# Tagged Questions

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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### Inverting a candidate one way function

Let $w = a_0 \cdot a_1 \cdots a_{n-1}$ be a word from $\{0,1\}^n$, $|w| = n$ Let $m = \sum_{i=0}^{n-1}{ a_i \cdot 2 ^ {n-1-i} }$ be the corresponding binary number constructed from the word. Let ...
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### hash function for elliptic curve co-ordinates

Is there any hash function which takes the co-ordinates of an elliptic curve $E_p(a,b)$ as input and gives an integer value i.e. $h(.) : \{(x,y) \in E_p(a,b)\} \rightarrow \mathbb{Z}$
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### Why are the bit lengths of keys and digests equal in Lamport signatures?

In Lamport's one time signature scheme: One way function to convert a pseudo random number private key to a public key takes $\{0,1\}^n$ and returns $\{0,1\}^n$. Cryptographic hash function to ...
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### Trapdoor and RSA (Schneier)

Disclaimer: I'm new to cryptography. Background: From Applied Cryptography (Bruce Schneier), page 30 of 2nd edition A trapdoor one-way function is a special type of one-way function, one with a ...
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### How to construct a collision resistant hash function that is not a one-way function?

How to construct a CRHF (collision resistant hash function) that is not a OWF (one-way function)? Not sure but I think it probably needs another CRHF?
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### Differences between OWP and OWF and their IND-CPA security

I am learning about one way permutations and one way functions and am not sure of the differences if there are any. Also in the random oracle model are they both IND-CPA secure?
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### One-Way property of Random Oracle

I'm currently working on a proof in the Random Oracle model, and could not find the formal argument on why the random oracle is one-way (i.e. for an Oracle $O$, it is easy to calculate $x=O(n)$, but ...
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### Is a random circuit likely to compute a one-way function?

I remember reading somewhere that (under certain reasonable assumptions) a Boolean circuit with many inputs and outputs (assume equal number for now) chosen at random will be a one-way function with ...
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### Is the identity function a one-way function?

The definition of the one way function says: it must be verifiable in polynomial time probability of inverting it less or equal to negligible Now, I am not sure I fully understand one way ...
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### Proving a function is a one way function

I am trying to prove that a function is a one-way function. The function I am working on in particular is $f'(x,y)=f(x)||f(x \oplus y)$. For what I have understood looking at similar solved ...
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### Is $f(f(x))$ a one way function?

I found from a book the following proof. Although I understand the initial construction, I don't understand the last sentence that proves the statement. Why $f(f(x))$, in the paper $h(h(x))$, is ...
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### Unkeyed, fast, one-way PRP

Are there any fast, secure, one-way, unkeyed almost-pseudorandom permutations? I am looking for something that can hide a MAC, without requiring a secret key and while being much faster than public ...
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### Periodic One Way Function

Is there any notion of a periodic OWF? I.e. an OWF $f$ that on every input $x$ in its domain it holds that $f(f(f\ldots f(x))\ldots )=x$ when $f$ applied many times, each time on the previous output....
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### Collision free one way function

I was playing with a function that I think is collision free and uninvertible assuming the hardness of integer factorization. I am unfortunately not as skilled at math as I would like to be, and do ...
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### Choice of the one-way function (OWF) for Lamport signatures

I am studying the Lamport signature scheme, and I found that in many sources (eg: Hash-based Digital Signature Schemes) the input and output bitstring of the OWF and the message digest have the same ...
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### What Does This Symbol Mean? (Hardcore Predicates for One-Way Functions)

I am studying Pseudorandom Number Generators and when reading the discussion on One-Way Functions and Hardcore Predicates, I came upon this equation. $$b(x,r)=\displaystyle \bigoplus_jx_jr_j$$ I ...
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### what is the difference between one way function and hard core predicate?

Does anyone know what the difference between a one way function is and a hard core predicate? Are they related to each other or different?
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### Why do cryptographic hashes need to be fixed length?

Why do cryptographic hashes need to have a fixed length output? I know that the shallow answer is that an output that varies by key size or file size can leak information somehow, leading to ...
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### Can the round function $F$ in a Feistel Network be practically any non-invertible function?

This question might seem silly, but how true is the fact that the round function $F$ does not have to be invertible? I am curious to know this, because non-invertible functions can be very lossy, i.e....
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### Fast forwarding hash functions

We know that a good hash function is a one way/trapdoor function. Easy to calculate one way, harder to work out a previous state. I was wondering if anyone knew a good hashing system that allowed you ...
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### Proving the security of a one-way function with partially known input

Let's say we have a construction like in this question: We have a OWF $h(.)$, a secret salt TXT, and a counter starting at 1, and we compute ...
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### Are there full cycle cryptographic/one-way hash primitives?

