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On partial lifting and the elliptic curve discrete logarithm problem
 PROCEEDING OF THE 15TH ANNUAL INTERNATIONAL SYMPOSIUM ON ALGORITHMS AND COMPUTATION, 342–351, LNCS 3341
"... It has been suggested that a major obstacle in finding an index calculus attack on the elliptic curve discrete logarithm problem lies in the difficulty of lifting points from elliptic curves over finite fields to global fields. We explore the possibility of circumventing the problem of explicitly ..."
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It has been suggested that a major obstacle in finding an index calculus attack on the elliptic curve discrete logarithm problem lies in the difficulty of lifting points from elliptic curves over finite fields to global fields. We explore the possibility of circumventing the problem of explicitly
Elliptic Curve Discrete Logarithms and the Index Calculus
"... . The discrete logarithm problem forms the basis of numerous cryptographic systems. The most effective attack on the discrete logarithm problem in the multiplicative group of a finite field is via the index calculus, but no such method is known for elliptic curve discrete logarithms. Indeed, Miller ..."
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Cited by 28 (4 self)
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. The discrete logarithm problem forms the basis of numerous cryptographic systems. The most effective attack on the discrete logarithm problem in the multiplicative group of a finite field is via the index calculus, but no such method is known for elliptic curve discrete logarithms. Indeed, Miller
Computing Elliptic Curve Discrete Logarithms with the Negation Map
, 2011
"... It is clear that the negation map can be used to speed up the computation of elliptic curve discrete logarithms with the Pollard rho method. However, the random walks defined on elliptic curve points equivalence class {±P} used by Pollard rho will always get trapped in fruitless cycles. We propose ..."
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Cited by 2 (1 self)
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It is clear that the negation map can be used to speed up the computation of elliptic curve discrete logarithms with the Pollard rho method. However, the random walks defined on elliptic curve points equivalence class {±P} used by Pollard rho will always get trapped in fruitless cycles. We
a Special Elliptic Curve Discrete Logarithm Problem
"... Cheon first proposed a novel algorithm for solving discrete logarithm problem with auxiliary inputs. Given some points , , 2 , . . . , ∈ G, an attacker can solve the secret key efficiently. In this paper, we propose a new algorithm to solve another form of elliptic curve discrete logarithm problem ..."
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Cheon first proposed a novel algorithm for solving discrete logarithm problem with auxiliary inputs. Given some points , , 2 , . . . , ∈ G, an attacker can solve the secret key efficiently. In this paper, we propose a new algorithm to solve another form of elliptic curve discrete logarithm problem
Attacks on the Elliptic Curve Discrete Logarithm Problem
, 1999
"... Elliptic curve cryptosystems appear to be more secure and efficient while requiring a smaller key size to implement than other public key cryptosystems. Its security is based upon the difficulty of solving the Elliptic Curve Discrete Logarithm Problem (ECDLP). This thesis gives a survey of known att ..."
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Elliptic curve cryptosystems appear to be more secure and efficient while requiring a smaller key size to implement than other public key cryptosystems. Its security is based upon the difficulty of solving the Elliptic Curve Discrete Logarithm Problem (ECDLP). This thesis gives a survey of known
The Xedni Calculus And The Elliptic Curve Discrete Logarithm Problem
 Designs, Codes and Cryptography
, 1999
"... . Let E=Fp be an elliptic curve defined over a finite field, and let S ..."
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Cited by 22 (1 self)
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. Let E=Fp be an elliptic curve defined over a finite field, and let S
Remarks on Elliptic Curve Discrete Logarithm Problems
, 2000
"... This paper studies these algorithmsan in troduces the followin three results. First, we show an explicitconcit(0 unc which the MOV algorithmcan be applied ton(:3== ersinz64G elliptic curves. Next, by comparin the e#ectiventi of the MOV algorithm to that of the FR algorithm, it is explicitly shown th ..."
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Cited by 4 (1 self)
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This paper studies these algorithmsan in troduces the followin three results. First, we show an explicitconcit(0 unc which the MOV algorithmcan be applied ton(:3== ersinz64G elliptic curves. Next, by comparin the e#ectiventi of the MOV algorithm to that of the FR algorithm, it is explicitly shown
Elliptic Curve Discrete Logarithms and Wieferich Primes
, 2000
"... ... and Kim et. al. [11, 5]. The Xedni addresses a novel idea, but has two difficulties. One is to nd good liftings and the other is to compute the dependence relation among lifted rational points. In this paper, we propose a fast algorithm to compute the dependence relation for given two dependent ..."
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rational points of elliptic curve over Q. Using this, we show that we can solve the ECDLP very fast if we could nd a lifting of rank 1(the lifting problem). That is, we show ECDLP is equivalent to the lifting problem. Moreover, we investigate the possibility to get such liftings for elliptic curves with a
Results 1  10
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692