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95,328
Short signatures from the Weil pairing
, 2001
"... Abstract. We introduce a short signature scheme based on the Computational DiffieHellman assumption on certain elliptic and hyperelliptic curves. The signature length is half the size of a DSA signature for a similar level of security. Our short signature scheme is designed for systems where signa ..."
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Cited by 743 (28 self)
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Abstract. We introduce a short signature scheme based on the Computational DiffieHellman assumption on certain elliptic and hyperelliptic curves. The signature length is half the size of a DSA signature for a similar level of security. Our short signature scheme is designed for systems where
IdentityBased Encryption from the Weil Pairing
, 2001
"... We propose a fully functional identitybased encryption scheme (IBE). The scheme has chosen ciphertext security in the random oracle model assuming an elliptic curve variant of the computational DiffieHellman problem. Our system is based on bilinear maps between groups. The Weil pairing on elliptic ..."
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Cited by 1699 (29 self)
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We propose a fully functional identitybased encryption scheme (IBE). The scheme has chosen ciphertext security in the random oracle model assuming an elliptic curve variant of the computational DiffieHellman problem. Our system is based on bilinear maps between groups. The Weil pairing
Discrete Logarithms on Elliptic Curves
"... Abstract. Cryptographic protocols often make use of the inherent hardness of the classical discrete logarithm problem, which is to solve gx ≡ y (mod p) for x. The hardness of this problem has been exploited in the DiffieHellman key exchange, as well as in cryptosystems such as ElGamal. There is a s ..."
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similar discrete logarithm problem on elliptic curves: solve kB = P for k. Therefore, DiffieHellman and ElGamal have been adapted for elliptic curves. There is an abundance of evidence suggesting that elliptic curve cryptography is even more secure, which means that we can obtain the same security
The irreducibility of the space of curves of given genus
 Publ. Math. IHES
, 1969
"... Fix an algebraically closed field k. Let Mg be the moduli space of curves of genus g over k. The main result of this note is that Mg is irreducible for every k. Of course, whether or not M s is irreducible depends only on the characteristic of k. When the characteristic s o, we can assume that k ~ ..."
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Cited by 512 (2 self)
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Fix an algebraically closed field k. Let Mg be the moduli space of curves of genus g over k. The main result of this note is that Mg is irreducible for every k. Of course, whether or not M s is irreducible depends only on the characteristic of k. When the characteristic s o, we can assume that k
Solving Elliptic Curve Discrete Logarithm Problems Using Weil Descent
 JOURNAL OF THE RAMANUJAN MATHEMATICAL SOCIETY
, 2001
"... We provide the first cryptographically interesting instance of the elliptic curve discrete logarithm problem which resists all previously known attacks, but which can be solved with modest computer resources using the Weil descent attack methodology of Frey. We report on our implementation of index ..."
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Cited by 19 (3 self)
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We provide the first cryptographically interesting instance of the elliptic curve discrete logarithm problem which resists all previously known attacks, but which can be solved with modest computer resources using the Weil descent attack methodology of Frey. We report on our implementation of index
Discrete Logarithms and MordellWeil Groups
"... Let Ep be an elliptic curve over a prime finite field Fp, p ≥ 5, and Pp, Qp ∈ Ep(Fp). The elliptic curve discrete logarithm problem, ECDLP, on Ep is to find mp ∈ F × p such that Qp = mpPp if Qp ∈ 〈Pp〉. We propose an algorithm to attack the ECDLP relying on a Hasse principle detecting linear dependen ..."
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Let Ep be an elliptic curve over a prime finite field Fp, p ≥ 5, and Pp, Qp ∈ Ep(Fp). The elliptic curve discrete logarithm problem, ECDLP, on Ep is to find mp ∈ F × p such that Qp = mpPp if Qp ∈ 〈Pp〉. We propose an algorithm to attack the ECDLP relying on a Hasse principle detecting linear
Solving multiclass learning problems via errorcorrecting output codes
 JOURNAL OF ARTIFICIAL INTELLIGENCE RESEARCH
, 1995
"... Multiclass learning problems involve nding a de nition for an unknown function f(x) whose range is a discrete set containing k>2values (i.e., k \classes"). The de nition is acquired by studying collections of training examples of the form hx i;f(x i)i. Existing approaches to multiclass l ..."
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Cited by 730 (8 self)
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Multiclass learning problems involve nding a de nition for an unknown function f(x) whose range is a discrete set containing k>2values (i.e., k \classes"). The de nition is acquired by studying collections of training examples of the form hx i;f(x i)i. Existing approaches to multiclass
Semantic Similarity in a Taxonomy: An InformationBased Measure and its Application to Problems of Ambiguity in Natural Language
, 1999
"... This article presents a measure of semantic similarityinanisa taxonomy based on the notion of shared information content. Experimental evaluation against a benchmark set of human similarity judgments demonstrates that the measure performs better than the traditional edgecounting approach. The a ..."
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Cited by 601 (9 self)
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. The article presents algorithms that take advantage of taxonomic similarity in resolving syntactic and semantic ambiguity, along with experimental results demonstrating their e#ectiveness. 1. Introduction Evaluating semantic relatedness using network representations is a problem with a long history
Lower Bounds for Discrete Logarithms and Related Problems
, 1997
"... . This paper considers the computational complexity of the discrete logarithm and related problems in the context of "generic algorithms"that is, algorithms which do not exploit any special properties of the encodings of group elements, other than the property that each group element is ..."
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Cited by 279 (11 self)
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. This paper considers the computational complexity of the discrete logarithm and related problems in the context of "generic algorithms"that is, algorithms which do not exploit any special properties of the encodings of group elements, other than the property that each group element
KodairaSpencer theory of gravity and exact results for quantum string amplitudes
 Commun. Math. Phys
, 1994
"... We develop techniques to compute higher loop string amplitudes for twisted N = 2 theories with ĉ = 3 (i.e. the critical case). An important ingredient is the discovery of an anomaly at every genus in decoupling of BRST trivial states, captured to all orders by a master anomaly equation. In a particu ..."
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Cited by 545 (60 self)
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’ of holomorphic curves of higher genus curves in Calabi–Yau manifolds. It is shown that topological amplitudes can also be reinterpreted as computing corrections to superpotential terms appearing in the effective 4d theory resulting from compactification of standard 10d superstrings on the corresponding N = 2
Results 1  10
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