Questions tagged [computational-complexity-theory]

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How to estimate the maximum computational cost bound for Key Derivation Functions (KDFs) before it becomes useless security-wise?

From my understanding of Key Derivation Functions (KDFs), e.g. scrypt, Argon2, etc, we can tune their parameters such that it eventually becomes harder for an attacker to brute force a password-to-key ...
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How to prove simultaneous security for the Rabin's function

Let $p,q$ be odd primes, $n:=pq$ and $a,x \in \mathbb{Z}/n\mathbb{Z}$ be quadratic residues such that $x^2 \equiv a \pmod n$. I have understood the proof that calculating the least significant bit of $...
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Has anyone implemented a public-key encryption scheme using a universal one-way function?

There exists a function $f$ such that if one-way functions exist then $f$ is a one-way function. Such a function is called a universal one-way function. Now the public-key encryption schemes that I’...
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Complexity of Gaussian Elimination over a Finite Field

I read somewhere that the complexity of solving a Linear $n\times n$ system over a Finite Field $\Bbb F_q$ using Gaussian Elimination is $\mathcal{O}(n^3)$ operations in $\Bbb F_q$. What's the role of ...
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(updated) Utilizing a non-computable function to create a one-way function

Why can't uncomputable functions be adapted to serve as theoretically perfect one-way functions? This has been bugging me for years, and I've never been able to track down an explanation of why it ...
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Meaning of “Security can be reduced to a problem”

I'm studying reductions in cryptography and confused about the way people use the word "reduction". My question is almost the same as a past question, but what I want to ask is slightly different. A ...
161
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Why is elliptic curve cryptography not widely used, compared to RSA?

I recently ran across elliptic curve crypto-systems: An Introduction to the Theory of Elliptic Curves (Brown University) Elliptic Curve Cryptography (Wikipedia) Performance analysis of identity ...