Linked Questions

25 votes
4 answers

Arguments for existence of one-way functions

I have read in several papers that the existence of one-way functions is widely believed. Can someone shed light on why this is the case? What arguments do we have for supporting the existence of one-...
Anonymous's user avatar
  • 4,041
17 votes
0 answers

Deeper look at Algorithmica?

Russell Impagliazzo published "A Personal View of Average-Case Complexity" (preprint) back in 1995. He presented five possible worlds we could be living in, depending on how P and NP were related. The ...
András Salamon's user avatar
16 votes
1 answer

Password hashing using NP complete problems

Commonly used password hashing algorithms work like this today: Salt the password and feed it into a KDF. For example, using PBKDF2-HMAC-SHA1, the password hashing process is ...
Cyker's user avatar
  • 779
16 votes
3 answers

Are there any classes of functions which require provably different resources to compute versus computing their inverse?

Apologies in advance if this question is too simple. Basically, what I want to know is if there are any functions $f(x)$ with the following properties: Take $f_n(x)$ to be $f(x)$ when the domain and ...
Joe Fitzsimons's user avatar
13 votes
3 answers

Why do computer scientists on the whole work under the assumption that P ≠ NP?

Coming from a math background, it seems interesting to me that on the whole computer scientists tend to work under the assumption that $P \neq NP$. While there is no proof either way, generally, ...
Eli Sadoff's user avatar
11 votes
5 answers

Complexity Classes for Cases Other Than "Worst Case"

Do we have complexity classes with respect to, say, average-case complexity? For instance, is there a (named) complexity class for problems which take expected polynomial time to decide? Another ...
Sadeq Dousti's user avatar
  • 16.5k
10 votes
1 answer

Worlds Relative to Which "Invulnerable Generators" Do Not Exist

Invulnerable generators are defined as follows: Let $R$ be an NP relation, and $M$ be a machine which accepts $L(R)$. Informally, a program is an invulnerable generator if, on input $1^n$, it produces ...
Sadeq Dousti's user avatar
  • 16.5k
8 votes
3 answers

Candidates for One-Way Function

Why are the candidates for one-way functions so few? Today, almost all candidates are based on elementary mathematics, except Goldreich's candidate 2000 and ... (?!). Why one can not generate ...
Arash Ahadi's user avatar
8 votes
0 answers

A generalisation of one-wayness

$\mathbf{NP}$-complete problems are worst-case hard. Their average-case counterpart are one-way functions. Is there an analogous one-wayness notion for $\mathbf{coNP}$-complete problems? More ...
Pooya Farshim's user avatar
7 votes
2 answers

P vs. NP and Pseudorandom Bit Generators

According to an article on pseudorandom number generators (PRNG) by Jeff Lagarias, he states that trying to prove that a PRNG is unpredictable (secure) is just "as hard" as trying to prove ...
user avatar
7 votes
1 answer

Public-key encryption without the assumption that $P \neq NP$

I'm not talking about the RSA, El-gamal, nor any specific encryption scheme. Rather, my question, as related to this and this threads, is why the idea of Public-Key encryption scheme cannot be secure ...
Bush's user avatar
  • 241