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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Worst case one way function

the worst-case one way function is defined as follows $$\forall A \exists x : pr(A(f(x))\in f^{-1}(f(x)))\neq 1$$ can you give any example of such function?
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0answers
54 views

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 ...
5
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1answer
73 views

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 ...
0
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1answer
61 views

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 ...
4
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2answers
76 views

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 ...
0
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3answers
67 views

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 ...
0
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1answer
31 views

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 ...
3
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1answer
260 views

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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2answers
196 views

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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2answers
61 views

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 ...
0
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1answer
61 views

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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2answers
392 views

Proving that a function is not invert-able (one way function)

I am having problems with proving if the one-way function (http://crypto.stackexchange.com/tags/one-way-function/info) is hard to invert or not. $2^\sqrt {m} $ one-way function $ f: \{0, 1\}^{2m} ...
0
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1answer
96 views

A one way Function provably reversible at N applications with the same seed?

I'm looking for a function that is generally one way from some secret $F(s, A) \rightarrow Y$, where $A$ is known, $Y$ is produced (also known), and $s$ is kept secret. But whose repeated application ...
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1answer
108 views

Question about second preimage resistance of hash function combiner

Let $\Pi=(Gen_1,H_1)$ and $\Pi=(Gen_2,H_2)$ be two hash functions. Define $(Gen, H)$ so that $Gen$ runs $Gen_1$ and $Gen_2$ obtaining $s_1$ and $s_2$ respectively. Then let ...
2
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1answer
126 views

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 ...
0
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2answers
70 views

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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1answer
94 views

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 ...
2
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1answer
285 views

Disadvantages of one-way accumulators?

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) ...
2
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1answer
161 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 ...
2
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1answer
230 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 ...
3
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1answer
268 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 ...
4
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1answer
153 views

Reason for difference in assumptions for practical private-key and public-key crypto

Theoretical cryptography tells us that everything in the world of private-key cryptography (CCA-secure symmetric encryption, message authentication codes, etc.) can be built from one-way functions and ...
2
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2answers
189 views

One-way function and uninvertible function [closed]

How can I prove the following: If $f$ is a one-way function, then it is an uninvertible function?
3
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2answers
387 views

unique one-way hash

For a 10-digits numeric domain (swedish social security numbers), is there a hash function with the following properties? no two numbers result in the same hash it is not possible to deduce the ...
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1answer
131 views

Does the key schedule function need to be a one-way function?

For some key schedule $e_n(e_{n-1}(k))$ (where $e_{n-1}(k)$ is the result of the previous round) , does $e$ need to be a one-way function? In the case of DES or Rijndael the key schedule doesn't ...
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3answers
446 views

Slow one-way pseudo-random permutation?

I'm looking for a slow one-way pseudo-random permutation; or in other words a block cipher $E_K: P\in\{0,1\}^b\mapsto C\in\{0,1\}^b$ with moderate block size $b\approx 64$ bits, wide key $K$, ...
4
votes
1answer
186 views

Keyed digest function with odds of collision below the birthday bound?

I wonder if it is possible to devise a function $F(K,S,R_S)\mapsto D$ where: $K$ is some key (I have freedom on $K$, it could even be generated by a trusted party); $S$ is in $\{0,1\}^s$, say ...
9
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3answers
256 views

How hard is to invert the function that computes the middle-bits of (x^2)?

I'm designing a function f that should be moderately hard to invert and very fast to evaluate in a modern CPU. The function will be used in a proof-of-work function. I've read that the middle-bits of ...
3
votes
1answer
122 views

Why is Lamport-Diffie secure?

Why is Lamport-Diffie secure? I note that there is a demonstration based on onewayness (in the book postquantum cryptography). But a one way function is not sufficient to ensure that it can not infer ...
3
votes
1answer
247 views

Is there a cryptographic hash function that can be performed with pencil and paper?

Imagine I'm signing up for the 99th new web site this month. I somehow take my secret key (which I have written down on a card in my wallet) and the domain name of the site and feed them both into ...
2
votes
2answers
345 views

Are there any bijective one-way functions not based on number-theoretic hardness assumptions?

I'm trying to find a bijective function $y=F(x)$ which should be easy to compute in one direction but hard to compute in the other, where the one-way property is not based on a number theoretic ...
2
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0answers
147 views

How can I construct a distinguisher given an inverter?

