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A public key cryptosystem and a signature scheme based on discrete logarithms
 Adv. in Cryptology, SpringerVerlag
, 1985
"... AbstractA new signature scheme is proposed, together with an implementation of the DiffieHellman key distribution scheme that achieves a public key cryptosystem. The security of both systems relies on the difficulty of computing discrete logarithms over finite fields. I. ..."
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AbstractA new signature scheme is proposed, together with an implementation of the DiffieHellman key distribution scheme that achieves a public key cryptosystem. The security of both systems relies on the difficulty of computing discrete logarithms over finite fields. I.
Algorithms for Quantum Computation: Discrete Logarithms and Factoring
, 1994
"... A computer is generally considered to be a universal computational device; i.e., it is believed able to simulate any physical computational device with a increase in computation time of at most a polynomial factor. It is not clear whether this is still true when quantum mechanics is taken into consi ..."
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Cited by 1103 (7 self)
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into consideration. Several researchers, starting with David Deutsch, have developed models for quantum mechanical computers and have investigated their computational properties. This paper gives Las Vegas algorithms for finding discrete logarithms and factoring integers on a quantum computer that take a number
Polynomial approximation of BilinearDiffieHellman maps
"... The problem of computing BilinearDiffieHellman maps is considered. It is shown that the problem of computing the map is equivalent to computing a diagonal version of it. Various lower bounds on the degree of any polynomial that interpolates this diagonal version of the map are found that shows tha ..."
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The problem of computing BilinearDiffieHellman maps is considered. It is shown that the problem of computing the map is equivalent to computing a diagonal version of it. Various lower bounds on the degree of any polynomial that interpolates this diagonal version of the map are found that shows
DISCRETE LOGARITHMS, DIFFIEHELLMAN, AND REDUCTIONS
"... Abstract. We consider the OnePrimeNotp and AllPrimesButp variants of the Discrete Logarithm (DL) problem in a group of prime order p. We give reductions to the DiffieHellman (DH) problem that do not depend on any unproved conjectures about smooth or prime numbers in short intervals. We show t ..."
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Abstract. We consider the OnePrimeNotp and AllPrimesButp variants of the Discrete Logarithm (DL) problem in a group of prime order p. We give reductions to the DiffieHellman (DH) problem that do not depend on any unproved conjectures about smooth or prime numbers in short intervals. We show
Towards the Equivalence of Breaking the DiffieHellman Protocol and Computing Discrete Logarithms
, 1994
"... Let G be an arbitrary cyclic group with generator g and order jGj with known factorization. G could be the subgroup generated by g within a larger group H. Based on an assumption about the existence of smooth numbers in short intervals, we prove that breaking the DiffieHellman protocol for G and ..."
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Cited by 78 (6 self)
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of jGj is such that one of a list of expressions in p, including p \Gamma 1 and p + 1, is smooth for an appropriate smoothness bound, then S can efficiently be constructed and therefore breaking the DiffieHellman protocol is equivalent to computing discrete logarithms.
The Relationship Between Breaking the DiffieHellman Protocol and Computing Discrete Logarithms
, 1998
"... Both uniform and nonuniform results concerning the security of the DiffieHellman keyexchange protocol are proved. First, it is shown that in a cyclic group G of order jGj = Q p e i i , where all the multiple prime factors of jGj are polynomial in log jGj, there exists an algorithm that re ..."
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Cited by 49 (3 self)
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]. Under the unproven but plausible assumption that (p) is polynomial in log p, this reduction implies that the DiffieHellman problem and the discrete logarithm problem are polynomialtime equivalent in G. Second, it is proved that the DiffieHellman problem and the discrete logarithm problem
DiffieHellman
, 2010
"... ◮ Asymmetric or publickey cryptography ◮ Originally attributed to Diffie and Hellman in 1975, but later discovered in British classified work of James Ellis in 1971 ◮ Basic idea involves altering traditional symmetry of cryptographic protocols to convey additional info in a public key. The message ..."
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◮ Asymmetric or publickey cryptography ◮ Originally attributed to Diffie and Hellman in 1975, but later discovered in British classified work of James Ellis in 1971 ◮ Basic idea involves altering traditional symmetry of cryptographic protocols to convey additional info in a public key. The message
The DiffieHellman Protocol
 DESIGNS, CODES, AND CRYPTOGRAPHY
, 1999
"... The 1976 seminal paper of Diffie and Hellman is a landmark in the history of cryptography. They introduced the fundamental concepts of a trapdoor oneway function, a publickey cryptosystem, and a digital signature scheme. Moreover, they presented a protocol, the socalled DiffieHellman protoco ..."
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Cited by 29 (0 self)
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The 1976 seminal paper of Diffie and Hellman is a landmark in the history of cryptography. They introduced the fundamental concepts of a trapdoor oneway function, a publickey cryptosystem, and a digital signature scheme. Moreover, they presented a protocol, the socalled DiffieHellman
IdentityBased Encryption from the Weil Pairing
, 2001
"... We propose a fully functional identitybased encryption scheme (IBE). The scheme has chosen ciphertext security in the random oracle model assuming an elliptic curve variant of the computational DiffieHellman problem. Our system is based on bilinear maps between groups. The Weil pairing on elliptic ..."
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Cited by 1699 (29 self)
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We propose a fully functional identitybased encryption scheme (IBE). The scheme has chosen ciphertext security in the random oracle model assuming an elliptic curve variant of the computational DiffieHellman problem. Our system is based on bilinear maps between groups. The Weil pairing
DiffieHellman Oracles
 ADVANCES IN CRYPTOLOGY  CRYPTO '96 , LECTURE NOTES IN COMPUTER SCIENCE
, 1996
"... This paper consists of three parts. First, various types of DiffieHellman oracles for a cyclic group G and subgroups of G are defined and their equivalence is proved. In particular, the security of using a subgroup of G instead of G in the DiffieHellman protocol is investigated. Second, we derive ..."
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Cited by 46 (3 self)
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several new conditions for the polynomialtime equivalence of breaking the DiffieHellman protocol and computing discrete logarithms in G which extend former results by den Boer and Maurer. Finally, efficient constructions of DiffieHellman groups with provable equivalence are described.
Results 1  10
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42,259