Results 1  10
of
26,024
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 ..."
Abstract

Cited by 743 (28 self)
 Add to MetaCart
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
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 ~ ..."
Abstract

Cited by 512 (2 self)
 Add to MetaCart
is to construct families of curves X, some singular, with pa(X)=g, over nonsingular parameter spaces, which in some sense contain enough singular curves to link together any two components that Mg might have. The essential thing that makes this method work now is a recent " stable reduction theorem "
Speeding up pairing computations on genus 2 hyperelliptic curves with efficiently computable automorphisms, Pairing 2008
 LNCS
, 2008
"... Abstract. Pairings on the Jacobians of (hyper)elliptic curves have received considerable attention not only as a tool to attack curve based cryptosystems but also as a building block for constructing cryptographic schemes with new and novel properties. Motivated by the work of Scott [34], we invest ..."
Abstract

Cited by 1 (0 self)
 Add to MetaCart
investigate how to use efficiently computable automorphisms to speed up pairing computations on two families of nonsupersingular genus 2 hyperelliptic curves over prime fields. Our findings lead to new variants of Miller’s algorithm in which the length of the main loop can be up to 4 times shorter than
Ate Pairing on Hyperelliptic Curves
 ADVANCES IN CRYPTOLOGY  EUROCRYPT 2007, SPRINGERVERLAG LNCS 4515
, 2007
"... In this paper we show that the Ate pairing, originally defined for elliptic curves, generalises to hyperelliptic curves and in fact to arbitrary algebraic curves. It has the following surprising properties: The loop length in Miller’s algorithm can be up to g times shorter than for the Tate pairin ..."
Abstract

Cited by 16 (3 self)
 Add to MetaCart
In this paper we show that the Ate pairing, originally defined for elliptic curves, generalises to hyperelliptic curves and in fact to arbitrary algebraic curves. It has the following surprising properties: The loop length in Miller’s algorithm can be up to g times shorter than for the Tate
Improved Weil and Tate pairings for elliptic and hyperelliptic curves
, 2003
"... We present algorithms for computing the squared Weil and Tate pairings on an elliptic curve and the squared Tate pairing for hyperelliptic curves. The squared pairings introduced in this paper have the advantage that our algorithms for evaluating them are deterministic and do not depend on a random ..."
Abstract

Cited by 8 (3 self)
 Add to MetaCart
We present algorithms for computing the squared Weil and Tate pairings on an elliptic curve and the squared Tate pairing for hyperelliptic curves. The squared pairings introduced in this paper have the advantage that our algorithms for evaluating them are deterministic and do not depend on a
PAIRINGS ON HYPERELLIPTIC CURVES
, 2009
"... We assemble and reorganize the recent work in the area of hyperelliptic pairings: We survey the research on constructing hyperelliptic curves suitable for pairingbased cryptography. We also showcase the hyperelliptic pairings proposed to date, and develop a unifying framework. We discuss the techni ..."
Abstract

Cited by 1 (0 self)
 Add to MetaCart
We assemble and reorganize the recent work in the area of hyperelliptic pairings: We survey the research on constructing hyperelliptic curves suitable for pairingbased cryptography. We also showcase the hyperelliptic pairings proposed to date, and develop a unifying framework. We discuss
Ate Pairing on Hyperelliptic Curves
"... In this paper we show that the Ate pairing, originally defined for elliptic curves, generalises to hyperelliptic curves and in fact to arbitrary algebraic curves. It has the following surprising properties: The loop length in Miller’s algorithm can be up to g times shorter than for the Tate pairing, ..."
Abstract
 Add to MetaCart
In this paper we show that the Ate pairing, originally defined for elliptic curves, generalises to hyperelliptic curves and in fact to arbitrary algebraic curves. It has the following surprising properties: The loop length in Miller’s algorithm can be up to g times shorter than for the Tate pairing
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 ..."
Abstract

Cited by 545 (60 self)
 Add to MetaCart
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
CONSTRUCTING PAIRINGFRIENDLY HYPERELLIPTIC CURVES USING WEIL RESTRICTION
"... Abstract. A pairingfriendly curve is a curve over a finite field whose Jacobian has small embedding degree with respect to a large primeorder subgroup. In this paper we construct pairingfriendly genus 2 curves over finite fields Fq whose Jacobians are ordinary and simple, but not absolutely simpl ..."
Abstract

Cited by 9 (0 self)
 Add to MetaCart
Abstract. A pairingfriendly curve is a curve over a finite field whose Jacobian has small embedding degree with respect to a large primeorder subgroup. In this paper we construct pairingfriendly genus 2 curves over finite fields Fq whose Jacobians are ordinary and simple, but not absolutely
Hyperelliptic pairings
 IN PAIRING 2007
, 2007
"... We survey recent research on pairings on hyperelliptic curves and present a comparison of the performance characteristics of pairings on elliptic curves and hyperelliptic curves. Our analysis indicates that hyperelliptic curves are not more efficient than elliptic curves for general pairing applicat ..."
Abstract

Cited by 7 (3 self)
 Add to MetaCart
We survey recent research on pairings on hyperelliptic curves and present a comparison of the performance characteristics of pairings on elliptic curves and hyperelliptic curves. Our analysis indicates that hyperelliptic curves are not more efficient than elliptic curves for general pairing
Results 1  10
of
26,024