Universally Composable Undeniable Signature

How to define the security of undeniable signature schemes is a challenging task. This paper presents two security definitions of undeniable signature schemes which are more useful or natural than the existing definition. It then proves their equivalence. We first define the UC-security, where UC means universal composability. We next show that there exists a UC-secure undeniable signature scheme which does not satisfy the standard definition of security that has been believed to be adequate so far. More precisely, it does not satisfy the invisibility defined by \cite{DP96}. We then show a more adequate definition of invisibility which captures a wider class of (naturally secure) undeniable signature schemes. We finally prove that the UC-security against non-adaptive adversaries is equivalent to this definition of invisibility and the strong unforgeability in \cF_{ZK}-hybrid model, where \cF_{ZK} is the ideal ZK functionality. Our result of equivalence implies that all the known proven secure undeniable signature schemes (including Chaum\u27s scheme) are UC-secure if the confirmation/disavowal protocols are both UC zero-knowledge

(Convertible) Undeniable Signatures without Random Oracles

We propose a convertible undeniable signature scheme without random oracles. Our construction is based on Waters\u27 and Kurosawa and Heng\u27s schemes that were proposed in Eurocrypt 2005. The security of our scheme is based on the CDH and the decision linear assumption. Comparing only the part of undeniable signatures, our scheme uses more standard assumptions than the existing undeniable signatures without random oracles due to Laguillamie and Vergnaud

Toward a Generic Construction of Convertible Undeniable Signatures from Pairing-Based Signatures

Undeniable signatures were proposed to limit the verification property of ordinary digital signatures. In fact, the verification of such signatures cannot be attained without the help of the signer, via the confirmation/denial protocols. Later, the concept was refined to give the possibility of converting a \emph{selected} signature into an ordinary one, or publishing a \emph{universal} receipt that turns all undeniable signatures publicly verifiable. In this paper, we present the first generic construction for convertible undeniable signatures from certain weakly secure cryptosystems and any secure digital signature scheme. Next, we give two specific approaches for building convertible undeniable signatures from a large class of pairing-based signatures. These methods find a nice and practical instantiation with known encryption and signature schemes. For instance, we achieve the most efficient undeniable signatures with regard to the signature length and cost, the underlying assumption and the security model. We believe these constructions could be an interesting starting point to develop more efficient schemes or give better security analyses of the existing ones

The Security of the FDH Variant of Chaum’s Undeniable Signature Scheme

In this paper, a new kind of adversarial goal called forge-and-impersonate in undeniable signature schemes is introduced. Note that forgeability does not necessarily imply impersonation ability. The security of the full-domain hash (FDH) variant of Chaum's undeniable signature scheme is then classified according to three dimensions, the goal of adversaries, the attacks, and the zero-knowledg (ZK) level of confirmation and disavowal protocols. Each security is then related to some well-known computational problem. In particular, the security of the FDH variant of Chaum's scheme with noninteractive zero-knowledge (NIZK) protocol confirmation and disavowal protocols is proven to be equivalent to the computational Diffie-Hellman (CDH) problem, as opposed to the gap Diffie-Hellman (GDH) problem as claimed by Okamoto and Pointcheval

An Efficient Convertible Undeniable Signature Scheme with Delegatable Verification

Undeniable signatures, introduced by Chaum and van Antwerpen, require a verifier to interact with the signer to verify a signature, and hence allow the signer to control the verifiability of his signatures. Convertible undeniable signatures, introduced by Boyar, Chaum, Damg\aa{}rd, and Pedersen, furthermore allow the signer to convert signatures to publicly verifiable ones by publicizing a verification token, either for individual signatures or for all signatures universally. In addition, the signer is able to delegate the ability to prove validity and convert signatures to a semi-trusted third party by providing a verification key. While the latter functionality is implemented by the early convertible undeniable signature schemes, most recent schemes do not consider this despite its practical appeal. In this paper we present an updated definition and security model for schemes allowing delegation, and highlight a new essential security property, token soundness, which is not formally treated in the previous security models for convertible undeniable signatures. We then propose a new convertible undeniable signature scheme. The scheme allows delegation of verification and is provably secure in the standard model assuming the computational co-Diffie-Hellman problem, a closely related problem, and the decisional linear problem are hard. Our scheme is, to the best of our knowledge, the currently most efficient convertible undeniable signature scheme which provably fulfills all security requirements in the standard model

