1
vote
1answer
364 views

ECC - Point Addition/Point Multiplication

So I have a very beginner-esque knowledge of ECDSA and I'm trying to write something in python to take a private key and output the public key (Basically from what I understand just trying to do the ...
1
vote
0answers
91 views

$\phi$ function in Dual_EC_DRBG

I am trying to understand the operation of the Dual_EC_DRBG. I'm reading the formal specification (SP 800-90) and can't seem to find a definition of the $\phi$ function used throughout the definition ...
1
vote
0answers
298 views

Understanding elliptic curve encryption

I'm having a hard time understanding the elliptic curve encryption. One thing thing I don't understand is listing all the points on the curve (mod p). Suppose I have the following elliptic curve: y^2 ...
1
vote
3answers
185 views

Which area of Maths should I pursue?

I would like to know which area of Mathematics would be most beneficial to cryptography. Surely Algebraic Number Theory and maybe to a lesser extend, Elliptic Curves, are closely linked to ...
2
votes
1answer
129 views

Discrete log analog of ECM factoring algorithm?

Anecdotally, most factoring algorithms have a corresponding variant algorithm that can be used to attack the discrete log problem using similar ideas. Is there an analog of the elliptic curve (ECM) ...
3
votes
1answer
176 views

Impact of algorithms for factoring using elliptic curves over $\mathbb{Q}$

Recently a few papers have appeared that describe a new approach to factoring, using elliptic curves over $\mathbb{Q}$. See, e.g., Factoring integers and computing elliptic curve rational points, ...
18
votes
4answers
10k views

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 ...
6
votes
1answer
176 views

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 ...