A Framework for Efficient Signatures, Ring Signatures and Identity Based Encryption in the Standard Model

In this work, we present a generic framework for constructing efficient signature schemes, ring signature schemes, and identity based encryption schemes, all in the standard model (without relying on random oracles). We start by abstracting the recent work of Hohenberger and Waters (Crypto 2009), and specifically their ``prefix method\u27\u27. We show a transformation taking a signature scheme with a very weak security guarantee (a notion that we call a-priori-message unforgeability under static chosen message attack) and producing a fully secure signature scheme (i.e., existentially unforgeable under adaptive chosen message attack). Our transformation uses the notion of chameleon hash functions, defined by Krawczyk and Rabin (NDSS 2000) and the ``prefix method\u27\u27. Constructing such weakly secure schemes seems to be significantly easier than constructing fully secure ones, and we present {\em simple} constructions based on the RSA assumption, the {\em short integer solution} (SIS) assumption, and the {\em computational Diffie-Hellman} (CDH) assumption over bilinear groups. Next, we observe that this general transformation also applies to the regime of ring signatures. Using this observation, we construct new (provably secure) ring signature schemes: one is based on the {\em short integer solution} (SIS) assumption, and the other is based on the CDH assumption over bilinear groups. As a building block for these constructions, we define a primitive that we call \emph{ring trapdoor functions}. We show that ring trapdoor functions imply ring signatures under a weak definition, which enables us to apply our transformation to achieve full security. Finally, we show a connection between ring signature schemes and identity based encryption (IBE) schemes. Using this connection, and using our new constructions of ring signature schemes, we obtain two IBE schemes: The first is based on the {\em learning with error} (LWE) assumption, and is similar to the recently introduced IBE scheme of Cash-Hofheinz-Kiltz-Peikert; The second is based on the $d$-linear assumption over bilinear groups

Short Group Signatures via Structure-Preserving Signatures: Standard Model Security from Simple Assumptions

International audienceGroup signatures are a central cryptographic primitive which allows users to sign messages while hiding their identity within a crowd of group members. In the standard model (without the random oracle idealization), the most efficient constructions rely on the Groth-Sahai proof systems (Euro-crypt'08). The structure-preserving signatures of Abe et al. (Asiacrypt'12) make it possible to design group signatures based on well-established, constant-size number theoretic assumptions (a.k.a. " simple assumptions ") like the Symmetric eXternal Diffie-Hellman or Decision Linear assumptions. While much more efficient than group signatures built on general assumptions, these constructions incur a significant overhead w.r.t. constructions secure in the idealized random oracle model. Indeed, the best known solution based on simple assumptions requires 2.8 kB per signature for currently recommended parameters. Reducing this size and presenting techniques for shorter signatures are thus natural questions. In this paper, our first contribution is to significantly reduce this overhead. Namely, we obtain the first fully anonymous group signatures based on simple assumptions with signatures shorter than 2 kB at the 128-bit security level. In dynamic (resp. static) groups, our signature length drops to 1.8 kB (resp. 1 kB). This improvement is enabled by two technical tools. As a result of independent interest, we first construct a new structure-preserving signature based on simple assumptions which shortens the best previous scheme by 25%. Our second tool is a new method for attaining anonymity in the strongest sense using a new CCA2-secure encryption scheme which is simultaneously a Groth-Sahai commitment

Security Pitfalls of a Provably Secure Identity-based Multi-Proxy Signature Scheme

An identity-based multi-proxy signature is a type of proxy signatures in which the delegation of signing right is distributed among a number of proxy signers. In this type of cryptographic primitive, cooperation of all proxy signers in the proxy group generates the proxy signatures of roughly the same size as that of standard proxy signatures on behalf of the original signer, which is more efficient than transmitting individual proxy signatures. Since identity-based multi-proxy signatures are useful in distributed systems, grid computing, presenting a provably secure identity-based multi-proxy scheme is desired. In 2013, Sahu and Padhye proposed the first provably secure identity-based multi-proxy signature scheme in the random oracle model, and proved that their scheme is existential unforgeable against adaptive chosen message and identity attack. Unfortunately, in this paper, we show that their scheme is insecure. We present two forgery attacks on their scheme. Furthermore, their scheme is not resistant against proxy key exposure attack. As a consequence, there is no provably secure identity-based multi-proxy signature scheme secure against proxy key exposure attack to date

Membership Privacy for Fully Dynamic Group Signatures

Group signatures present a compromise between the traditional goals of digital signatures and the need for signer privacy, allowing for the creation of unforgeable signatures in the name of a group which reveal nothing about the actual signer's identity beyond their group membership. An important consideration that is absent in prevalent models is that group membership itself may be sensitive information, especially if group membership is dynamic, i.e. membership status may change over time. We address this issue by introducing formal notions of membership privacy for fully dynamic group signature schemes, which can be easily integrated into the most expressive models of group signature security to date. We then propose a generic construction for a fully dynamic group signature scheme with membership privacy that is based on signatures with flexible public key (SFPK) and signatures on equivalence classes (SPSEQ). Finally, we devise novel techniques for SFPK to construct a highly efficient standard model scheme (i.e. without random oracles) that provides shorter signatures than even the non-private state-of-the-art from standard assumptions. This shows that, although the strictly stronger security notions we introduce have been completely unexplored in the study of fully dynamic group signatures so far, they do not come at an additional cost in practice

