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The computational and decisional DiffieHellman assumptions in CryptoVerif
"... We present an extension of CryptoVerif to DiffieHellman key agreements. CryptoVerif [1] is a security protocol verifier sound in the computational model, which produces proofs by sequences of games. CryptoVerif provides a generic method for specifying security assumptions on primitives. However, th ..."
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, this method did not support the computational and decisional DiffieHellman assumptions. We have extended it to support these assumptions, which required the following additions: – DiffieHellman key agreements consider a cyclic group G with generator g. One protocol participant A chooses a random exponent a
The Group DiffieHellman Problems
 INTERNATIONAL WORKSHOP ON SELECTED AREAS IN CRYPTOGRAPHY
, 2002
"... In this paper we study generalizations of the DiffieHellman problems recently used to construct cryptographic schemes for practical purposes. The Group Computational and the Group Decisional DiffieHellman assumptions not only enable one to construct efficient pseudorandom functions but also to na ..."
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Cited by 22 (4 self)
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In this paper we study generalizations of the DiffieHellman problems recently used to construct cryptographic schemes for practical purposes. The Group Computational and the Group Decisional DiffieHellman assumptions not only enable one to construct efficient pseudorandom functions but also
Dynamic Group DiffieHellman Key Exchange under Standard Assumptions
 EUROCRYPT
, 2002
"... Authenticated DiffieHellman key exchange allows two principals communicating over a public network, and each holding public /private keys, to agree on a shared secret value. In this paper we study the natural extension of this cryptographic problem to a group of principals. We begin from existin ..."
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Cited by 72 (11 self)
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existing formal security models and refine them to incorporate major missing details (e.g., strongcorruption and concurrent sessions). Within this model we define the execution of a protocol for authenticated dynamic group DiffieHellman and show that it is provably secure under the decisional DiffieHellman
Using Hash Functions as a Hedge against Chosen Ciphertext Attack
, 2000
"... The cryptosystem recently proposed by Cramer and Shoup [5] is a practical public key cryptosystem that is secure against adaptive chosen ciphertext attack provided the Decisional DiffieHellman assumption is true. Although this is a reasonable intractability assumption, it would be preferable to bas ..."
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Cited by 73 (7 self)
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The cryptosystem recently proposed by Cramer and Shoup [5] is a practical public key cryptosystem that is secure against adaptive chosen ciphertext attack provided the Decisional DiffieHellman assumption is true. Although this is a reasonable intractability assumption, it would be preferable
Computationally Sound Verification of Security Protocols Using DiffieHellman Exponentiation
, 2005
"... In this paper, we follow the recent trend in bridging the gap that separates the symbolic and computational views of cryptographic protocols. Recent papers have proven that computational security can be automatically verified using the DolevYao abstraction. We extend these results by adding a widel ..."
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widely used component for cryptographic protocols: DiffieHellman exponentiation. Thus our main result is: if the Decisional DiffieHellman assumption is verified and the cryptographic primitives used to implement the protocol are secure, then safety in the symbolic world implies safety
A Practical Elliptic Curve Public Key Encryption Scheme Provably Secure Against Adaptive Chosenmessage Attack
, 2003
"... We study elliptic curve cryptosystems by first investigating the schemes defined over Z_p and show that the scheme is provably secure against adaptive chosen ciphertext attack under the decisional DiffieHellman assumption. Then we derive a practical elliptic curve cryptosystem by making use of som ..."
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We study elliptic curve cryptosystems by first investigating the schemes defined over Z_p and show that the scheme is provably secure against adaptive chosen ciphertext attack under the decisional DiffieHellman assumption. Then we derive a practical elliptic curve cryptosystem by making use
Provably Secure Lengthsaving PublicKey Encryption Scheme under the Computational DiffieHellman Assumption
 ETRI Journal
, 2000
"... A design of secure and efficient publickey encryption schemes under weaker computational assumptions has been regarded as an important and challenging task. As far as ElGamaltype encryption schemes are concerned, some variants of the original ElGamal encryption scheme based on the weaker comput ..."
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Cited by 6 (0 self)
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computational assumption have been proposed. For instance, security of the ElGamal variant of FujisakiOkamoto publickey encryption scheme and Cramer and Shoup's encryption scheme is based on the decisional DiffieHellman assumption (DDHA). However, security of the recent scheme, such as Pointcheval
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 34 (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
Secure Hashed DiffieHellman over NonDDH Groups
, 2004
"... We show that in applications that use the DiffieHellman (DH) transform but take care of hashing the DH output (as required, for example, for secure DHbased encryption and key exchange) the usual requirement to work over a DDH group (i.e., a group in which the Decisional DiffieHellman assumption h ..."
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Cited by 21 (3 self)
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We show that in applications that use the DiffieHellman (DH) transform but take care of hashing the DH output (as required, for example, for secure DHbased encryption and key exchange) the usual requirement to work over a DDH group (i.e., a group in which the Decisional DiffieHellman assumption
Efficient chosen ciphertext secure public key encryption under the computational DiffieHellman assumption
 In ASIACRYPT 2008, LNCS
, 2008
"... Recently Cash, Kiltz, and Shoup [20] showed a variant of the CramerShoup (CS) public key encryption (PKE) scheme [21] whose chosenciphertext (CCA) security relies on the computational DiffieHellman (CDH) assumption. The cost for this high security is that the size of ciphertexts is much longer th ..."
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Cited by 14 (2 self)
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Desmedt (KD) scheme [42]. Note that the CDH and HDH assumptions are weaker than the decisional DiffieHellman assumption which the CS and KD schemes rely on. Both of our schemes are based on a certain broadcast encryption (BE) scheme while the CashKiltzShoup scheme is based on a different paradigm which
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