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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88 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 ...
2
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0answers
47 views

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?
1
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1answer
289 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 ...
1
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0answers
59 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 ...
0
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1answer
62 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 ...
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81 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
79 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
33 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
votes
1answer
261 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
197 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?
2
votes
2answers
62 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 ...
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3answers
1k views

Lamport signature: How many signatures are needed to forge a signature?

Lamport signature: Signing the message Note that now Alice's private key is used and should never be used again. The other 256 random numbers that she did not use for the signature she must never ...
0
votes
1answer
64 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 ⊕ ...
3
votes
2answers
393 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} ...
11
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4answers
942 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 ...
0
votes
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
votes
1answer
381 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 ...
2
votes
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 ...
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 ...
2
votes
1answer
242 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 ...
0
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2answers
72 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
votes
1answer
314 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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2answers
190 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?
2
votes
1answer
164 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 ...
3
votes
1answer
270 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
votes
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 ...
1
vote
1answer
132 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 ...
3
votes
2answers
405 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 ...
4
votes
1answer
187 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 ...
6
votes
3answers
449 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 $K$, ...
9
votes
3answers
257 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 ...
2
votes
2answers
356 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
votes
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) ...
3
votes
1answer
262 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
0answers
83 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 ...
4
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1answer
164 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
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 ...
2
votes
3answers
407 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
331 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 ...
1
vote
1answer
186 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
votes
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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2answers
142 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 $P\neq EXP$? ...
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5answers
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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 ...
3
votes
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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1answer
123 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: ...
3
votes
2answers
242 views

Quadratic residuosity problem reduction to integer factorization

How can one show how to reduce the quadratic residuosity problem to an integer factorization?
1
vote
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 ...
5
votes
2answers
293 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 ...