Improved Lattice-based CCA2-Secure PKE in the Standard Model

Based on the identity-based encryption (IBE) from lattices by Agrawal et al. (Eurocrypt\u2710), Micciancio and Peikert (Eurocrypt\u2712) presented a CCA1-secure public-key encryption (PKE), which has the best known efficiency in the standard model and can be used to obtain a CCA2-secure PKE from lattices by using the generic BCHK transform (SIAM J. Comput., 2006) with a cost of introducing extra overheads to both computation and storage for the use of other primitives such as signatures and commitments. In this paper, we propose a more efficient standard model CCA2-secure PKE from lattices by carefully combining a different message encoding (which encodes the message into the most significant bits of the LWE\u27s ``secret term\u27\u27) with several nice algebraic properties of the tag-based lattice trapdoor and the LWE problem (such as unique witness and additive homomorphism). Compared to the best known lattice-based CCA1-secure PKE in the standard model due to Micciancio and Peikert (Eurocrypt\u2712), we not only directly achieve the CCA2-security without using any generic transform (and thus do not use signatures or commitments), but also reduce the noise parameter roughly by a factor of 3. This improvement makes our CCA2-secure PKE more efficient in terms of both computation and storage. In particular, when encrypting a 256-bit (resp., 512-bit) message at 128-bit (resp., 256-bit) security, the ciphertext size of our CCA2-secure PKE is even 33-44% (resp., 36-46%) smaller than that of their CCA1-secure PKE

One-round strong oblivious signature-based envelope

Oblivious Signature-Based Envelope (OSBE) has been widely employed for anonymity-orient and privacy-preserving applications. The conventional OSBE execution relies on a secure communication channel to protect against eavesdroppers. In TCC 2012, Blazy, Pointcheval and Vergnaud proposed a framework of OSBE (BPV-OSBE) without requiring any secure channel by clarifying and enhancing the OSBE security notions. They showed how to generically build an OSBE scheme satisfying the new strong security in the standard model with a common-reference string. Their framework requires 2-round interactions and relies on the smooth projective hash function (SPHF) over special languages, i.e., languages from encryption of signatures. In this work, we investigate the study on the strong OSBE and make the following contributions. First, we propose a generic construction of one-round yet strong OSBE system. Compared to the 2-round BPV-OSBE, our one-round construction is more appealing, as its noninteractive setting accommodates more application scenarios in the real word. Moreover, our framework relies on the regular (identity-based) SPHF, which can be instantiated from extensive languages and hence is more general. Second, we also present an efficient instantiation, which is secure under the standard model from classical assumptions, DDH and DBDH, to illustrate the feasibility of our one-round framework. We remark that our construction is the first one-round OSBE with strong securit

Homomorphic Trapdoors for Identity-based and Group Signatures

Group signature (GS) schemes are an important primitive in cryptography that provides anonymity and traceability for a group of users. In this paper, we propose a new approach to constructing GS schemes using the homomorphic trapdoor function (HTDF). We focus on constructing an identity-based homomorphic signature (IBHS) scheme using the trapdoor, providing a simpler scheme that has no zero-knowledge proofs. Our scheme allows packing more data into the signatures by elevating the existing homomorphic trapdoor from the SIS assumption to the MSIS assumption to enable packing techniques. Compared to the existing group signature schemes, we provide a straightforward and alternate construction that is efficient and secure under the standard model. Overall, our proposed scheme provides an efficient and secure solution for GS schemes using HTDF

Maintaining unlinkability in group based P2P environments

In the wake of the success of Peer-to-Peer (P2P) networking, security has arisen as one of its main concerns, becoming a key issue when evaluating a P2P system. Unfortunately, some systems' design focus targeted issues such as scalabil-ity or overall performance, but not security. As a result, security mechanisms must be provided at a later stage, after the system has already been designed and partially (or even fully) implemented, which may prove a cumbersome proposition. This work exposes how a security layer was provided under such circumstances for a specic Java based P2P framework: JXTA-Overlay.Arran de l'èxit de (P2P) peer-to-peer, la seguretat ha sorgit com una de les seves principals preocupacions, esdevenint una qüestió clau en l'avaluació d'un sistema P2P. Malauradament, alguns sistemes de disseny apunten focus de problemes com l'escalabilitat o l'acompliment general, però no de seguretat. Com a resultat d'això, els mecanismes de seguretat s¿han de proporcionar en una etapa posterior, després que el sistema ja ha estat dissenyat i parcialment (o fins i tot totalment) implementat, la qual cosa pot ser una proposició incòmode. Aquest article exposa com es va proveir una capa de seguretat sota aquestes circumstàncies per un Java específic basat en un marc P2P: JXTA-superposició.A raíz del éxito de (P2P) peer-to-peer, la seguridad ha surgido como una de sus principales preocupaciones, convirtiéndose en una cuestión clave en la evaluación de un sistema P2P. Desgraciadamente, algunos sistemas de diseño apuntan un foco de problemas como la escalabilidad o el desempeño general, pero no de seguridad. Como resultado de ello, los mecanismos de seguridad se proporcionarán en una etapa posterior, después de que el sistema ya ha sido diseñado y parcialmente (o incluso totalmente) implementado, lo que puede ser una proposición incómodo. Este artículo expone cómo se proveyó una capa de seguridad bajo estas circunstancias por un Java específico basado en un marco P2P: JXTA-superposición