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Results 1 - 10
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4,283
On the construction of prime order elliptic curves
- Progress in cryptology—INDOCRYPT 2003, Springer Lecture Notes in Computer Science
"... Abstract. We consider a variant of the Complex Multiplication (CM) method for constructing elliptic curves (ECs) of prime order with additional security properties. Our variant uses Weber polynomials whose discriminant D is congruent to 3 (mod 8), and is based on a new transformation for converting ..."
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Cited by 5 (1 self)
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Abstract. We consider a variant of the Complex Multiplication (CM) method for constructing elliptic curves (ECs) of prime order with additional security properties. Our variant uses Weber polynomials whose discriminant D is congruent to 3 (mod 8), and is based on a new transformation for converting
Pairing-friendly elliptic curves of prime order
- IN SELECTED AREAS IN CRYPTOGRAPHY – SAC 2005
, 2006
"... Previously known techniques to construct pairing-friendly curves of prime or near-prime order are restricted to embedding degree k � 6. More general methods produce curves over Fp where the bit length of p is often twice as large as that of the order r of the subgroup with embedding degree k; the b ..."
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Cited by 217 (13 self)
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; the best published results achieve ρ ≡ log(p) / log(r) ∼ 5/4. In this paper we make the first step towards surpassing these limitations by describing a method to construct elliptic curves of prime order and embedding degree k = 12. The new curves lead to very efficient implementation: non
Axiomatic quantum field theory in curved spacetime
, 2008
"... The usual formulations of quantum field theory in Minkowski spacetime make crucial use of features—such as Poincare invariance and the existence of a preferred vacuum state—that are very special to Minkowski spacetime. In order to generalize the formulation of quantum field theory to arbitrary globa ..."
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Cited by 689 (18 self)
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and covariantly constructed from the spacetime metric), a microlocal spectrum condition, an "associativity" condition, and the requirement that the coefficient of the identity in the OPE of the product of a field with its adjoint have positive scaling degree. We prove curved spacetime versions
The Contourlet Transform: An Efficient Directional Multiresolution Image Representation
- IEEE TRANSACTIONS ON IMAGE PROCESSING
"... The limitations of commonly used separable extensions of one-dimensional transforms, such as the Fourier and wavelet transforms, in capturing the geometry of image edges are well known. In this paper, we pursue a “true” two-dimensional transform that can capture the intrinsic geometrical structure t ..."
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Cited by 513 (20 self)
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-domain construction and then studies its convergence to an expansion in the continuous domain. Specifically, we construct a discrete-domain multiresolution and multidirection expansion using non-separable filter banks, in much the same way that wavelets were derived from filter banks. This construction results in a
Generating Prime Order Elliptic Curves: Difficulties and Efficiency
- Considerations, in International Conference on Information Security and Cryptology – ICISC 2004, Lecture Notes in Computer Science
, 2005
"... Abstract. We consider the generation of prime order elliptic curves (ECs) over a prime field Fp using the Complex Multiplication (CM) method. A crucial step of this method is to compute the roots of a special type of class field polynomials with the most commonly used being the Hilbert and Weber one ..."
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Cited by 4 (4 self)
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Abstract. We consider the generation of prime order elliptic curves (ECs) over a prime field Fp using the Complex Multiplication (CM) method. A crucial step of this method is to compute the roots of a special type of class field polynomials with the most commonly used being the Hilbert and Weber
On the Efficient Generation of Prime-Order Elliptic Curves∗
, 2009
"... Abstract. We consider the generation of prime-order elliptic curves (ECs) over a prime field Fp using the Complex Multiplication (CM) method. A crucial step of this method is to compute the roots of a special type of class field polynomials with the most commonly used being the Hilbert and Weber one ..."
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ones. These polynomials are uniquely determined by the CM discriminant D. In this paper, we consider a variant of the CM method for constructing elliptic curves (ECs) of prime order using Weber polynomials. In attempting to construct prime-order ECs using Weber polynomials, two difficulties arise (in
Selecting Cryptographic Key Sizes
- TO APPEAR IN THE JOURNAL OF CRYPTOLOGY, SPRINGER-VERLAG
, 2001
"... In this article we offer guidelines for the determination of key sizes for symmetric cryptosystems, RSA, and discrete logarithm based cryptosystems both over finite fields and over groups of elliptic curves over prime fields. Our recommendations are based on a set of explicitly formulated parameter ..."
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Cited by 323 (8 self)
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In this article we offer guidelines for the determination of key sizes for symmetric cryptosystems, RSA, and discrete logarithm based cryptosystems both over finite fields and over groups of elliptic curves over prime fields. Our recommendations are based on a set of explicitly formulated
A taxonomy of pairing-friendly elliptic curves
, 2006
"... Elliptic curves with small embedding degree and large prime-order subgroup are key ingredients for implementing pairingbased cryptographic systems. Such “pairing-friendly” curves are rare and thus require specific constructions. In this paper we give a single coherent framework that encompasses all ..."
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Cited by 111 (11 self)
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Elliptic curves with small embedding degree and large prime-order subgroup are key ingredients for implementing pairingbased cryptographic systems. Such “pairing-friendly” curves are rare and thus require specific constructions. In this paper we give a single coherent framework that encompasses
Generating Elliptic Curves of Prime Order
- in Cryptographic Hardware and Embedded Systems – CHES 2001, LNCS
, 2001
"... Abstract. Avariation of the Complex Multiplication (CM) method for generating elliptic curves of known order over finite fields is proposed. We give heuristics and timing statistics in the mildly restricted setting of prime curve order. These may be seen to corroborate earlier work of Koblitz in the ..."
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Cited by 6 (0 self)
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Abstract. Avariation of the Complex Multiplication (CM) method for generating elliptic curves of known order over finite fields is proposed. We give heuristics and timing statistics in the mildly restricted setting of prime curve order. These may be seen to corroborate earlier work of Koblitz
Results 1 - 10
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4,283
