way or not

I read a book about one-way function. In this book, I saw 2 exercises that I can't understand and don't know how to solve. Can anyone help me to solve these? Is $f(x,y)=x+y$ a one way function? Is $f(...
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Other than password hashes, are there other uses for non-reversible crypto

Hashing is useful for checking that an input matches expectations without giving away the stored expected version - so confirming passwords etc. But are there other use cases? In general, ...
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1answer
39 views

Prove: If there exist OWF then there exist OWF $f$ such that $ \forall x$ $f(x,x)=x$

I wrote the definition, but I don't know what should I do. Can you help me? I want to prove the following: If there exist one-way function then there exist a one-way function $f$ such that for every ...
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0answers
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Is the concatenation of one-way compression functions one-way?

Given two independently keyed compression functions $h_1$ and $h_2$: $h_b(x): \{0,1\}^{3n} \to \{0,1\}^{n}$, where $b \in \{1,2\}$. Let $h(x) = h_1(x) \| h_2(x)$. Given at least one of $h_1$ and $...
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Can we construct a PRF directly from a one way permutation function?

In Introduction to Modern Cryptography first a pseudo random generator (PRG) is constructed from a one way function (OWF). After that the PRG is used to to construct pseudorandom functions (PRF). Is ...
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What is the expected number of messages for which Eve can forge the signature in (repeated) Lamport?

Alice and Bob use the Lamport scheme, but Alice uses the same key to sign two messages (of length $n$). Eve intercepts both these messages. What is the expected number of messages (length $n$) Eve ...
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1answer
78 views

Newbie question: one-way functions in cryptography

I'm reading this article on the basics of cryptography and it says that the main principle is about taking such an algorithm that knowing the end result and the algorithm, an eavesdropper wouldn't be ...
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If trapdoor OWF exists then f is a trapdoor OWF, is there such a construction?

Is there a known construction of f, such that given that a trapdoor OWF exists then f is a trapdoor OWF, so we can construct inefficient cryptomania, ala Levin's construction for minicrypt in "The ...
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2answers
147 views

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

Let $g$ be a one-way function, and let $f(x) = g(x) ⊕ g(\bar{x})$ (where the bar over x denotes bitwise complement). Is $f$ necessarily a one-way function?
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Clarification of one-way property of hash functions

One-way property: computationally infeasible to find data mapping to specific hash The definition above is a little vague, if we have h(x) = floor(log(x)), ...
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1answer
228 views

Is a one-way function pseudorandom?

For one-way function $f$ I understand that $g(x)=0^{n}\mathbin\|f(x)$ is a one- way function with respect to $2n$, where there is $n$ bits of $0$ in the beginning and the output of $f$ in the second ...
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1answer
36 views

Concept of hashing a group of data and validating if a value exists within the group

When learning about cryptography and hashing, I remember seeing a concept where you could hash a number of values (ID's for example) and then validate against the hash, not storing the original IDs. ...
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Composition of weak one way function is not a strong one way function

Given $f(x)$, a weak one-way permutation, how to prove that $f^T(x)$ is not a strong one-way function? Here $f^T$ denotes $T$ times self composition of $f$ and $T$ is a polynomial in input length.
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1answer
24 views

Why the output length of a KDF should be the same as the underlying OWF?

Quote: The chosen output length of the key derivation function SHOULD be the same as the length of the underlying one-way function output. Could someone please help explain the benefits and ...
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1answer
54 views

What does approved one-way function mean?

In one of their documents, NIST recommends using an approved one-way function, followed by a list of such functions, such as HMAC, KMAC, etc.. However, the wikipedia page says: Unsolved problem in ...
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1answer
107 views

What is the one way function in ECC?

In the RSA algorithm it's the the integer factorisation problem, it's easy to multiply the two large primes to generate n, but given just n it's very difficult to find the constitutent primes. In the ...
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1answer
152 views

Is there a deterministic one-way collision-free crypto algorithm?

