Improved Structure Preserving Signatures under Standard Bilinear Assumptions

We show that the recent structure-preserving signature (SPS) scheme of Kiltz, Pan and Wee [CRYPTO 2015], provably secure under the standard bilinear pairings group assumption SXDH, can be improved to have one less group element and one less pairing product equation in the signature verification step. Our improved SPS scheme only requires six group elements (five in one group, and one in the other), and two pairing product equations for verification. The number of pairing product equations is optimal, as it matches a known lower bound of Abe et al [CRYPTO 2011]. The number of group elements in the signature also approaches the known lower bound of four for SXDH assumption. Further, while the earlier scheme had a security reduction which incurred a security loss that is quadratic in number of queries $Q$, our novel security reduction incurs only a $Q \log{Q}$ factor loss in security. Structure-preserving signatures are used pervasively in group signatures, group encryptions, blind signatures, proxy signatures and many other anonymous credential applications. Our work directly leads to improvements in these schemes. Moreover, the improvements are usually of a higher multiplicative factor order, as these constructions use Groth-Sahai NIZK proofs for zero-knowledge verification of pairing-product equations. We also give our construction under the more general and standard \D_k-MDDH (Matrix-DDH) assumption. The signature size in our scheme is $3k+2$ elements in one group, and one element in the other. The number of pairing product equations required for verification is only $2k$, whereas the earlier schemes required at least $2k+1$ equations

Improved (Almost) Tightly-Secure Simulation-Sound QA-NIZK with Applications

We construct the first (almost) tightly-secure unbounded-simulation-sound quasi-adaptive non-interactive zero-knowledge arguments (USS-QA-NIZK) for linear-subspace languages with compact (number of group elements independent of the security parameter) common reference string (CRS) and compact proofs under standard assumptions in bilinear-pairings groups. Specifically, our construction has $O(\log Q)$ reduction to the SXDH, DLIN and matrix-DDH assumptions, where $Q$ is the number of simulated proofs given out. The USS-QA-NIZK primitive has many applications, including structure-preserving signatures (SPS), CCA2-secure publicly-verifiable public-key encryption (PKE), which in turn have applications to CCA-anonymous group signatures, blind signatures and unbounded simulation-sound Groth-Sahai NIZK proofs. We show that the almost tight security of our USS-QA-NIZK translates into constructions of all of the above applications with (almost) tight-security to standard assumptions such as SXDH and, more generally, \D_k-MDDH. Thus, we get the first publicly-verifiable (almost) tightly-secure multi-user/multi-challenge CCA2-secure PKE with practical efficiency under standard bilinear assumptions. Our (almost) tight SPS construction is also improved in the signature size over previously known constructions

Still Wrong Use of Pairings in Cryptography

Several pairing-based cryptographic protocols are recently proposed with a wide variety of new novel applications including the ones in emerging technologies like cloud computing, internet of things (IoT), e-health systems and wearable technologies. There have been however a wide range of incorrect use of these primitives. The paper of Galbraith, Paterson, and Smart (2006) pointed out most of the issues related to the incorrect use of pairing-based cryptography. However, we noticed that some recently proposed applications still do not use these primitives correctly. This leads to unrealizable, insecure or too inefficient designs of pairing-based protocols. We observed that one reason is not being aware of the recent advancements on solving the discrete logarithm problems in some groups. The main purpose of this article is to give an understandable, informative, and the most up-to-date criteria for the correct use of pairing-based cryptography. We thereby deliberately avoid most of the technical details and rather give special emphasis on the importance of the correct use of bilinear maps by realizing secure cryptographic protocols. We list a collection of some recent papers having wrong security assumptions or realizability/efficiency issues. Finally, we give a compact and an up-to-date recipe of the correct use of pairings.Comment: 25 page

Efficient distributed tag-based encryption and its application to group signatures with efficient distributed traceability

In this work, we first formalize the notion of dynamic group signatures with distributed traceability, where the capability to trace signatures is distributed among n managers without requiring any interaction. This ensures that only the participation of all tracing managers permits tracing a signature, which reduces the trust placed in a single tracing manager. The threshold variant follows easily from our definitions and constructions. Our model offers strong security requirements. Our second contribution is a generic construction for the notion which has a concurrent join protocol, meets strong security requirements, and offers efficient traceability, i.e. without requiring tracing managers to produce expensive zero-knowledge proofs for tracing correctness. To dispense with the expensive zero-knowledge proofs required in the tracing, we deploy a distributed tag-based encryption with public verifiability. Finally, we provide some concrete instantiations, which, to the best of our knowledge, are the first efficient provably secure realizations in the standard model simultaneously offering all the aforementioned properties. To realize our constructions efficiently, we construct an efficient distributed (and threshold) tag-based encryption scheme that works in the efficient Type-III asymmetric bilinear groups. Our distributed tag-based encryption scheme yields short ciphertexts (only 1280 bits at 128-bit security), and is secure under an existing variant of the standard decisional linear assumption. Our tag-based encryption scheme is of independent interest and is useful for many applications beyond the scope of this paper. As a special case of our distributed tag-based encryption scheme, we get an efficient tag-based encryption scheme in Type-III asymmetric bilinear groups that is secure in the standard model