Let $ PRG: \{ 0, 1\}^n \rightarrow \{ 0, 1\}^{n+s}$ be a pseudo random generator and let $A$ be an inverter that runs in polynomial time, specifically: $\large \mathbb P_{d \leftarrow PRG(U_n)}[ A(d) ...
4
votes
1answer
158 views

Can I use the ChaCha core as a 256-bit to 256-bit one-way function?

I'm looking to implement Lamport signatures as a little fun project, and I need a fast one way function that maps $\{0,1\}^{256} \rightarrow \{0,1\}^{256}$. I was wondering whether I could safely use ...
2
votes
1answer
323 views

Is SHA-256 a one way permutation when restricting the domain to {0,1}^256? [duplicate]

Suppose we consider the space of $\lbrace 0,1 \rbrace^{256}$ as the domain and SHA-256 as our hash function. Does SHA-256 become a one way permutation? Has anyone tried to prove this? Or can it be ...
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1answer
181 views

what is an injective trapdoor function?

The answer to this question at Crypto.SE is clear about what a trapdoor function is, but what makes a trapdoor function "injective"?
3
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1answer
151 views

What does it mean to be simultaneously hardcore?

In this paper the term "simultaneously hardcore" is defined as: "We say that a block of bits of $x$ are simultaneously hard-core for a one-way function $f(x)$, if given $f(x)$ they cannot be ...
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5answers
2k views

Using one-way hash functions as the encryption method

Suppose two parties want to communicate securely with each other (Bob and Alice) using a simple messaging system in English. There are approximately 180,000 currently used words in the English ...
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2answers
140 views

One-way function and $EXP$

All examples of one-way functions I have see till now are closely related to the assumption that $NP\neq P $ (or even weaker ones, such as $UP\neq P$), but why not considering the theorem $P\neq EXP$? ...
2
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1answer
3k views

What is the meaning of “trapdoor” in cryptography?

I do not really understand the meaning of a "trapdoor" in cryptography, so here are my questions: What is the meaning of trapdoor and how can I convert a word or string using a trapdoor in ...
11
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4answers
910 views

Are there cryptographic hash functions that can be computed using only paper and pen without leaking any information about the plaintext?

I am looking for a cryptographic hash function that can be computed by a human using only paper and pen without ever leaking any information about the plaintext on the paper. The cryptographic hash ...
2
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0answers
80 views

partial-domain permutation and strong assumption

Quoting "Verified Security of Redundancy-Free Encryption from Rabin and RSA", Chapter 2 (on page 4): OAEP was proved IND-CCA-secure by Fujisaki et al. [28] under the assumption that the underlying ...
3
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2answers
238 views

Quadratic residuosity problem reduction to integer factorization

How can one show how to reduce the quadratic residuosity problem to an integer factorization?
1
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1answer
101 views

constructing QR-like one way function

I am wondering whether the following form is a one way function with collision resistance: $$ax^2+by^2 \mod p$$ where $a$ and $b$ are given, and $p$ is a prime number. Since the QR (quadratic ...
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1answer
282 views

modular exponentiation as a one-way-hash

As far as I can tell most one-way hashes apply some iterated encryption algorithm to the input data. What would be the issues with a one-way hash based on some fixed large prime p and a generator g ...
5
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2answers
288 views

Pen-and-paper one-way function for externally-anonymous survey

When conducting surveys, an Administrator might send an Enumerator to survey a Respondent. For "sensitive" questions (e.g. about embarrassing behavior), the Respondent may be fine with the truth being ...
0
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1answer
184 views

Weak One Way Function

Show The function $mult(a,b)$ is weak one way if the Integer Factorization Assumption is true. I am read the proof of this enunciated but I want know if I understand this in my way. The proof use the ...
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1answer
121 views

Pseudo Random Generator (PRG) from Rabin function

I'm trying to make a PRG using the Rabin function. The code (in Java) I wrote to implement the function is: ...
2
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3answers
406 views

Can one build a one-way function from AES?

We change the AES block cipher encryption: we delete the key schedule algorithm the user now provides a string of 1408 bits we divide the string to 11 sub keys, and use them directly in the ...
2
votes
1answer
375 views

Hash collision resistance requirements for Lamport signatures

According to the original paper, Lamport one-time signature scheme uses two one-way functions: $F$ and $G$. The former one, $F$, is used to create a public key by hashing elements of the private key ...
6
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5answers
4k views

Are there hash algorithms with variable length output?

I understand that for example MD5 produces a 128 bit hash value from a given text of variable size. My question is if there is a hash-like algorithm that will produce a hash value where one can ...