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,...

Verifiable random functions (VRF) and selectively-convertible undeniable signature (SCUS) schemes were proposed independently in the literature. In this paper, we observe that they are tightly related. This directly yields several deterministic SCUS schemes based on existing VRF constructions. In addition, we create a new probabilistic SCUS scheme, which is very compact. The confirmation and disavowal protocols of these SCUS are efficient, and can be run either sequentially, concurrently, or...

In Undeniable Signature, a signature's 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...

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,...

This paper shows some efficient and provably-secure convertible undeniable signature schemes (with both selective conversion and all conversion), in the standard model and discrete logarithm setting. They further satisfy unambiguity, which is traditionally required for anonymous signatures. Briefly, unambiguity means that it is hard to generate a (message, signature) pair which is valid for two {\em different} public-keys. In other words, our schemes can be viewed as anonymous signature...

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...

We propose a convertible undeniable signature scheme without random oracles. Our construction is based on Waters' and Kurosawa and Heng's 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.

Verifiable Pairing and its Applications. In Chae Hoon Lim and Moti Yung, editors, Information Security Applications: 5th International Workshop, WISA 2004, Jeju Island, Korea, August 23-25, 2004, Revised Selected Papers, volume 3325 of Lecture Notes in Computer Science, pp. 170-187. (http://www.springerlink.com/index/C4QB7C13NL0EY5VN) which contains an improved and generalized result of this paper.