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

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

Design and Analysis of Opaque Signatures

Digital signatures were introduced to guarantee the authenticity and integrity of the underlying messages. A digital signature scheme comprises the key generation, the signature, and the verification algorithms. The key generation algorithm creates the signing and the verifying keys, called also the signer’s private and public keys respectively. The signature algorithm, which is run by the signer, produces a signature on the input message. Finally, the verification algorithm, run by anyone who knows the signer’s public key, checks whether a purported signature on some message is valid or not. The last property, namely the universal verification of digital signatures is undesirable in situations where the signed data is commercially or personally sensitive. Therefore, mechanisms which share most properties with digital signatures except for the universal verification were invented to respond to the aforementioned need; we call such mechanisms “opaque signatures”. In this thesis, we study the signatures where the verification cannot be achieved without the cooperation of a specific entity, namely the signer in case of undeniable signatures, or the confirmer in case of confirmer signatures; we make three main contributions. We first study the relationship between two security properties important for public key encryption, namely data privacy and key privacy. Our study is motivated by the fact that opaque signatures involve always an encryption layer that ensures their opacity. The properties required for this encryption vary according to whether we want to protect the identity (i.e. the key) of the signer or hide the validity of the signature. Therefore, it would be convenient to use existing work about the encryption scheme in order to derive one notion from the other. Next, we delve into the generic constructions of confirmer signatures from basic cryptographic primitives, e.g. digital signatures, encryption, or commitment schemes. In fact, generic constructions give easy-to-understand and easy-to-prove schemes, however, this convenience is often achieved at the expense of efficiency. In this contribution, which constitutes the core of this thesis, we first analyze the already existing constructions; our study concludes that the popular generic constructions of confirmer signatures necessitate strong security assumptions on the building blocks, which impacts negatively the efficiency of the resulting signatures. Next, we show that a small change in these constructionsmakes these assumptions drop drastically, allowing as a result constructions with instantiations that compete with the dedicated realizations of these signatures. Finally, we revisit two early undeniable signatures which were proposed with a conjectural security. We disprove the claimed security of the first scheme, and we provide a fix to it in order to achieve strong security properties. Next, we upgrade the second scheme so that it supports a iii desirable feature, and we provide a formal security treatment of the new scheme: we prove that it is secure assuming new reasonable assumptions on the underlying constituents