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247
The Quadratic Extension Extractor for (Hyper)elliptic Curves
 in Odd Characteristic, Lecture Notes In Computer Science
"... Abstract. We propose a simple and efficient deterministic extractor for the (hyper)elliptic curve C, defined over F q 2 , where q is some power of an odd prime. Our extractor, for a given point P on C, outputs the first Fqcoefficient of the abscissa of the point P . We show that if a point P is ch ..."
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Cited by 1 (0 self)
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Abstract. We propose a simple and efficient deterministic extractor for the (hyper)elliptic curve C, defined over F q 2 , where q is some power of an odd prime. Our extractor, for a given point P on C, outputs the first Fqcoefficient of the abscissa of the point P . We show that if a point P
Design of Hyper Elliptic Curve System Digital Signature in Identity Authentication
"... Aiming at characteristics of rigorous identity authentication for both two trading parties in network transactions and based on analysis and study on Hyper Elliptic Curve (HEC) and ElGamal based on discrete logarithm problem, these two approaches were combined organically to design a digital signatu ..."
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Aiming at characteristics of rigorous identity authentication for both two trading parties in network transactions and based on analysis and study on Hyper Elliptic Curve (HEC) and ElGamal based on discrete logarithm problem, these two approaches were combined organically to design a digital
A Secured Cloud System using Hyper Elliptic Curve Cryptography
"... Abstract — Secure and efficient data storage is needed in the cloud environment in modern era of information technology industry. In the present scenario the cloud verifies the authenticity of the cloud services without the knowledge of user’s identity. The cloud provides massive data access directl ..."
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is enhanced through cryptography technique applied to the cloud security to avoid vulnerability. The intractable computability is achieved in the cloud by using the public key cryptosystem. This paper proposed the approach of applying Hyper elliptic curve cryptography for data protection in the cloud
Lowlying zeros of quadratic Dirichlet lfunctions, hyperelliptic curves and random matrix theory
, 2012
"... ..."
Short signatures from the Weil pairing
, 2001
"... 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 signatures ar ..."
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Cited by 755 (25 self)
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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 signatures
Speeding Up the Discrete Log Computation on Curves With Automorphisms
, 1999
"... We show how to speed up the discrete log computations on curves having automorphisms of large order, thus generalizing the attacks on ABC elliptic curves. This includes the first known attack on CM (hyper)elliptic curves, as well as most of the hyperelliptic curves described in the literature. ..."
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Cited by 37 (2 self)
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We show how to speed up the discrete log computations on curves having automorphisms of large order, thus generalizing the attacks on ABC elliptic curves. This includes the first known attack on CM (hyper)elliptic curves, as well as most of the hyperelliptic curves described in the literature.
Invalidcurve attacks on hyperelliptic curve cryptosystems’, Adv
 Math. of Comm
"... Abstract. We extend the notion of an invalidcurve attack from elliptic curves to genus 2 hyperelliptic curves. We also show that invalid singular (hyper)elliptic curves can be used in mounting invalidcurve attacks on (hyper)elliptic curve cryptosystems, and make quantitative estimates of the prac ..."
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Cited by 1 (0 self)
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Abstract. We extend the notion of an invalidcurve attack from elliptic curves to genus 2 hyperelliptic curves. We also show that invalid singular (hyper)elliptic curves can be used in mounting invalidcurve attacks on (hyper)elliptic curve cryptosystems, and make quantitative estimates
Hyperelliptic curves over F2 of every 2rank without extra automorphisms
 PROC. AMER. MATH. SOC
, 2006
"... We prove that for any pair of integers 0 ≤ r ≤ g such that g ≥ 3 or r> 0, there exists a (hyper)elliptic curve C over F2 of genus g and 2rank r whose automorphism group consists of only identity and the (hyper)elliptic involution. As an application, we prove the existence of principally polariz ..."
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Cited by 9 (1 self)
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We prove that for any pair of integers 0 ≤ r ≤ g such that g ≥ 3 or r> 0, there exists a (hyper)elliptic curve C over F2 of genus g and 2rank r whose automorphism group consists of only identity and the (hyper)elliptic involution. As an application, we prove the existence of principally
An Improved Bound for the Dimension of Subfield Subcodes
, 1997
"... this paper, we give a new lower bound for the dimension of subfield subcodes. This bound improves the lower bound given by Stichtenoth. A BCH code and a subfield subcode of algebraic geometric code on a hyper elliptic curve are discussed as special cases. ..."
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this paper, we give a new lower bound for the dimension of subfield subcodes. This bound improves the lower bound given by Stichtenoth. A BCH code and a subfield subcode of algebraic geometric code on a hyper elliptic curve are discussed as special cases.
Classi cation of genus 2 curves over F2n and optimization of their arithmetic
"... To obtain ecient cryptosystems based on hyperelliptic curves, we studied genus 2 isomorphism classes of hyperelliptic curves in characteristic 2. We found general and optimal form for these curves, just as the short Weierstrass form for elliptic curves. We studied the security and the arithmetic on ..."
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on their jacobian. We also rewrote and optimized the formulas of Lange in characteristic 2, and we introduced a new system of coordinate. Therefore, we deduced the best form of hyperelliptic curves of genus 2 in characteristic 2 to use in cryptography. Key words. hyperelliptic curve cryptography, genus 2
Results 1  10
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