Algebraic Curves and Cryptographic Protocols for the e-society

Amb l'augment permanent de l'adopció de sistemes intel·ligents de tot tipus en la societat actual apareixen nous reptes. Avui en dia quasi tothom en la societat moderna porta a sobre almenys un telèfon intel·ligent, si no és que porta encara més dispositius capaços d'obtenir dades personals, com podria ser un smartwatch per exemple. De manera similar, pràcticament totes les cases tindran un comptador intel·ligent en el futur pròxim per a fer un seguiment del consum d'energia. També s'espera que molts més dispositius del Internet de les Coses siguin instal·lats de manera ubiqua, recol·lectant informació dels seus voltants i/o realitzant accions, com per exemple en sistemes d'automatització de la llar, estacions meteorològiques o dispositius per la ciutat intel·ligent en general. Tots aquests dispositius i sistemes necessiten enviar dades de manera segura i confidencial, les quals poden contindre informació sensible o de caire privat. A més a més, donat el seu ràpid creixement, amb més de nou mil milions de dispositius en tot el món actualment, s'ha de tenir en compte la quantitat de dades que cal transmetre. En aquesta tesi mostrem la utilitat de les corbes algebraiques sobre cossos finits en criptosistemes de clau pública, en particular la de les corbes de gènere 2, ja que ofereixen la mida de clau més petita per a un nivell de seguretat donat i això redueix de manera significativa el cost total de comunicacions d'un sistema, a la vegada que manté un rendiment raonable. Analitzem com la valoració 2-àdica del cardinal de la Jacobiana augmenta en successives extensions quadràtiques, considerant corbes de gènere 2 en cossos de característica senar, incloent les supersingulars. A més, millorem els algoritmes actuals per a computar la meitat d'un divisor d'una corba de gènere 2 sobre un cos binari, cosa que pot ser útil en la multiplicació escalar, que és l'operació principal en criptografia de clau pública amb corbes. Pel que fa a la privacitat, presentem un sistema de pagament d'aparcament per mòbil que permet als conductors pagar per aparcar mantenint la seva privacitat, i per tant impedint que el proveïdor del servei o un atacant obtinguin un perfil de conducta d'aparcament. Finalment, oferim protocols de smart metering millorats, especialment pel que fa a la privacitat i evitant l'ús de terceres parts de confiança.Con el aumento permanente de la adopción de sistemas inteligentes de todo tipo en la sociedad actual aparecen nuevos retos. Hoy en día prácticamente todos en la sociedad moderna llevamos encima al menos un teléfono inteligente, si no es que llevamos más dispositivos capaces de obtener datos personales, como podría ser un smartwatch por ejemplo. De manera similar, en el futuro cercano la mayoría de las casas tendrán un contador inteligente para hacer un seguimiento del consumo de energía. También se espera que muchos más dispositivos del Internet de las Cosas sean instalados de manera ubicua, recolectando información de sus alrededores y/o realizando acciones, como por ejemplo en sistemas de automatización del hogar, estaciones meteorológicas o dispositivos para la ciudad inteligente en general. Todos estos dispositivos y sistemas necesitan enviar datos de manera segura y confidencial, los cuales pueden contener información sensible o de ámbito personal. Además, dado su rápido crecimiento, con más de nueve mil millones de dispositivos en todo el mundo actualmente, hay que tener en cuenta la cantidad de datos a transmitir. En esta tesis mostreamos la utilidad de las curvas algebraicas sobre cuerpos finitos en criptosistemas de clave pública, en particular la de las curvas de género 2, ya que ofrecen el tamaño de clave más pequeño para un nivel de seguridad dado y esto disminuye de manera significativa el coste total de comunicaciones del sistema, a la vez que mantiene un rendimiento razonable. Analizamos como la valoración 2-ádica del cardinal de la Jacobiana aumenta en sucesivas extensiones cuadráticas, considerando curvas de género 2 en cuerpos de característica importa, incluyendo las supersingulares. Además, mejoramos los algoritmos actuales para computar la mitad de un divisor de una curva de género 2 sobre un cuerpo binario, lo cual puede ser útil en la multiplicación escalar, que es la operación principal en criptografía de clave pública con curvas. Respecto a la privacidad, presentamos un sistema de pago de aparcamiento por móvil que permite a los conductores pagar para aparcar manteniendo su privacidad, y por lo tanto impidiendo que el proveedor del servicio o un atacante obtengan un perfil de conducta de aparcamiento. Finalmente, ofrecemos protocolos de smart metering mejorados, especialmente en lo relativo a la privacidad y evitando el uso de terceras partes de confianza.With the ever increasing adoption of smart systems of every kind throughout society, new challenges arise. Nowadays, almost everyone in modern societies carries a smartphone at least, if not even more devices than can also gather personal data, like a smartwatch or a fitness wristband for example. Similarly, practically all homes will have a smart meter in the near future for billing and energy consumption monitoring, and many other Internet of Things devices are expected to be installed ubiquitously, obtaining information of their surroundings and/or performing some action, like for example, home automation systems, weather detection stations or devices for the smart city in general. All these devices and systems need to securely and privately transmit some data, which can be sensitive and personal information. Moreover, with a rapid increase of their number, with already more than nine billion devices worldwide, the amount of data to be transmitted has to be considered. In this thesis we show the utility of algebraic curves over finite fields in public key cryptosystems, specially genus 2 curves, since they offer the minimum key size for a given security level and that significantly reduces the total communication costs of a system, while maintaining a reasonable performance. We analyze how the 2-adic valuation of the cardinality of the Jacobian increases in successive quadratic extensions, considering genus 2 curves with odd characteristic fields, including supersingular curves. In addition, we improve the current algorithms for computing the halving of a divisor of a genus 2 curve over binary fields, which can be useful in scalar multiplication, the main operation in public key cryptography using curves. As regards to privacy, we present a pay-by-phone parking system which enables drivers to pay for public parking while preserving their privacy, and thus impeding the service provider or an attacker to obtain a profile of parking behaviors. Finally, we offer better protocols for smart metering, especially regarding privacy and the avoidance of trusted third parties

