Universally Convertible Directed Signatures

Many variants of Chaum and van Antwerpen's undeniable signatures have been proposed to achieve specific properties desired in real-world applications of cryptography. Among them, directed signatures were introduced by Lim and Lee in 1993. Directed signatures differ from the well-known confirmer signatures in that the signer has the simultaneous abilities to confirm, deny and individually convert a signature. The universal conversion of these signatures has remained an open problem since their introduction in 1993. This paper provides a positive answer to this quest by showing a very efficient design for universally convertible directed signatures (UCDS) both in terms of computational complexity and signature size. Our construction relies on the so-called xyz-trick applicable to bilinear map groups. We define proper security notions for UCDS schemes and show that our construction is secure, in the random oracle model, under computational assumptions close to the CDH and DDH assumptions. Finally, we introduce and realize traceable universally convertible directed signatures where a master tracing key allows to link signatures to their direction

An efficient ID- based directed signature scheme from bilinear pairings

A directed signature scheme allows a designated verifier to directly verify a signature issued to him, and a third party to check the signature validity with the help of the signer or the designated verifier as well. Directed signatures are applicable where the signed message is sensitive to the signature receiver. Due to its merits, directed signature schemes are suitable for applications such as bill of tax and bill of health. In this paper, we proposed an efficient identity based directed signature scheme from bilinear pairings. Our scheme is efficient than the existing directed signature schemes. In the random oracle model, our scheme is unforgeable under the Computational Diffie-Hellman (CDH) assumption, and invisible under the Decisional Bilinear Diffie-Hellman (DBDH)

Identity-Based Directed Signature Scheme from Bilinear Pairings

In a directed signature scheme, a verifier can exclusively verify the signatures designated to himself, and shares with the signer the ability to prove correctness of the signature to a third party when necessary. Directed signature schemes are suitable for applications such as bill of tax and bill of health. This paper studies directed signatures in the identity-based setting. We first present the syntax and security notion that includes unforgeability and invisibility, then propose a concrete identity-based directed signature scheme from bilinear pairings. We then prove our scheme existentially unforgeable under the computational Diffie-Hellman assumption, and invisible under the decisional Bilinear Diffie-Hellman assumption, both in the random oracle model

Matrix computational assumptions in multilinear groups

We put forward a new family of computational assumptions, the Kernel Matrix Di e- Hellman Assumption. Given some matrix A sampled from some distribution D `;k , the kernel as- sumption says that it is hard to nd \in the exponentPreprin

Matrix Computational Assumptions in Multilinear Groups

We put forward a new family of computational assumptions, the Kernel Matrix Diffie-Hellman Assumption. Given some matrix $\mathbf{A}$ sampled from some distribution $\mathcal{D}$, the kernel assumption says that it is hard to find in the exponent a nonzero vector in the kernel of $\mathbf{A}^\top$. This family is the natural computational analogue of the Matrix Decisional Diffie-Hellman Assumption (MDDH), proposed by Escala et al. As such it allows to extend the advantages of their algebraic framework to computational assumptions. The $k$-Decisional Linear Assumption is an example of a family of decisional assumptions of strictly increasing hardness when $k$ grows. We show that for any such family of MDDH assumptions, the corresponding Kernel assumptions are also strictly increasingly weaker. This requires ruling out the existence of some black-box reductions between flexible problems (i.e., computational problems with a non unique solution)

Universally Convertible Directed Signatures

Many variants of Chaum and van Antwerpen's undeniable signatures have been proposed to achieve specific properties desired in real-world applications of cryptography. Among them, directed signatures were introduced by Lim and Lee in 1993. Directed signatures di#er from the well-known confirmer signatures in that the signer has the simultaneous abilities to confirm, deny and individually convert a signature. The universal conversion of these signatures has remained an open problem since their introduction in 1993. This paper provides a positive answer to this quest by showing a very e#cient design for universally convertible directed signatures (UCDS) both in terms of computational complexity and signature size. Our construction relies on the so-called xyz-trick applicable to bilinear map groups. We define proper security notions for UCDS schemes and show that our construction is secure in the random oracle model, under computational assumptions close to the CDH and DDH assumptions. Finally, we introduce and realize traceable universally convertible directed signatures where a master tracing key allows to link signatures to their direction