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Pythagoras0 (토론 | 기여)님의 2021년 9월 14일 (화) 20:11 판
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
- In this paper, we propose a new algorithm to solve another form of elliptic curve discrete logarithm problem with auxiliary inputs.[1]
- The computational problem is called elliptic curve discrete logarithm problem (ECDLP).[1]
- This is called as Elliptic Curve Discrete Logarithm Problem.[2]
- Even though, this approach reduces the complexity dramatically, elliptic curve cryptography is still too powerful and elliptic curve discrete logarithm problem is still hard.[2]
- This problem is called Elliptic Curve Discrete Logarithm Problem – or ECDLP for short.[3]
- Along this line, we show that the elliptic curve discrete logarithm problem can be reduced to three partial lifting problems.[4]
- 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.[4]
- Computing the private key from the public key in this kind of cryptosystem is called the elliptic curve discrete logarithm function.[5]
- The elliptic curve discrete logarithm is the hard problem underpinning elliptic curve cryptography.[5]
- We study the elliptic curve discrete logarithm problem over finite extension fields.[6]
- We continue our study on the elliptic curve discrete logarithm problem over finite extension fields.[7]
- The security of several elliptic curve cryptosystems is based on the difficulty to compute the discrete logarithm problem.[8]
- 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.[8]
- As an aside, Semaev’s choice of title “New algorithm for the discrete logarithm problem on elliptic curves” seems exaggerated.[9]
- The MOV attack reduces an elliptic curve discrete logarithm to a logarithm over a finite field using the Weil pairing.[10]
- The discrete logarithm problem in a finite field can be solved efficiently using Index Calculus.[10]
- 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.[11]
- 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.[12]
- rho() : the discrete logarithm operation, using Pollard's rho algorithm.[13]
- 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.[14]
소스
- ↑ 1.0 1.1 Research on Attacking a Special Elliptic Curve Discrete Logarithm Problem
- ↑ 2.0 2.1 Solving Elliptic Curve Discrete Logarithm Problem
- ↑ Elliptic curves: discrete logarithm problem
- ↑ 4.0 4.1 Partial Lifting and the Elliptic Curve Discrete Logarithm Problem
- ↑ 5.0 5.1 A (Relatively Easy To Understand) Primer on Elliptic Curve Cryptography
- ↑ On the discrete logarithm problem in elliptic curves
- ↑ Diem : On the discrete logarithm problem in elliptic curves II
- ↑ 8.0 8.1 Computation of the discrete logarithm on elliptic curves of trace one
- ↑ Elliptic curve discrete logarithm problem in characteristic two
- ↑ 10.0 10.1 The Discrete Logarithm Problem on Supersingular Elliptic Curves
- ↑ On Pollard's rho method for solving the elliptic curve discrete logarithm problem
- ↑ The height function and the elliptic curve discrete logarithm problem
- ↑ zhangyuesai/elliptic-curve: Pollard's rho algorithm for discrete logarithms on elliptic curves.
- ↑ Elliptic Curve Discrete Logarithm Problem (ECDLP) Research Papers