11 questions linked to/from Status of Impagliazzo's Worlds?
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### 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 ...
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### 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-...
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### 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 ...
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### 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, ...
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### 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 ...
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### 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 ...
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### 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 ...
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### 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 ...
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### 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 ...
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$\mathbf{NP}$-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 ...