# Tagged Questions

Number theory is the study of the properties and construction of numbers, particularly integers. Prime numbers are of particular interest to number theorists and consequently cryptographers as they are considered the "building blocks" of numbers and produce many interesting results which are useful ...

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### Background for modular arithmetic function

I'm investigating this function: $a := ((b\cdot c) \bmod k) - (b \cdot c)/k$ where $/$ indicates integer division. Two things I've noticed: It's equivalent to multiplying a·b, and then ...
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### Basic explanation of Elliptic Curve Cryptography?

I have been studying Elliptic Curve Cryptography as part of a course based on the book Cryptography and Network Security. The text for provides an excellent theoretical definition of the algorithm but ...
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### How to practically find solutions to a discrete logarithm?

Are there any ongoing or current practical attempts to solve instances of the discrete logarithm problem of the order of magnitude used in cryptographic applications, for example with a 256 bit ...
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### What place do prime numbers have in cryptography?

My understanding of hashing and encryption is rather limited. I certainly do not understand the mathematical formulas at play in these algorithms. With that said, what part do prime numbers play in ...
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### What is the relation between RSA & Fermat's little theorem?

I came across this while refreshing my cryptography brain cells. From the RSA algorithm I understand that it somehow depends on the fact that, given a large number (A) it is computationally ...
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### Which algorithms are used to factorize large integers?

Even if RSA decided to cancel the Factoring Challenge, it seems that some teams keep working on it. According to Wikipedia, RSA-768 has been factored in late 2009. What are the current large integer ...
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### Are there security issues with discrete logarithm keys not being uniformly distributed?

Generally, algorithms based on discrete logarithm specify that private keys are chosen as scalars between 1 and the order of the group (denoted $q$ here). For instance IEEE P1363 and FIPS 186-3 both ...
### How robust is discrete logarithm in $GF(2^n)$?
"Normal" discrete logarithm based cryptosystems (DSA, Diffie-Hellman, ElGamal) work in the finite field of integers modulo a big prime $p$. However, there exist other finite fields out there, in ...