# Tagged Questions

Complexity describes - in simple words - how hard (complex) it is to reach a specific goal; and under which conditions. In cryptography, this mostly ends up in using the complexity theory to analyze things. One of the main goals of complexity theory is to prove lower bounds on the resources (e.g. ...

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### McEliece Public Key Encryption

The definition of Public Key Encryption(PKE) say that: A PKE scheme is a triple of probabilistic polynomial time algorithm (PPT) (Gen,Enc,Dec). The definition of PPT say: In complexity ...
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### How to develop a public key cryptosystem based on a hard problem?

Recently, I found a function that is performed on a sequence to return another sequence. All known algorithms for finding the input, given the output are of exponential complexity. I want to propose ...
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### Why does Merkle's Puzzle requires Eve quadratic complexity of effort to break the system?

The way Applied cryptography 2ED explains the puzzle is as follows (I paraphrase it): Bob generates 2^20 messages of the form x,y where ...
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### Complexity class of an idealised version of Bitcoin's proof-of-work (hashcash)? [closed]

To formulate this question precisely, I will define an idealized hypothetical "perfect" hash function $H(n)$ which has nice scalability properties, and will formulate a problem PERFECT HASHCASH in ...
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### Formal definition of “explicit” algorithm?

A long time ago, I read that the definition of "cryptographic hash function" is "collision-resistant one-way function". (A similar definition shows up in the FIPS standards for SHA-1 etc.) But this ...
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### 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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### Discrete log problem, when we have many examples

Suppose I have many instances of the discrete log problem, all using the same unknown exponent. Is this problem easier than the standard discrete log problem? Oh, heck, I should be more precise. ...
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### What is the time complexity of the RC4 encryption & decryption algorithms?

I'm trying to figure out what the time complexity of RC4 encryption & decryption algorithms is, in big-O-notation.
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### Complexity of ECB and OFB

What is the complexity of ECB in terms of Time and Memory? and also in OFB? I can't find it in the internet, so I decided to ask it in here.
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### Are asymptotic lower bounds relevant to cryptography?

An asymptotic lower bound such as exponential-hardness is generally thought to imply that a problem is "inherently difficult". Encryption that is "inherently difficult" to break is thought to be ...
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### Big-O Notation: Encryption Algorithms

I am currently completing a dissertation concerning the encryption of data through a variety of cryptographic algorithms. I have spent much time reading journals and papers but as yet have been ...
I am wondering what the complexities are of adding/subtracting and muliplying/dividing numbers in a finite field $\mathbb{F}_q$. I need it to understand an article I am reading. Thank you