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A practical public key cryptosystem provably secure against adaptive chosen ciphertext attack
 CRYPTO '98
, 1998
"... A new public key cryptosystem is proposed and analyzed. The scheme is quite practical, and is provably secure against adaptive chosen ciphertext attack under standard intractability assumptions. There appears to be no previous cryptosystem in the literature that enjoys both of these properties simu ..."
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Cited by 460 (16 self)
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A new public key cryptosystem is proposed and analyzed. The scheme is quite practical, and is provably secure against adaptive chosen ciphertext attack under standard intractability assumptions. There appears to be no previous cryptosystem in the literature that enjoys both of these properties simultaneously.
The Decision DiffieHellman Problem
, 1998
"... The Decision DiffieHellman assumption (ddh) is a gold mine. It enables one to construct efficient cryptographic systems with strong security properties. In this paper we survey the recent applications of DDH as well as known results regarding its security. We describe some open problems in this are ..."
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Cited by 198 (6 self)
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The Decision DiffieHellman assumption (ddh) is a gold mine. It enables one to construct efficient cryptographic systems with strong security properties. In this paper we survey the recent applications of DDH as well as known results regarding its security. We describe some open problems in this area. 1 Introduction An important goal of cryptography is to pin down the exact complexity assumptions used by cryptographic protocols. Consider the DiffieHellman key exchange protocol [12]: Alice and Bob fix a finite cyclic group G and a generator g. They respectively pick random a; b 2 [1; jGj] and exchange g a ; g b . The secret key is g ab . To totally break the protocol a passive eavesdropper, Eve, must compute the DiffieHellman function defined as: dh g (g a ; g b ) = g ab . We say that the group G satisfies the Computational DiffieHellman assumption (cdh) if no efficient algorithm can compute the function dh g (x; y) in G. Precise definitions are given in the next sectio...
Numbertheoretic constructions of efficient pseudorandom functions
 In 38th Annual Symposium on Foundations of Computer Science
, 1997
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Key Agreement Protocols and their Security Analysis
, 1997
"... This paper proposes new protocols for two goals: authenticated key agreement and authenticated key agreement with key confirmation in the asymmetric (publickey) setting. A formal ..."
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Cited by 136 (6 self)
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This paper proposes new protocols for two goals: authenticated key agreement and authenticated key agreement with key confirmation in the asymmetric (publickey) setting. A formal
The Two Faces of Lattices in Cryptology
, 2001
"... Lattices are regular arrangements of points in ndimensional space, whose study appeared in the 19th century in both number theory and crystallography. Since the appearance of the celebrated LenstraLenstra Lov'asz lattice basis reduction algorithm twenty years ago, lattices have had surprising ..."
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Cited by 69 (16 self)
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Lattices are regular arrangements of points in ndimensional space, whose study appeared in the 19th century in both number theory and crystallography. Since the appearance of the celebrated LenstraLenstra Lov'asz lattice basis reduction algorithm twenty years ago, lattices have had surprising applications in cryptology. Until recently, the applications of lattices to cryptology were only negative, as lattices were used to break various cryptographic schemes. Paradoxically, several positive cryptographic applications of lattices have emerged in the past five years: there now exist publickey cryptosystems based on the hardness of lattice problems, and lattices play a crucial role in a few security proofs.
The Insecurity of the Digital Signature Algorithm with Partially Known Nonces
 Journal of Cryptology
, 2000
"... . We present a polynomialtime algorithm that provably recovers the signer's secret DSA key when a few bits of the random nonces k (used at each signature generation) are known for a number of DSA signatures at most linear in log q (q denoting as usual the small prime of DSA), under a reasonable ass ..."
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Cited by 66 (16 self)
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. We present a polynomialtime algorithm that provably recovers the signer's secret DSA key when a few bits of the random nonces k (used at each signature generation) are known for a number of DSA signatures at most linear in log q (q denoting as usual the small prime of DSA), under a reasonable assumption on the hash function used in DSA. The number of required bits is about log 1=2 q, and can be further decreased to 2 if one assumes access to ideal lattice basis reduction, namely an oracle for the lattice closest vector problem for the infinity norm. All previously known results were only heuristic, including those of HowgraveGraham and Smart who recently introduced that topic. Our attack is based on a connection with the hidden number problem (HNP) introduced at Crypto '96 by Boneh and Venkatesan in order to study the bitsecurity of the DiffieHellman key exchange. The HNP consists, given a prime number q, of recovering a number ff 2 IFq such that for many known random t 2 IFq ...
Lattice Reduction in Cryptology: An Update
 Lect. Notes in Comp. Sci
, 2000
"... Lattices are regular arrangements of points in space, whose study appeared in the 19th century in both number theory and crystallography. ..."
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Cited by 36 (7 self)
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Lattices are regular arrangements of points in space, whose study appeared in the 19th century in both number theory and crystallography.
The Insecurity of the Elliptic Curve Digital Signature Algorithm with Partially Known Nonces
 Design, Codes and Cryptography
, 2000
"... Nguyen and Shparlinski recently presented a polynomialtime algorithm that provably recovers the signer's secret DSA key when a few bits of the random nonces k (used at each signature generation) are known for a number of DSA signatures at most linear in log q (q denoting as usual the small prime of ..."
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Cited by 34 (10 self)
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Nguyen and Shparlinski recently presented a polynomialtime algorithm that provably recovers the signer's secret DSA key when a few bits of the random nonces k (used at each signature generation) are known for a number of DSA signatures at most linear in log q (q denoting as usual the small prime of DSA), under a reasonable assumption on the hash function used in DSA. The number of required bits is about log 1/2 q, and can be further decreased to 2 if one assumes access to ideal lattice basis reduction, namely an oracle for the lattice closest vector problem for the infinity norm. All previously known results were only heuristic, including those of HowgraveGraham and Smart who introduced the topic. Here, we obtain similar results for the elliptic curve variant of DSA (ECDSA).
On the statistical properties of Diffie–Hellman distributions
 MR 2001k:11258 Zbl 0997.11066
"... Let p be a large prime such that p−1 has some large prime factors, and let ϑ ∈ Z ∗ p be an rth power residue for all small factors of p − 1. The corresponding DiffieHellman (DH) distribution is (ϑ x, ϑ y, ϑ xy) where x, y are randomly chosen from Z ∗ p. A recently formulated assumption is that giv ..."
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Cited by 29 (10 self)
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Let p be a large prime such that p−1 has some large prime factors, and let ϑ ∈ Z ∗ p be an rth power residue for all small factors of p − 1. The corresponding DiffieHellman (DH) distribution is (ϑ x, ϑ y, ϑ xy) where x, y are randomly chosen from Z ∗ p. A recently formulated assumption is that given p, ϑ of the above form it is infeasible to distinguish in reasonable time between DH distribution and triples of numbers chosen
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 26 (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 protocol, allowing two parties who share no secret information initially, to generate a mutual secret key. This paper summarizes the present knowledge on the security of this protocol.