I'm looking for behavior similiar to that of LCGs, (i.e. input and output sizes are same). Full cycle of $2^{32}$ different inputs generates full cycle of $2^{32}$ different outputs, distribution of ...
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### Lightweight hash function

I am researching about lightweight hash functions and I've got two related questions: What is the standard or requirement for a hash function in general to be considered lightweight ? Why can it be ...
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### Hard-core predicates: should the adversary be given $1^n$?

In most (all?) classical sources such as the book of Goldreich (2001), hard-core predicated are defined thus: A polynomial-time computable predicate $b : \{0,1\}^* \to \{0,1\}$ is a hard-core of a ...
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### How do we know one-way functions can be iterated?

Suppose we have some one-way function $h$. Without further specification of $h$, how can we be sure that we can define another function $g(n) = h(h(n))$? That is, how do we know the range of $h$ is a ...
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### Discrete logarithm over prime modulo: small input, large exponent, larger prime

I am considering using modular exponentiation as a one-way hash function. More specifically, here is the scenario. 1) Input ($m$): the input messages are small (16-bit) 2) Exponent ($e$): the ...
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### Is the Salsa20/ChaCha20 keystream generation one-way?

Is it possible to recompute the Salsa20 or ChaCha20 key in a realistic time if the keystream and the nonce are given to an attacker? Or is the keystream generation one-way, like a cryptographic has ...
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### Deterministic outputs based on non-connected inputs

I am looking for a one way function that can generate outputs deterministically. However, revealing any of the inputs dont allow the person to generate other inputs. E.g: lets say we have a list of ...
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### Composing two one-way functions such that the result is not a one-way function

Is it possible to have two distinct one-way functions (called, say, $h$ and $g$) such that their composition $h \circ g = [\, x \mapsto h(g(x)) \,]$ is not one-way?
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### Is $f(x)\oplus x$ a one-way function?

Given that $f$ is a OWF and $|f(x)|=|x|$ for all $x$, is $g(x)=f(x)\oplus x$ necessarily also a OWF?
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### One-way function definition

I cannot understand why a one-way function $f$ is defined in this way $\text{Pr}(f(A(f(x))) = f(x)) < \frac{1}{p(n)}$ and not $\text{Pr}(A(f(x)) = x) < \frac{1}{p(n)}$ where $A$ is a ...
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### Davies-Meyer Hash Function

So the Davies-Meyer Hash Function is: Hi = Hi−1 ⊕ exi (Hi−1) Say I pick H0 = 1110 0011 And the message x1 = "5" or "0000 0101" Is this the correct way to compute H1? H1 = 1110 0011 ⊕ (0000 0101 ⊕ ...
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### One Way function and Merkle Damgård

Is it possible keep the "one wayness property" of certain one way function in Merkle-Damgård construction? I'm asking this question because according to Collision-Resistant hashing: Towards making ...
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### Building cryptographic primitives using additive maps?

Suppose we have a one-way function F(x) that exhibits the property F(a + b) = F(a) + F(b). Such a function could be used as a cryptographic primitive, no?
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### Definition of one-way functions: randomly-chosen point vs every point

Notation: $\Sigma^k$ is the set of $k$-strings on the alphabet $\Sigma$; $\Sigma^\ast$ is the set of all finite dimensional strings on the alphabet $\Sigma$. In the context of computer-science a ...
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One-way accumulators are built upon a (quasi)-commutative one-way function. With quasi-commutativity, I refer to the following property: For $f : X \times Y \to X$, it is true that $f(f(x, y_1), y_2) ... 1answer 374 views ### Proving that a function is not a OWF (One-way-function) I was trying to prove that a given function is not a one way function and I was not sure how to do it because maybe I had unclear what a one way function was (OWF). The definition that I have for a ... 1answer 389 views ### Help in understanding exactly how lattices used as one way functions for hashing I am doing a cryptography course via long distance and we have been given an assignment which is based on lattice-based cryptography. I have spent the majority of the past week sifting through papers ... 1answer 318 views ### One-way permutation over a small interval? I am wondering what concrete computable functions we know that are a permutation over an integer interval of parameterizable size$s$, for relatively small$s$starting circa$2^{64}$, to perhaps$2^...
How can I prove the following: If $f$ is a one-way function, then it is an uninvertible function?