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.

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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 ...
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Question About ECC Primitives (GnuPG)

In version 2.1, GnuPG featured primitives that use elliptic curves. For encryption, one option was ECDH, which confused me. I thought ECDH was for key agreement, not public key encryption. How does ...
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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,...
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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 = $2^{384} − 2^{128} − 2^{96} + 2^{32} − 1$ ...
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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 (...
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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 ...
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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 ...