Magda Valls

Sensor networks and distributed CSP: communication, computation and complexity

We introduce SensorDCSP, a naturally distributed benchmark based on a real-world application that arises in the context of networked distributed systems. In order to study the performance of Distributed CSP (DisCSP) algorithms in a truly distributed setting, we use a discrete-event network simulator, which allows us to model the impact of different network traffic conditions on the performance of the algorithms. We consider two complete DisCSP algorithms: asynchronous backtracking (ABT) and asynchronous weak commitment search (AWC), and perform performance comparison for these algorithms on both satisfiable and unsatisfiable instances of SensorDCSP. We found that random delays (due to network traffic or in some cases actively introduced by the agents) combined with a dynamic decentralized restart strategy can improve the performance of DisCSP algorithms. In addition, we introduce GSensorDCSP, a plain-embedded version of SensorDCSP that is closely related to various real-life dynamic tracking systems. We perform both analytical and empirical study of this benchmark domain. In particular, this benchmark allows us to study the attractiveness of solution repairing for solving a sequence of DisCSPs that represent the dynamic tracking of a set of moving objects.

A secure elliptic curve-based RFID protocol

Nowadays, the use of Radio Frequency Identification (RFID) systems in industry and stores has increased. Nevertheless, some of these systems present privacy problems that may discourage potential users. Hence, high confidence and effient privacy protocols are urgently needed. Previous studies in the literature proposed schemes that are proven to be secure, but they have scalability problems. A feasible and scalable protocol to guarantee privacy is presented in this paper. The proposed protocol uses elliptic curve cryptography combined with a zero knowledge-based authentication scheme. An analysis to prove the system secure, and even forward secure is also provided.

Determining the 2-Sylow subgroup of an elliptic curve over a finite field

In this paper we describe an algorithm that outputs the order and the structure, including generators, of the 2-Sylow subgroup of an elliptic curve over a finite field. To do this, we do not assume any knowledge of the group order. The results that lead to the design of this algorithm are of inductive type. Then a right choice of points allows us to reach the end within a linear number of successive halvings. The algorithm works with abscissas, so that halving of rational points in the elliptic curve becomes computing of square roots in the finite field. Efficient methods for this computation determine the efficiency of our algorithm.

An algorithm to compute volcanoes of 2-isogenies of elliptic curves over finite fields

The goal of this paper is presenting an algorithm to determine the structure of the volcano of 2-isogenies of a given elliptic curve over a finite field. The core of the algorithm relies on the relationship between the 2-torsion structure of the curves and its level in the volcano, as well as on those results that determine the direction of the different outgoing isogenies from each vertex. The algorithm is specially efficient for the so-called regular volcanoes, where the 2-torsion structure is different at every level.

Computing the height of volcanoes of ℓ-isogenies of elliptic curves over finite fields

The structure of the volcano of l-isogenies, l-prime, of elliptic curves over finite fields has been extensively studied over recent years. Previous works present some results and algorithms concerning the height of such volcanoes in the case of isogenies whose kernels are generated by a rational point. The main goal of this paper is to extend such works to the case of l-isogenies whose kernels are defined by a rational subgroup. In particular, the height of such volcanoes is completely characterized and can be computationally obtained.

Computing the ℓ-power torsion of an elliptic curve over a finite field

The algorithm we develop outputs the order and the structure, including generators, of the l-Sylow subgroup of the group of rational points of an elliptic curve defined over a finite field. To do this, we do not assume any knowledge of the group order. We are able to choose points in such a way that a linear number of successive l-divisions leads to generators of the subgroup under consideration. After the computation of a couple of polynomials, each division step relies on finding rational roots of polynomials of degree l. We specify in complete detail the case l = 3, when the complexity of each trisection is given by the computation of cubic roots in finite fields.

Parallel calculation of volcanoes for cryptographic uses

Elliptic curve crypto systems are nowadays widely used in the design of many security devices. Nevertheless, since not every elliptic curve is useful for cryptographic purposes, mechanisms for providing good curves are highly needed. The generation of the volcano graph of elliptic curves can help to provide such good curves. However, this procedure turns out to be very expensive when performed sequentially. Hence, a parallel application for the calculation of such volcano graphs is proposed in this paper. In order to obtain high efficiency, a theoretical analysis is provided for obtaining an accurate granularity and for giving the appropriate number of tasks to be created. Experimental results show the benefits obtained in the speedup when executing the application in a cluster of workstations with message-passing for the generation of different volcano graphs. By the use of simulation, we study the scalability of the implementation and show that a speedup of more than 80 can be achieved in some cases

Efficient smart metering based on homomorphic encryption

Abstract Smart meters send fine-grained client electricity consumption readings to suppliers. Although this presents advantages for both entities, it results in a serious loss of privacy for customers. We present a monitoring-purpose system that preserves customers’ privacy by homomorphically aggregating the consumptions of all n members of a neighborhood. The proposal has an efficient linear O(n) communication cost and is proven to preserve customers’ privacy even in the presence of a corrupted substation and some malicious smart meters. It requires neither secure communication channels nor a trusted third party (except for issuing public-key certificates). Computation on the smart meters is limited to modular exponentiations. These favorable properties come at the expense of increased computation cost on the electricity suppliers’ side. We show that the computation is easily feasible for realistic parameter choices.

On Avoiding ZVP-Attacks Using Isogeny Volcanoes

The usage of elliptic curve cryptography in smart cards has been shown to be efficient although, when considering curves, one should take care about their vulnerability against the Zero-Value Point Attacks (ZVP). In this paper, we present a new procedure to find elliptic curves which are resistant against these attacks. This algorithm finds, in an efficient way, a secure curve by means of volcanoes of isogenies. Moreover, we can deal with one more security condition than Akishita-Takagi method with our search.

Constructing credential-based E-voting systems from offline E-coin protocols

Abstract Mu and Varadharajan proposed a remote voting paradigm in which participants receive a blindly signed voting credential that permits them to cast a vote anonymously. If some participant tries to cheat by submitting more than one vote, her anonymity will be lifted. In the last years, several proposals following this paradigm, including Mu and Varadharajan׳s, have been shown to be cryptographically weak. In this paper we first show that a recent proposal by Baseri et al. is also weak. After that, we give a general construction that, employing an offline e-coin protocol as a building block, provides an anonymous voting system following the aforementioned paradigm.