# Questions tagged [complexity]

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. time and/or space) needed to solve a certain computational problem. Cryptography can therefore be seen as the complexity theory's main field of use.

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### Could we build PSPACE-based cryptography - more secure post-quantum? [closed]

It seems not safe to exclude possibility of e.g. some next generation quantum computers being able to attack NP problems (e.g. 2WQC) - so maybe it is worth to start thinking of shifting the ...
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### Time Complexity Of Solving DLog When g and P are known

This (https://en.m.wikipedia.org/wiki/Discrete_logarithm) Wikipedia article confuses me. If you have the equation a = g^n (mod P), and g, P and a are all known, then how does a brute force solving for ...
1 vote
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### Comparing complexity of RSA decryption with/without CRT

(Cross-listed on math stackexchange, received no replies) For context, this is a homework question from an assignment already turned in. I am looking for better understanding of the concepts involved, ...
1 vote
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### Berlekamp–Massey input sequence length

For a given periodic sequence of length $N$ for which minimal polynomial is being constructed. Does the Berlekamp-Massey algorithm take the input of $2N$, i.e., the repeated input sequence or just the ...
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### Why Zero-Knowledge protocols are used for NP problems if IP is the class of interactive proof systems where they come from?

As stated in the title, I'm studying ZKPs and I see they are just interactive proof systems that respect the zero-knowledge property. Now, if that's true, why aren't they used for IP problems, the ...
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### Rabin-Miller primality test complexity

I was thinking about the complexity of the Rabin-Miller primality test. On wikipedia I find O(k log3n), but there is no explanation. My idea was too simple. To see if n is prime, we have k attempts ...
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### Which contemporary programming language is apt for implementation of algorithms in cryptography?

I am a researcher in cryptography. Most of the time I generally do theoretical/Mathematical work only and not doing the implementation part. I am not able to get the feel about the time complexity of ...
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### Does SHA-256 have (128-time + 128-space = 256-overall)-bit collision resistance?

First, we consider those hash functions that can actually provide 256-bit pre-image security, and not something like SHAKE128<l=256bits> where the sponge ...
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### Detailed running time analysis for Shamir secret sharing scheme

I am successfully working on Shamir's secret sharing scheme for few months. But the only issue I am facing is the calculation of theoretical time complexity. Since I am from algorithmic background, I ...
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### Complexity of Hash mining/signing

While reading about mining in crypto currency, I found that it requires some leading bits of a hash function output to be 0. This boils down to preimage resistance of the hash function, hence done ...
1 vote
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### Time complexity of a brute force attack on Shamir's Secret Sharing SSS

I have searched everywhere in academic papers about time complexity of a brute force attack on a Shamir's Secret Sharing key. I'm confused between if it is $O(p^k)$ or $O(p)$, such that $p$ is the ...
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### Why do Problems for Post-Quantum algorithms have to be NP-Hard?

The mathematical problems used for Post-Quantum Cryptography problems I came across, are NP-complete, e.g. Solving quadratic equations over finite fields short lattice vectors and close lattice ...
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### Cryptomania and NP $\cap$ co-NP

Cryptomania is usually presented as the Impagliazzo's world, which gives us public-key cryptography under the assumption that trapdoor OWFs exist. For purposes of constructing public-key cryptography ...
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### How efficiently can an attacker forge parts of a fingerprint?

If two devices do not trust each other yet, you can't simply send the correct fingerprint across: you have to manually verify it. I am looking into the security of comparing only random parts of a ...
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### How fast is hashing and is it always regarded as an O(1) operation? [closed]

I've wondered how hashing can be such a fast operation. It's so fast that nobody talks about it in terms of performance and complexity. I know that in terms of big O notation, you can drop all the ...
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### How to compare the time of encryption, cracking and verification elliptic curve problem in the same framework？

everyone! As a beginner, I would like to ask you a question. The best algorithm known for cracking (done by anonymous snooper) this problem （Discrete logarithm problem of elliptic curve or ECDSA）is ...
I want to find out how many bit operations are performed for encryption in AES-128 with messages size $128$ bits. For public key encryptions such as RSA and ElGamal, I know that number of bit ...
While discussing proving a language in $\Sigma_2$ from a client to a server with a friend we realized that while we know that such a language is provable in zero-knowledge, we didn't know whether it ...