Generalized ElGamal Public Key Cryptosystem Based on a New Diffie-Hellman Problem

A new public key encryption scheme is proposed and analyzed, which is based on a vector space over some finite field with respect to a class of matrix semigroup action. The scheme is proved secure against adaptive chosen ciphertext attack under EDDH assumption. Since EDDH assumption is weaker than DDH assumption for generic bilinear groups, the new encryption scheme is a good replacement for Cramer-Shoup encryption scheme when bilinear group is adopted as construction platform.

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“…We refer to the reader to [3], [5] for the notions of public key encryption scheme and security against adaptive ciphertext attack. …”

Section: Preliminariesmentioning

confidence: 99%

“…In 2008, H.W. Huang et al [5] proposed a new DDH assumption, that is, EDDH assumption, which is weaker than DDH assumption and linear DDH assumption.…”

Section: Introductionmentioning

confidence: 98%

A New Public-Key Encryption Scheme Secure against Adaptive Chosen Ciphertext Attack

Huang

Chen

2009

2009 First International Conference on Information Science and Engineering

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“…In such a group it is well-known that DDH is easy, and we show that this is also the case for d-DDH. The EDDH assumption presented in [HYZX08] is equivalent to d-DDH for d = 2. It was claimed that EDDH is hard also in generic bilinear groups, which is however refuted by the following result:…”

Section: The D-ddh Problemmentioning

confidence: 99%

“…A final related work that should be mentioned is [HYZX08] in which an assumption called EDDH is proposed, which is our 2-DDH assumption. This is the only prior work we know of that mentions a DDH variant based on ring extensions.…”

Section: Introductionmentioning

confidence: 99%

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DDH-Like Assumptions Based on Extension Rings

Cramer

Damgård

Kiltz

et al. 2012

Public Key Cryptography – PKC 2012

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Abstract. We introduce and study a new type of DDH-like assumptions based on groups of prime order q. Whereas standard DDH is based on encoding elements of Fq "in the exponent" of elements in the group, we ask what happens if instead we put in the exponent elements of the extension ring R f = Fq[X]/(f ) where f is a degree-d polynomial. The decision problem that follows naturally reduces to the case where f is irreducible. This variant is called the d-DDH problem, where 1-DDH is standard DDH. We show in the generic group model that d-DDH is harder than DDH for d > 1 and that we obtain, in fact, an infinite hierarchy of progressively weaker assumptions whose complexities lie "between" DDH and CDH. This leads to a large number of new schemes because virtually all known DDH-based constructions can very easily be upgraded to be based on d-DDH. We use the same construction and security proof but get better security and moreover, the amortized complexity (e.g, computation per encrypted bit) is the same as when using DDH. We also show that d-DDH, just like DDH, is easy in bilinear groups. We therefore suggest a different type of assumption, the d-vector DDH problems (d-VDDH), which are based on f (X) = X d , but with a twist to avoid problems with reducible polynomials. We show in the generic group model that d-VDDH is hard in bilinear groups and that the problems become harder with increasing d. We show that hardness of d-VDDH implies CCA-secure encryption, efficient Naor-Reingold style pseudorandom functions, and auxiliary input secure encryption. This can be seen as an alternative to the known family of k-LIN assumptions.

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A privacy preserving authentication scheme for roaming services in global mobility networks

Zhang

Fan

Zhang

et al. 2015

Security Comm Networks

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To provide secure roaming services for mobile users in Global Mobility Networks, many schemes have been proposed in recent years. However, most of them focus only on authentication and fail to satisfy many practical security requirements such as user anonymity and untraceability. To address this problem, we propose a privacy-preserving authentication scheme based on elliptic curve cryptography. The proposed scheme is provably secure under a formal model that satisfies all practical security requirements. Compared with existing authentication schemes, ours enjoys better performance in terms of computation cost and security. Perfect Forward Secrecy: An adversary cannot obtain the session keys established between an MU and an FA (HA) in advance, even if it has compromised MU's password or smart card.

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Generalized ElGamal Public Key Cryptosystem Based on a New Diffie-Hellman Problem

Cited by 5 publications

References 11 publications

A New Public-Key Encryption Scheme Secure against Adaptive Chosen Ciphertext Attack

A New Public-Key Encryption Scheme Secure against Adaptive Chosen Ciphertext Attack

DDH-Like Assumptions Based on Extension Rings

A privacy preserving authentication scheme for roaming services in global mobility networks

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