I use usernames encrypted using a function f as ids of records. Users see records identified by f(username). I must not know real usernames. I want to be protected from attack when adversary who has ...
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0answers
54 views

Are there any one-way operations that could be used for Diffie-Hellman post-quantum? (See criteria)

With quantum-computers looming, there is a need for Public Key Cryptosystems that can withstand attacks by quantum-computers. Are there any known one-way operations that fit the following criteria? ...
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1answer
32 views

DLP-based keyed one-way function

I am trying to understand if it possible to use DLP to build a keyed one-way function with the following properties: $H_a(H_b(M)) = H_c(M)$, where $a$ and $b$ are the keys, and $c=a*b$ The output of ...
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1answer
78 views

Function families from lattices

On this course, Micciancio talks about function families (functions parametrized by some value) that can be used in cryptography. On page 2, he presents the following function family parametrized by ...
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Concatenating a one way function

Let $f$ be a length preserving one way function. Show that $g(x)=f(x)|x_{[1:\log n]}$, where $|$ indicates concatenation and $x_{[1:\log n]}$ indicates the first $\log n$ bits of x, is also a one way ...
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1answer
235 views

Collision-free one-wayish function mapping 32 bit to 32 bit

As simple as it may sound, I was unable to find a collsion free one-way(ish) function which takes 32 bits of input and produces 32 bits of output. I apologize if I just didn't knew the right keywords ...
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1answer
175 views

Hash function composition - security level

When using two hash functions, g(x)=SHA-512 and f(x)=MD5 g(x) has 512 bit output (using salt) f(x) has 128 bit output. Let's say that z(x)=f(g(x)) meaning the output is 128 bit long. The Question: ...
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1answer
284 views

Is Diffie Hellman key exchange based on one-way function or trapdoor function?

I have a question for my information security lab, which I am not able to find online. As the title says, is Diffie Hellman key exchange based on a one-way or a trapdoor function? In case of RSA I ...
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1answer
87 views

How to show that the following function is not a OWF?

Given F, which is a Pseudo Random Permutation, I need to prove that the following function f is not a OWF: f(x, y) = Fx(y) My first thought would be to create an adversary which tries and compute Fx-...
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1answer
47 views

Signature scheme against an unbounded rival

I've seen this: Can a computationally unbounded adversary break any public-key encryption scheme? And I've read the following theorem: Theorem (Lamport, GMR, Naor-Yung, Rompel, Goldreich) If one-way ...
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1answer
93 views

Practical OWP of the set of $k$-bit bitstrings for low $k$

Down to what $k$ and how can we devise a practical, public, efficiently computable One Way Permutation $P$ of the set $\{0,1\}^k$ of $k$-bit bitstrings, if possible without involving a trusted party ...
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1answer
71 views

What is the purpose of having a one-way function also be a permutation on it's on domain?

From a cryptographic sense, what value is added from setting the domain to be the image in the mapping?
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302 views

Making a one-way function harder to reverse

Let's suppose that for a crypto protocol a 32-byte-to-32-byte one-way function is needed. Proposals are: $\textrm{sha256}(x)$ $\textrm{hmac}(\textrm{sha256}, x, x)$ $\textrm{hmac}(\textrm{sha256}, x, ...
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1answer
300 views

is the XOR of PRG outputs a PRG?

I am going through the course http://u.cs.biu.ac.il/~lindell/89-856/main-89-856.html, as it has a good lecture notes. I found exercise 2 solution a puzzling statement: it says that $G^\prime (x_1 , ...
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1answer
422 views

Prove that pseudorandom generator is a one way function

Suppose the following PRG $G : \{0,1\}^n \rightarrow \{0,1\}^{n +l}$, I want to prove that $G$ is one way function (and not building one), for: $l = \omega (\log n)$ $l = 1$ For $l = \log n$, ...
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2answers
701 views

Using ChaCha20 as a PRNG with a variable-length seed

As far as I understand, the key stream of the ChaCha20 cipher may be used as a seeded PRNG, where the seed is used to set the key and the nonce. As described in RFC7539, ChaCha20 can be used with a ...
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1answer
310 views

Overview of relations between cryptographic primitives?

Is there a web page that gives a graphical (or, alternatively, a textual) overview of known implications and separations between cryptographic primitives? More specifically, I am looking for ...
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1answer
1k views

Collision Resistant Hashing from One-Way Functions?

