Questions tagged [elliptic-curves]

Elliptic curves are algebraic-geometric structures with applications in cryptography. Such a curve consists of the set of solutions to a cubic equation over a finite field equipped with a group operation. Questions relating to elliptic curves and derived algorithms should use this tag and might also consider more specific tags such as discrete-logarithm and ecdsa.

158 questions with no upvoted or accepted answers
Filter by
Sorted by
Tagged with
0
votes
0answers
182 views

Is there any patent free EC point compression available? If not, should I GPL/LGPL my code?

I'm currently using the BouncyCastle implementation in uncompressed mode, and considering releasing an optimized version of EC code that uses point compression. It appears the only thing limiting me ...
0
votes
0answers
183 views

processing time for multiplication and exponentiation in pairing base cryptography

I'm using the Boneh-Boyen-Shacham signature scheme and want to estimate complexity in my scheme. As reported in "Scott M., Efficient Implementation of Cryptographic pairings", if we set parameters ...
0
votes
0answers
363 views

Polynomial Inversion over Galois Field

Hello guys I am looking to calculate the Inverse of a given polynomial in Galois field I have found the little Fermat's algorithm and the Itoh-Tsujii I am getting a bit confused with both algorithm ...
-1
votes
1answer
340 views

Elliptic curve discrete logarithm problem and mini example

Consider the group E23(9,17), this the group defined by the equation y2 mod 23 = x3 + 9x + 17 mod 23. What is the discrete logarithm k of Q = (4,5) to the base P = (16,5)? the solution is: 2P = (20,...
-1
votes
1answer
59 views

Simple hexadecimal to 2s complement question

From 2.5.1 in this paper, how is $p$ = FFFFFFFF FFFFFFFF FFFFFFFF FFFFFFFF FFFFFFFF FFFFFFFF FFFFFFFF FFFFFFFE FFFFFFFF 00000000 00000000 FFFFFFFF = $2^{384} − 2^{128} − 2^{96} + 2^{32} − 1$ ...
-1
votes
2answers
96 views

Table of Curve Paramters

I'm studying Elliptic Cruve Cryptograhpy. When I do a search on Google of ECC, I find some pdf where I see these curve's paramters: $q, h, r, exp1, exp2$. What are these parameters ? Are there tables (...
-2
votes
1answer
137 views

Can an elliptic curve have the form y^2 ≡ x^2 + 2x + 2 mod 17?

I'm new to cryptography and the associated level of maths. I'm practising past papers for an exam and found the question: Show that the condition 4a^3 + 27b^2 ≠ 0 mod p is fulfilled for the ...
-2
votes
1answer
89 views

if ABE scheme based on RSA generate constant secret key will get better resutls than schemes based on Elliptic curve?

We know in term of security level, ECC key is stronger than RSA , 160 bit ECC equivalent to 1024 bit key in RSA. If I can generate constant secret key based on RSA is that mean my scheme performance ...