Efficient Deniable Authentication for Signatures, Application to Machine-Readable Travel Document

Releasing a classical digital signature faces to privacy issues. Indeed, there are cases where the prover needs to authenticate some data without making it possible for any malicious verifier to transfer the proof to anyone else. It is for instance the case for e-passports where the signature from the national authority authenticates personal data. To solve this problem, we can prove knowledge of a valid signature without revealing it. This proof should be non-transferable. We first study deniability for signature verification. Deniability is essentially a weaker form of non-transferability. It holds as soon as the protocol is finished (it is often called offline non-transferability). We introduce Offline Non-Transferable Authentication Protocol (ON-TAP) and we show that it can be built by using a classical signature scheme and a deniable zero-knowledge proof of knowledge. For that reason, we use a generic transform for Σ-protocols. Finally, we give examples to upgrade signature standards based on RSA or ElGamal into an ONTAP. Our examples are well-suited for implementation in e-passports

New Constructions and Applications of Trapdoor DDH Groups

Trapdoor Decisional Diffie-Hellman (TDDH) groups, introduced by Dent and Galbraith (ANTS 2006), are groups where the DDH problem is hard, unless one is in possession of a secret trapdoor which enables solving it efficiently. Despite their intuitively appealing properties, they have found up to now very few cryptographic applications. Moreover, among the two constructions of such groups proposed by Dent and Galbraith, only a single one based on hidden pairings remains unbroken. In this paper, we extend the set of trapdoor DDH groups by giving a construction based on composite residuosity. We also introduce a more restrictive variant of these groups that we name \emph{static} trapdoor DDH groups, where the trapdoor only enables to solve the DDH problem with respect to a fixed pair $(G,G^x)$ of group elements. We give two constructions for such groups whose security relies respectively on the RSA and the factoring assumptions. Then, we show that static trapdoor DDH groups yield elementary constructions of convertible undeniable signature schemes allowing delegatable verification. Using our constructions of static trapdoor DDH groups from the RSA or the factoring assumption, we obtain slightly simpler variants of the undeniable signature schemes of respectively Gennaro, Rabin, and Krawczyk (J. Cryptology, 2000) and Galbraith and Mao (CT-RSA 2003). These new schemes are conceptually more satisfying since they can strictly be viewed as instantiations, in an adequate group, of the original undeniable signature scheme of Chaum and van Antwerpen (CRYPTO~\u2789)

New Constructions of Convertible Undeniable Signature Schemes without Random Oracles

In Undeniable Signature, a signature\u27s validity can only be confirmed or disavowed with the help of an alleged signer via a confirmation or disavowal protocol. A Convertible undeniable signature further allows the signer to release some additional information which can make an undeniable signature become publicly verifiable. In this work we introduce a new kind of attacks, called \emph{claimability attacks}, in which a dishonest/malicious signer both disavows a signature via the disavowal protocol and confirms it via selective conversion. Conventional security requirement does not capture the claimability attacks. We show that some convertible undeniable signature schemes are vulnerable to this kind of attacks. We then propose a new efficient construction of fully functional convertible undeniable signature, which supports both selective conversion and universal conversion, and is immune to the claimability attacks. To the best of our knowledge, it is the most efficient convertible undeniable signature scheme with provable security in the standard model. A signature is comprised of three elements of a bilinear group. Both the selective converter of a signature and the universal converter consist of one group element only. Besides, the confirmation and disavowal protocols are also very simple and efficient. Furthermore, the scheme can be extended to support additional features which include the delegation of conversion and confirmation/disavowal, threshold conversion and etc. We also propose an alternative generic construction of convertible undeniable signature schemes. Unlike the conventional sign-then-encrypt paradigm, the signer encrypts its (standard) signature with an identity-based encryption instead of a public key encryption. It enjoys the advantage of short selective converter, which is simply an identity-based user private key, and security against claimability attacks