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111
The DiffieHellman problem and generalization of Verheul’s theorem
, 2009
"... Bilinear pairings on elliptic curves have been of much interest in cryptography recently. Most of the protocols involving pairings rely on the hardness of the bilinear DiffieHellman problem. In contrast to the discrete log (or DiffieHellman) problem in a finite field, the difficulty of this proble ..."
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Bilinear pairings on elliptic curves have been of much interest in cryptography recently. Most of the protocols involving pairings rely on the hardness of the bilinear DiffieHellman problem. In contrast to the discrete log (or DiffieHellman) problem in a finite field, the difficulty
Bit Security of the Hyperelliptic Curves DiffieHellman Problem
"... Abstract. The DiffieHellman problem as a cryptographic primitive plays an important role in modern cryptology. The Bit Security or HardCore Bits of DiffieHellman problem in arbitrary finite cyclic group is a longstanding open problem in cryptography. Until now, only few groups have been studied. ..."
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Abstract. The DiffieHellman problem as a cryptographic primitive plays an important role in modern cryptology. The Bit Security or HardCore Bits of DiffieHellman problem in arbitrary finite cyclic group is a longstanding open problem in cryptography. Until now, only few groups have been studied
The equivalence of the computational Diffie–Hellman and discrete logarithm problems in certain groups
, 2012
"... Whether the discrete logarithm problem can be reduced to the Diffie–Hellman problem is a celebrated open question. The security of Diffie–Hellman key exchange and other cryptographic protocols rests on the assumed difficulty of the computational Diffie–Hellman problem; such a reduction would show th ..."
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that this is equivalent to assuming that computing discrete logarithms is hard. What is known is that a nearreduction exists for general groups, assuming that a conjecture about the existence of smooth numbers in an interval is true. Given access to a Diffie–Hellman oracle, and a small amount of additional information
DHAES: An Encryption Scheme Based on the DiffieHellman Problem
, 1998
"... This paper describes a DiffieHellman based encryption scheme, DHAES. The scheme is as efficient as ElGamal encryption, but has stronger security properties. Furthermore, these security properties are proven to hold under appropriate assumptions on the underlying primitive. We show that DHAES has no ..."
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Cited by 61 (5 self)
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on appropriate assumptions about the hardness of the DiffieHellman problem and the assumption that the underly...
On the bit security of the DiffieHellman key
 In Appl. Algebra in Engin., Commun. and Computing
, 2006
"... Let IFp be a finite field of p elements, where p is prime. The bit security of the DiffieHellman function over subgroups of IF ∗ p and of an elliptic curve over IFp, is considered. It is shown that if the Decision DiffieHellman problem is hard in these groups, then the two most significant bits of ..."
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Let IFp be a finite field of p elements, where p is prime. The bit security of the DiffieHellman function over subgroups of IF ∗ p and of an elliptic curve over IFp, is considered. It is shown that if the Decision DiffieHellman problem is hard in these groups, then the two most significant bits
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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curve discrete logarithm problem faster than the known algorithms. In the other words, if the Decisional DiffieHellman problem over finite fields turns out to be nonuniformly hard, then the effective bound in UBT should be very small. 1
Making the DiffieHellman Protocol IdentityBased
, 2010
"... This paper presents a new identity based key agreement protocol. In idbased cryptography (introduced by Adi Shamir in [33]) each party uses its own identity as public key and receives his secret key from a master Key Generation Center, whose public parameters are publicly known. The novelty of our ..."
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Cited by 7 (1 self)
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protocol is that it can be implemented over any cyclic group of prime order, where the DiffieHellman problem is supposed to be hard. It does not require the computation of expensive bilinear maps, or additional assumptions such as factoring or RSA. The protocol is extremely efficient, requiring only twice
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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pairing is feasible. We prove that this scheme is secure against active attacks as well as passive attacks if the bilinear DiffieHellman problem is intractable. Our proof is based on the fact that the computational DiffieHellman problem is hard in the additive group of points of an elliptic curve over a finite
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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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
Hardcore Predicates for a DiffieHellman Problem over Finite Fields
, 2013
"... A longstanding open problem in cryptography is proving the existence of (deterministic) hardcore predicates for the DiffieHellman problem defined over finite fields. In this paper we make progress on this problem by defining a very natural variation of the DiffieHellman problem over Fp2 and provi ..."
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and proving the unpredictability of every single bit of one of the coordinates of the secret DH value. To achieve our result we modify an idea presented at CRYPTO’01 by Boneh and Shparlinski [4] originally developed to prove that the LSB of the Elliptic Curve DiffieHellman problem is hard. We extend
Results 1  10
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