Variations of Diffie-Hellman Problem

Bao, Feng; Deng, Robert H.; Zhu, Huafei

doi:10.1007/978-3-540-39927-8_28

Cited by 222 publications

(101 citation statements)

References 17 publications

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“…We are not going to study the possible reductions between MCDH problems, due to the fact that, essentially, any MCDH problem amounts to computing some polynomial on the elements of A, and it is then equivalent to CDH ( [4,23]), although the tightness of the reduction depends on the degree of the polynomial.…”

Section: The Matrix Diffie-hellman Computational Problemsmentioning

confidence: 99%

“…But unforgeability actually means the inability to produce one among many solutions to a given problem (e.g., in many signature schemes or zero knowledge proofs). Thus, unforgeability is more naturally captured by a flexible computational problem, namely, a problem which admits several solutions 4 . This maybe explains why several new flexible assumptions have appeared recently when considering "unforgeability-type" security notions in structure-preserving cryptography [2].…”

Section: Introductionmentioning

confidence: 99%

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The Kernel Matrix Diffie-Hellman Assumption

Morillo

Ràfols

Villar

2016

Lecture Notes in Computer Science

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Abstract. We put forward a new family of computational assumptions, the Kernel Matrix Diffie-Hellman Assumption. Given some matrix A sampled from some distribution D, the kernel assumption says that it is hard to find "in the exponent" a nonzero vector in the kernel of A . This family is a natural computational analogue of the Matrix Decisional Diffie-Hellman Assumption (MDDH), proposed by Escala et al. As such it allows to extend the advantages of their algebraic framework to computational assumptions. The k-Decisional Linear Assumption is an example of a family of decisional assumptions of strictly increasing hardness when k grows. We show that for any such family of MDDH assumptions, the corresponding Kernel assumptions are also strictly increasingly weaker. This requires ruling out the existence of some black-box reductions between flexible problems (i.e., computational problems with a non unique solution).

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Section: The Matrix Diffie-hellman Computational Problemsmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

The Kernel Matrix Diffie-Hellman Assumption

Morillo

Ràfols

Villar

2016

Lecture Notes in Computer Science

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“…A similar assumption is also used in [13] to prove the security of the proposed anonymous fingerprinting scheme. And in [2], Bao et al prove that if the Computational DiffieHellman (CDH) assumption holds, there is no probabilistic polynomial time Turing machine that outputs g x −1 on inputs g and g x with non-negligible probability. Note that the CDH assumption states that there is no probabilistic polynomial-time Turing machine that outputs g xy on inputs g, g x , and g y with non-negligible probability.…”

Section: Security Analysismentioning

confidence: 99%

Sharing DSS by the Chinese Remainder Theorem

Kaya

Selçuk

2014

Journal of Computational and Applied Mathematics

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In this paper, we propose a new threshold scheme for the Digital Signature Standard (DSS) using Asmuth-Bloom secret sharing based on the Chinese Remainder Theorem (CRT). To achieve the desired result, we first show how to realize certain other threshold primitives using Asmuth-Bloom secret sharing, such as joint random secret sharing, joint exponential random secret sharing, and joint exponential inverse random secret sharing. We prove the security of our scheme against a static adversary. To the best of our knowledge, this is the first provably secure threshold DSS scheme based on the CRT.

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“…More precisely, in Protocol 1 this case is reduced to solve SCDH problem given DDH oracle, and in Protocol 2 reduced to solve SCDH problem. Also, note that CDH problem is equivalent to SCDH problem in prime order cyclic group G, see [2].…”

Section: Security Proofmentioning

confidence: 99%

Strongly Secure Authenticated Key Exchange without NAXOS’ Approach

Kim

Fujioka

Ustaoğlu

2009

Advances in Information and Computer Security

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Abstract. LaMacchia, Lauter and Mityagin [15] proposed the extended Canetti-Krawczyk (eCK) model and an AKE protocol, called NAXOS. Unlike previous security models, the adversary in the eCK model is allowed to obtain ephemeral secret information related to the test session, which makes the security proof difficult. To overcome this NAXOS combines an ephemeral private key x with a static private key a to generate an ephemeral public key X; more precisely X = g H(x,a) . As a result, no one is able to query the discrete logarithm of X without knowing both the ephemeral and static private keys. In other words, the discrete logarithm of an ephemeral public key, which is typically the ephemeral secret, is hidden via an additional random oracle. In this paper, we show that it is possible to construct eCK-secure protocol without the NAXOS' approach by proposing two eCK-secure protocols. One is secure under the GDH assumption and the other under the CDH assumption; their efficiency and security assurances are comparable to the well-known HMQV [12] protocol. Furthermore, they are at least as secure as protocols that use the NAXOS' approach but unlike them and HMQV, the use of the random oracle is minimized and restricted to the key derivation function.

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Variations of Diffie-Hellman Problem

Cited by 222 publications

References 17 publications

The Kernel Matrix Diffie-Hellman Assumption

The Kernel Matrix Diffie-Hellman Assumption

Sharing DSS by the Chinese Remainder Theorem

Strongly Secure Authenticated Key Exchange without NAXOS’ Approach

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