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Lecture notes in computer science

Analysis and Improvement of Lindell’s UC-Secure Commitment Schemes

Olivier Blazy, Céline Chevalier, David Pointcheval, Damien Vergnaud

Published Jan 1, 2013• 31 citations
Publisher
DOI
10.1007/978-3-642-38980-1_34

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At Eurocrypt 2011, Lindell presented practical static and adaptively UC-secure commitment schemes based on the DDH assumption. Later, Blazy et al. (at ACNS 2013) improved the efficiency of the Lindell's commitment schemes. In this paper, we present static and adaptively UC-secure commitment schemes based on the same assumption and further improve the communication and computational complexity, as well as the size of the common reference string.

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Analysis and Improvement of Lindell's UC-Secure Commitment Schemes.

Olivier Blazy, Céline Chevalier, David Pointcheval +1 more

Abstract. In 2011, Lindell proposed an efficient commitment scheme, with a non-interactive opening algorithm, in the Universal Composability (UC) framework. He recently acknowledged a bug in its security analysis for the adaptive case. We analyze the proof of the original paper and propose a simple patch of the scheme. More interestingly, we then modify it and present a more efficient commitment scheme secure in the UC framework, with the same level of security as Lindell’s protocol: adaptive corruptions, with erasures. The security is proven in the standard model (with a Common Reference String) under the classical Decisional Diffie-Hellman assumption. Our proposal is the most efficient UC-secure commitment proposed to date (in terms of computational workload and communication complexity).

•Jan 1, 2013•0 citations

Efficient UC-Secure Authenticated Key-Exchange for Algebraic Languages.

Olivier Blazy, Céline Chevalier, David Pointcheval +1 more

Authenticated Key Exchange (AKE) protocols enable two parties to establish a shared, cryptographically strong key over an insecure network using various authentication means, such as cryptographic keys, short (i.e., lowentropy) secret keys or credentials. In this paper, we provide a general framework, that encompasses several previous AKE primitives such as (Verifier-based) Password-Authenticated Key Exchange or Secret Handshakes, we call LAKE for Language-Authenticated Key Exchange. We first model this general primitive in the Universal Composability (UC) setting. Thereafter, we show that the Gennaro-Lindell approach can efficiently address this goal. But we need smooth projective hash functions on new languages, whose efficient implementations are of independent interest. We indeed provide such hash functions for languages defined by combinations of linear pairing product equations. Combined with an efficient commitment scheme, that is derived from the highly-efficient UC-secure Lindell’s commitment, we obtain a very practical realization of Secret Handshakes, but also Credential-Authenticated Key Exchange protocols. All the protocols are UC-secure, in the standard model with a common reference string, under the classical Decisional Linear assumption.

•Jan 1, 2012•0 citations
Abstract. In 2011, Lindell proposed an efficient commitment scheme, with a non-interactive opening algorithm, in the Universal Composability (UC) framework. He recently acknowledged a bug in its security analysis for the adaptive case. We analyze the proof of the original paper and propose a simple patch of the scheme. More interestingly, we then modify it and present a more efficient commitment scheme secure in the UC framework, with the same level of security as Lindell’s protocol: adaptive corruptions, with erasures. The security is proven in the standard model (with a Common Reference String) under the classical Decisional Diffie-Hellman assumption. Our proposal is the most efficient UC-secure commitment proposed to date (in terms of computational workload and communication complexity).
Authenticated Key Exchange (AKE) protocols enable two parties to establish a shared, cryptographically strong key over an insecure network using various authentication means, such as cryptographic keys, short (i.e., lowentropy) secret keys or credentials. In this paper, we provide a general framework, that encompasses several previous AKE primitives such as (Verifier-based) Password-Authenticated Key Exchange or Secret Handshakes, we call LAKE for Language-Authenticated Key Exchange. We first model this general primitive in the Universal Composability (UC) setting. Thereafter, we show that the Gennaro-Lindell approach can efficiently address this goal. But we need smooth projective hash functions on new languages, whose efficient implementations are of independent interest. We indeed provide such hash functions for languages defined by combinations of linear pairing product equations. Combined with an efficient commitment scheme, that is derived from the highly-efficient UC-secure Lindell’s commitment, we obtain a very practical realization of Secret Handshakes, but also Credential-Authenticated Key Exchange protocols. All the protocols are UC-secure, in the standard model with a common reference string, under the classical Decisional Linear assumption.