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개요

• Given an elliptic curve \(E\) defined over a finite field and two points \(P, Q \in E\), find an integer \(x\) such that \(Q=x P\).

노트

말뭉치

1. In this paper, we propose a new algorithm to solve another form of elliptic curve discrete logarithm problem with auxiliary inputs.
2. The computational problem is called elliptic curve discrete logarithm problem (ECDLP).
3. This is called as Elliptic Curve Discrete Logarithm Problem.
4. Even though, this approach reduces the complexity dramatically, elliptic curve cryptography is still too powerful and elliptic curve discrete logarithm problem is still hard.
5. This problem is called Elliptic Curve Discrete Logarithm Problem – or ECDLP for short.
6. Along this line, we show that the elliptic curve discrete logarithm problem can be reduced to three partial lifting problems.
7. Should the elliptic curve discrete logarithm problem admit no subexponential time attack, then our results suggest that gaining partial information about lifting would be at least as hard.
8. Computing the private key from the public key in this kind of cryptosystem is called the elliptic curve discrete logarithm function.
9. The elliptic curve discrete logarithm is the hard problem underpinning elliptic curve cryptography.
10. We study the elliptic curve discrete logarithm problem over finite extension fields.
11. We continue our study on the elliptic curve discrete logarithm problem over finite extension fields.
12. The security of several elliptic curve cryptosystems is based on the difficulty to compute the discrete logarithm problem.
13. The motivation of using elliptic curves in cryptography is that there is no known sub-exponential algorithm which solves the Elliptic Curve Discrete Logarithm Problem (ECDLP) in general.
14. As an aside, Semaev’s choice of title “New algorithm for the discrete logarithm problem on elliptic curves” seems exaggerated.
15. The MOV attack reduces an elliptic curve discrete logarithm to a logarithm over a finite field using the Weil pairing.
16. The discrete logarithm problem in a finite field can be solved efficiently using Index Calculus.
17. Cryptosystems based on elliptic curves are in wide-spread use, they are considered secure because of the difficulty to solve the elliptic curve discrete logarithm problem.
18. From the inception of elliptic curve cryptography it has been suggested that the height function on elliptic curves provides a barrier to solving the elliptic curve discrete logarithm problem.
19. rho() : the discrete logarithm operation, using Pollard's rho algorithm.
20. This paper introduces a new proxy signcryption scheme based on the Discrete Logarithm Problem (DLP) with a reduced computational complexity compared to other schemes in literature.