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The Decisional DiffieHellman Problem and the Uniform Boundedness Theorem ∗
, 2003
"... In this paper, we propose an algorithm to solve the Decisional DiffieHellman problem over finite fields, whose time complexity depends on the effective bound in the Uniform Boundedness Theorem (UBT). We show that curves which are defined over a number field of small degree but have a large torsion ..."
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In this paper, we propose an algorithm to solve the Decisional DiffieHellman problem over finite fields, whose time complexity depends on the effective bound in the Uniform Boundedness Theorem (UBT). We show that curves which are defined over a number field of small degree but have a large torsion
On the Decisional DiffieHellman Problem in genus 2
"... Memòria presentada per optar al grau de Doctor en Matemàtiques. Barcelona, juliol de 2006. Directors: Dra. Paz Morillo, Dr. Steven GalbraithResum En aquesta tesi tractem el problema Decisional de DiffieHellman en el grup de punts de la varietat Jacobiana de corbes supersingulars de gènere dos sobre ..."
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Memòria presentada per optar al grau de Doctor en Matemàtiques. Barcelona, juliol de 2006. Directors: Dra. Paz Morillo, Dr. Steven GalbraithResum En aquesta tesi tractem el problema Decisional de DiffieHellman en el grup de punts de la varietat Jacobiana de corbes supersingulars de gènere dos
http://www.rhul.ac.uk/mathematics/techreports On the Decisional DiffieHellman Problem
, 2009
"... Memòria presentada per optar al grau de Doctor en Matemàtiques. Barcelona, juliol de 2006. Directors: Dra. Paz Morillo, Dr. Steven GalbraithResum En aquesta tesi tractem el problema Decisional de DiffieHellman en el grup de punts de la varietat Jacobiana de corbes supersingulars de gènere dos sobre ..."
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Memòria presentada per optar al grau de Doctor en Matemàtiques. Barcelona, juliol de 2006. Directors: Dra. Paz Morillo, Dr. Steven GalbraithResum En aquesta tesi tractem el problema Decisional de DiffieHellman en el grup de punts de la varietat Jacobiana de corbes supersingulars de gènere dos
Variations of diffiehellman problem
 In ICICS ’03, volume 2836 of LNCS
, 2003
"... Abstract. This paper studies various computational and decisional DiffieHellman problems by providing reductions among them in the high granularity setting. We show that all three variations of computational DiffieHellman problem: square DiffieHellman problem, inverse DiffieHellman problem and d ..."
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Cited by 38 (1 self)
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Abstract. This paper studies various computational and decisional DiffieHellman problems by providing reductions among them in the high granularity setting. We show that all three variations of computational DiffieHellman problem: square DiffieHellman problem, inverse DiffieHellman problem
A New Identification Scheme based on the Bilinear DiffieHellman Problem
 In Proc. ACISP 2002, volume 2384 of LNCS
, 2002
"... We construct an interactive identification scheme based on the bilinear DiffieHellman problem and analyze its security. This scheme is practical in terms of key size, communication complexity, and availability of identityvariance provided that an algorithm of computing the Weilpairing is feasible ..."
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Cited by 5 (1 self)
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field, on the other hand, the decisional DiffieHellman problem is easy in the multiplicative group of the finite field mapped by a bilinear map. Finally, this scheme is compared with other identification schemes.
A New Identification Scheme based on the Gap DiffieHellman Problem
, 2002
"... We introduce a new identification scheme based on the Gap DiffieHellman problem. Our identification scheme makes use of the fact that the computational DiffieHellman problem is hard in the additive group of points of an elliptic curve over a finite field, on the other hand, the decisional DiffieH ..."
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Cited by 1 (0 self)
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We introduce a new identification scheme based on the Gap DiffieHellman problem. Our identification scheme makes use of the fact that the computational DiffieHellman problem is hard in the additive group of points of an elliptic curve over a finite field, on the other hand, the decisional DiffieHellman
Efficient signature schemes with tight reductions to the DiffieHellman problems
 Journal of Cryptology
"... We propose and analyze two efficient signature schemes whose security is tightly related to the DiffieHellman problems in the random oracle model. Security of our first scheme relies on the hardness of the computational DiffieHellman problem; security of our second scheme — which is more efficient ..."
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Cited by 11 (0 self)
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efficient than the first — is based on the hardness of the decisional DiffieHellman problem, a stronger assumption. Given current state of the art, it is as difficult to solve the DiffieHellman problems as it is to solve the discrete logarithm problem in many groups of cryptographic interest. Thus
Efficient threshold signature, multisignature and blind signature schemes based on the GapDiffieHellmanGroup signature scheme
 PROCEEDINGS OF PKC 2003, VOLUME 2567 OF LNCS
, 2003
"... We propose a robust proactive threshold signature scheme, a multisignature scheme and a blind signature scheme which work in any Gap DiffieHellman (GDH) group (where the Computational DiffieHellman problem is hard but the Decisional DiffieHellman problem is easy). Our constructions are based on t ..."
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Cited by 191 (0 self)
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We propose a robust proactive threshold signature scheme, a multisignature scheme and a blind signature scheme which work in any Gap DiffieHellman (GDH) group (where the Computational DiffieHellman problem is hard but the Decisional DiffieHellman problem is easy). Our constructions are based
Conjectured security of the ANSINIST Elliptic Curve RNG, Cryptology ePrint Archive, Report 2006/117
, 2006
"... An elliptic curve random number generator (ECRNG) has been proposed in ANSI and NIST draft standards. This paper proves that, if three conjectures are true, then the ECRNG is secure. The three conjectures are hardness of the elliptic curve decisional DiffieHellman problem and the hardness of two ne ..."
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Cited by 3 (0 self)
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An elliptic curve random number generator (ECRNG) has been proposed in ANSI and NIST draft standards. This paper proves that, if three conjectures are true, then the ECRNG is secure. The three conjectures are hardness of the elliptic curve decisional DiffieHellman problem and the hardness of two
A Security Analysis of the NIST SP 80090 Elliptic Curve Random Number Generator. Cryptology ePrint Archive, Report 2007/048
, 2007
"... An elliptic curve random number generator (ECRNG) has been approved in a NIST standards and proposed for ANSI and SECG draft standards. This paper proves that, if three conjectures are true, then the ECRNG is secure. The three conjectures are hardness of the elliptic curve decisional DiffieHellman ..."
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Cited by 6 (1 self)
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problem and the hardness of two newer problems, the xlogarithm problem and the truncated point problem. The xlogarithm problem is shown to be hard if the decisional DiffieHellman problem is hard, although the reduction is not tight. The truncated point problem is shown to be solvable when the minimum
Results 1  10
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901