Reusable mesh signature scheme for protecting identity privacy of IoT devices

Peer reviewedPublisher PD

Research on security and privacy in vehicular ad hoc networks

Los sistemas de redes ad hoc vehiculares (VANET) tienen como objetivo proporcionar una plataforma para diversas aplicaciones que pueden mejorar la seguridad vial, la eficiencia del tráfico, la asistencia a la conducción, la regulación del transporte, etc. o que pueden proveer de una mejor información y entretenimiento a los usuarios de los vehículos. Actualmente se está llevando a cabo un gran esfuerzo industrial y de investigación para desarrollar un mercado que se estima alcance en un futuro varios miles de millones de euros. Mientras que los enormes beneficios que se esperan de las comunicaciones vehiculares y el gran número de vehículos son los puntos fuertes de las VANET, su principal debilidad es la vulnerabilidad a los ataques contra la seguridad y la privacidad.En esta tesis proponemos cuatro protocolos para conseguir comunicaciones seguras entre vehículos. En nuestra primera propuesta empleamos a todas las unidades en carretera (RSU) para mantener y gestionar un grupo en tiempo real dentro de su rango de comunicación. Los vehículos que entren al grupo de forma anónima pueden emitir mensajes vehículo a vehículo (V2V) que inmediatamente pueden ser verificados por los vehículos del mismo grupo (y grupos de vecinos). Sin embargo, en la primera fase del despliegue de este sistema las RSU pueden no estar bien distribuídas. Consecuentemente, se propone un conjunto de mecanismos para hacer frente a la seguridad, privacidad y los requisitos de gestión de una VANET a gran escala sin la suposición de que las RSU estén densamente distribuidas. La tercera propuesta se centra principalmente en la compresión de las evidencias criptográficas que nos permitirán demostrar, por ejemplo, quien era el culpable en caso de accidente. Por último, investigamos los requisitos de seguridad de los sistemas basados en localización (LBS) sobre VANETs y proponemos un nuevo esquema para la preservación de la privacidad de la localización en estos sistemas sobre dichas redes.Vehicular ad hoc network (VANET) systems aim at providing a platform for various applications that can improve traffic safety and efficiency, driver assistance, transportation regulation, infotainment, etc. There is substantial research and industrial effort to develop this market. It is estimated that the market for vehicular communications will reach several billion euros. While the tremendous benefits expected from vehicular communications and the huge number of vehicles are strong points of VANETs, their weakness is vulnerability to attacks against security and privacy.In this thesis, we propose four protocols for secure vehicle communications. In our first proposal, we employ each road-side unit (RSU) to maintain and manage an on-the-fly group within its communication range. Vehicles entering the group can anonymously broadcast vehicle-to-vehicle (V2V) messages, which can be instantly verified by the vehicles in the same group (and neighbor groups). However, at the early stage of VANET deployment, the RSUs may not be well distributed. We then propose a set of mechanisms to address the security, privacy, and management requirements of a large-scale VANET without the assumption of densely distributed RSUs. The third proposal is mainly focused on compressing cryptographic witnesses in VANETs. Finally, we investigate the security requirements of LBS in VANETs and propose a new privacy-preserving LBS scheme for those networks

Automated Analysis in Generic Groups

This thesis studies automated methods for analyzing hardness assumptions in generic group models, following ideas of symbolic cryptography. We define a broad class of generic and symbolic group models for different settings---symmetric or asymmetric (leveled) k-linear groups - and prove \u27\u27computational soundness\u27\u27 theorems for the symbolic models. Based on this result, we formulate a master theorem that relates the hardness of an assumption to solving problems in polynomial algebra. We systematically analyze these problems identifying different classes of assumptions and obtain decidability and undecidability results. Then, we develop automated procedures for verifying the conditions of our master theorems, and thus the validity of hardness assumptions in generic group models. The concrete outcome is an automated tool, the Generic Group Analyzer, which takes as input the statement of an assumption, and outputs either a proof of its generic hardness or shows an algebraic attack against the assumption. Structure-preserving signatures are signature schemes defined over bilinear groups in which messages, public keys and signatures are group elements, and the verification algorithm consists of evaluating \u27\u27pairing-product equations\u27\u27. Recent work on structure-preserving signatures studies optimality of these schemes in terms of the number of group elements needed in the verification key and the signature, and the number of pairing-product equations in the verification algorithm. While the size of keys and signatures is crucial for many applications, another aspect of performance is the time it takes to verify a signature. The most expensive operation during verification is the computation of pairings. However, the concrete number of pairings is not captured by the number of pairing-product equations considered in earlier work. We consider the question of what is the minimal number of pairing computations needed to verify structure-preserving signatures. We build an automated tool to search for structure-preserving signatures matching a template. Through exhaustive search we conjecture lower bounds for the number of pairings required in the Type~II setting and prove our conjecture to be true. Finally, our tool exhibits examples of structure-preserving signatures matching the lower bounds, which proves tightness of our bounds, as well as improves on previously known structure-preserving signature schemes

Conjugate points and Maslov index in locally symmetric semi-Riemannian manifolds

We study the singularities of the exponential map in semi Riemannian locally symmetric manifolds. Conjugate points along geodesics depend only on real negative eigenvalues of the curvature tensor, and their contribution to the Maslov index of the geodesic is computed explicitly. We prove that degeneracy of conjugate points, which is a phenomenon that can only occur in semi-Riemannian geometry, is caused in the locally symmetric case by the lack of diagonalizability of the curvature tensor. The case of Lie groups endowed with a bi-invariant metric is studied in some detail, and conditions are given for the lack of local injectivity of the exponential map around its singularities.Comment: LaTeX2e, 27 page