In general, can we construct a collision resistant hash function from a one-way function?
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1answer
106 views

Why can't construct PRG from one-way function and hc, but only one-way permutation

In Katz & Lindell's book, theorem 7.19 stressed that let f be a one way permutation with hard-core predicate hc. Then algorithm $G(s)=f(s)||hc(s)$ is a PRG with expansion factor $\ell(n)=n+1$. ...
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1answer
207 views

Katz/Lindell Problem 7.6

Let $f$ be a length-preserving one-way function, and let $\text{hc}$ be a hard-core predicate of $f$. Define $G$ as $G(x)=f(x)\|\text{hc}(x)$. Is $G$ necessarily a pseudorandom generator? The answer ...
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One Way Function - How to Prove?

Function $f$ is a length shortening function. It reduces to log of size of input, i.e $|f(x)|/\log(|x|) \leq$ $a\ positive\ constant$. Is this a one way function? Edit: $f$ is any function. Unknown ...
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1answer
93 views

Probability amplication in OWF without hardcore bits

We know that OWF $f$ such that none of its bits are hardcore exists. We also know that given an algorithm that solves a problem with non-negligible probability, we can repeat it many times and take ...
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Polynomially many iterations of one way permutation

I have seen that the existence of weak OWFs implies the existence of strong OWFs. It comes from repeating the weak OWF polynomially many times on different random inputs. However, I have a different ...
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Can we come up with a counterexample?

Suppose $\epsilon$ : $N\in~ [0,1]$ is not a negligible function. Does it follow that for some polynomial $p$ (where $p(k)$ > 0 for all $k$) and some $k_0$, $\epsilon(k) > \frac{1}{p(k)}$ for all $k ...
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Is this a one-way function?

Let $f$ be length preserving one way functions, i.e. $|f(x)|$ = $|x|$. Then, ${f^{'}_{p,h,y}}$ = $h^{x_1}y^{x_2} mod ~p$. Here $h,y$ <- ${Z^{*}_{p}}$ and $x_1,x_2$ <- $Z_{p-1}$ and $p$ is a ...
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1answer
580 views

Is the concatenation of two one-way functions a one-way function?

Suppose we are given two one way functions $f$ and $g$. We define a new function h that is the concatenation of f and g. That is, $h(x)=f(x), g(x)$, where the comma indicates concatenation. We want to ...
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1answer
331 views

How to prove that a one way function is uninvertible?

Suppose we define the "hard to invert" part in the definition of one-way functions differently: A function $\ f : \{0,1\}^* \to \{0,1\}^*$ is called uninvertible if it is easy to compute $f$ but ...
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3answers
732 views

Secure and efficient encryption of a continuous data stream on behalf of a third party using asymmetric cryptography

I want to design an API-based system that is able to securely encrypt a stream of data received on behalf of an external user in such a way that the data can only be decrypted using a secret that only ...
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1answer
169 views

Proof that a given function is not a OWF

I'm currently learning about one-way functions. I have a book with the following exercise (Sadly there is no solution in the book...) Let $g\colon \{0,1\}^n \to \{0,1\}^n$ be a one way function. ...
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1answer
274 views

Relationship between existence of OWFs and OWPs

OWPs are bijective OWFs, so every OWP is a OWF, but not the other way around. However, I'm wondering what the relationship between the existence of both types of functions is. Obviously if one ...
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Is there a one-way key for data depersonalization?

Given a secure database that continues to receive updates on user data, and permission from the users (that complies with laws and regulations in effect) to depersonalize that data, export to another ...
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2answers
246 views

Is there a standard one way function that does not produce collision

Is there any standard or accepted one way function that does not produce collisions? I'm not looking for hash functions. Does that make sense at all? for example given string with length ...
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1answer
286 views

Using states of a double pendulum as a one-way function [closed]

Hello, as a non-professional (at all) but a fan of cryptography, I have one idea and I would love to hear your input on it. As I understand cryptographic functions they should have following ...
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1answer
147 views

Sub exponentially hard OWF , PRF and iO

I'm currently reading the work "Obfuscation of probabilistic circuits and Applications' by Canetti Lin Tessaro and Vaikuntanathan 2015. It says sub exponentially hard OWF implies sub exponentially ...