4 research outputs found

    An FPGA-based programmable processor for bilinear pairings

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    Bilinear pairings on elliptic curves are an active research field in cryptography. First cryptographic protocols based on bilinear pairings were proposed by the year 2000 and they are promising solutions to security concerns in different domains, as in Pervasive Computing and Cloud Computing. The computation of bilinear pairings that relies on arithmetic over finite fields is the most time-consuming in Pairing-based cryptosystems. That has motivated the research on efficient hardware architectures that improve the performance of security protocols. In the literature, several works have focused in the design of custom hardware architectures for pairings, however, flexible designs provide advantages due to the fact that there are several types of pairings and algorithms to compute them. This work presents the design and implementation of a novel programmable cryptoprocessor for computing bilinear pairings over binary fields in FPGAs, which is able to support different pairing algorithms and parameters as the elliptic curve, the tower field and the distortion map. The results show that high flexibility is achieved by the proposed cryptoprocessor at a competitive timing and area usage when it is compared to custom designs for pairings defined over singular/supersingular elliptic curves at a 128-bit security level

    Security of Prime Field Pairing Cryptoprocessor Against Differential Power Attack

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    This paper deals with the differential power attack on a pairing cryptoprocessor. The cryptoprocessor is designed for pairing computations on elliptic curves defined over finite fields with large prime characteristic. The work pinpoints the vulnerabilities of such pairing computations against side-channel attacks. By exploiting the power consumptions, the paper experimentally demonstrates such vulnerability on FPGA platform. A suitable counteracting technique is also suggested to overcome such vulnerability

    Hardware processors for pairing-based cryptography

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    Bilinear pairings can be used to construct cryptographic systems with very desirable properties. A pairing performs a mapping on members of groups on elliptic and genus 2 hyperelliptic curves to an extension of the finite field on which the curves are defined. The finite fields must, however, be large to ensure adequate security. The complicated group structure of the curves and the expensive field operations result in time consuming computations that are an impediment to the practicality of pairing-based systems. The Tate pairing can be computed efficiently using the ɳT method. Hardware architectures can be used to accelerate the required operations by exploiting the parallelism inherent to the algorithmic and finite field calculations. The Tate pairing can be performed on elliptic curves of characteristic 2 and 3 and on genus 2 hyperelliptic curves of characteristic 2. Curve selection is dependent on several factors including desired computational speed, the area constraints of the target device and the required security level. In this thesis, custom hardware processors for the acceleration of the Tate pairing are presented and implemented on an FPGA. The underlying hardware architectures are designed with care to exploit available parallelism while ensuring resource efficiency. The characteristic 2 elliptic curve processor contains novel units that return a pairing result in a very low number of clock cycles. Despite the more complicated computational algorithm, the speed of the genus 2 processor is comparable. Pairing computation on each of these curves can be appealing in applications with various attributes. A flexible processor that can perform pairing computation on elliptic curves of characteristic 2 and 3 has also been designed. An integrated hardware/software design and verification environment has been developed. This system automates the procedures required for robust processor creation and enables the rapid provision of solutions for a wide range of cryptographic applications

    Physical attacks on pairing-based cryptography

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    In dieser Dissertation analysieren wir Schwächen paarungsbasierter kryptographischer Verfahren gegenüber physikalischen Angriffen wie Seitenkanalangriffen und Fehlerangriffen. Verglichen mit weitverbreiteten Primitiven, beispielsweise basierend auf elliptischen Kurven, ist noch relativ wenig über Angriffsmöglichkeiten aufpaarungsbasierte Verfahren bekannt. Ein Grund dafür ist die hohe Komplexität paarungsbasierter Kryptographie und fehlende Standards für die Festlegung von Parametern, Algorithmen und Verfahren. Des Weiteren läßt sich Wissen aus dem Zusammenhang mit elliptischen Kurven aufgrundstruktureller Unterschiede nicht direkt übertragen. Um ein besseres Verständnis des Problems zu erlangen, präsentieren wir in dieser Arbeit neue physikalische Angriffe auf paarungsbasierte Kryptographie. Unsere Ergebnisse, einschließlich deren praktische Umsetzung, machen deutlich, dass physikalische Angriffe eine Gefahr für die Implementierung paarungsbasierter kryptographischer Verfahren darstellen. Diese Gefahr sollte weiter untersucht und bei der Realisierung dieser Verfahren berücksichtig werden. Weiterhin zeigen unsere Ergebnisse, dass eine Einigung über verwendete Parameter, Algorithmen und Verfahren erzielt werden sollte, um die Komplexität von paarungsbasierter Kryptographie hinischtlich physikalische rAngriffe zu vermindern.In this thesis, we analyze the vulnerability of pairing-based cryptographic schemes against physical attacks like side-channel attacks (SCAs) or fault attacks (FAs). Compared to well-established cryptographic schemes, for example, from standard elliptic curve cryptography (ECC), less is known about weaknesses of pairing-based cryptography (PBC) against those attacks. Reasons for this shortcoming are the complexity of PBC and a missing consensus on parameters, algorithms, and schemes,e.g., in the form of standards. Furthermore, the structural difference between ECC and PBC prevents a direct application of the results from ECC. To get a better understanding of the subject, we present new physical attacks on PBC. Our results, including the practical realizations of our attacks, show that physical attacks are a threat for PBC and need further investigation. Our work also shows that the community should agree on parameters, algorithms, and schemes to reduce the complexity of PBC with respect to physical attacks.Peter Günther ; Supervisor: Prof. Dr. rer. nat. Johannes BlömerTag der Verteidigung: 14.03.2016Universität Paderborn, Univ., Dissertation, 201
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