Cryptography for Bitcoin and friends

Numerous cryptographic extensions to Bitcoin have been proposed since Satoshi Nakamoto introduced the revolutionary design in 2008. However, only few proposals have been adopted in Bitcoin and other prevalent cryptocurrencies, whose resistance to fundamental changes has proven to grow with their success. In this dissertation, we introduce four cryptographic techniques that advance the functionality and privacy provided by Bitcoin and similar cryptocurrencies without requiring fundamental changes in their design: First, we realize smart contracts that disincentivize parties in distributed systems from making contradicting statements by penalizing such behavior by the loss of funds in a cryptocurrency. Second, we propose CoinShuffle++, a coin mixing protocol which improves the anonymity of cryptocurrency users by combining their transactions and thereby making it harder for observers to trace those transactions. The core of CoinShuffle++ is DiceMix, a novel and efficient protocol for broadcasting messages anonymously without the help of any trusted third-party anonymity proxies and in the presence of malicious participants. Third, we combine coin mixing with the existing idea to hide payment values in homomorphic commitments to obtain the ValueShuffle protocol, which enables us to overcome major obstacles to the practical deployment of coin mixing protocols. Fourth, we show how to prepare the aforementioned homomorphic commitments for a safe transition to post-quantum cryptography.Seit seiner revolutionären Erfindung durch Satoshi Nakamoto im Jahr 2008 wurden zahlreiche kryptographische Erweiterungen für Bitcoin vorgeschlagen. Gleichwohl wurden nur wenige Vorschläge in Bitcoin und andere weit verbreitete Kryptowährungen integriert, deren Resistenz gegen tiefgreifende Veränderungen augenscheinlich mit ihrer Verbreitung wächst. In dieser Dissertation schlagen wir vier kryptographische Verfahren vor, die die Funktionalität und die Datenschutzeigenschaften von Bitcoin und ähnlichen Kryptowährungen verbessern ohne deren Funktionsweise tiefgreifend verändern zu müssen. Erstens realisieren wir Smart Contracts, die es erlauben widersprüchliche Aussagen einer Vertragspartei mit dem Verlust von Kryptogeld zu bestrafen. Zweitens schlagen wir CoinShuffle++ vor, ein Mix-Protokoll, das die Anonymität von Benutzern verbessert, indem es ihre Transaktionen kombiniert und so deren Rückverfolgung erschwert. Sein Herzstück ist DiceMix, ein neues und effizientes Protokoll zur anonymen Veröffentlichung von Nachrichten ohne vertrauenswürdige Dritte und in der Präsenz von bösartigen Teilnehmern. Drittens kombinieren wir dieses Protokoll mit der existierenden Idee, Geldbeträge in Commitments zu verbergen, und erhalten so das ValueShuffle-Protokoll, das uns ermöglicht, große Hindernisse für den praktischen Einsatz von Mix-Protokollen zu überwinden. Viertens zeigen wir, wie die dabei benutzten Commitments für einen sicheren Übergang zu Post-Quanten-Kryptographie vorbereitet werden können

High Security by using Triple Wrapping Feature and their Comparison

In the age of information, cryptography is a predominant obligation for the security of our documents. Cryptography inclusive of authentication, integrity, confidentiality and non-repudiation has lot to offer. To protect users2019; information and their data from being attacked, encryption and digital signature algorithms could be utilized with distinct approaches to administer secure network and security solutions. In the current scenario, encryption alone cannot withstand the novel attacks; for notable security, we require encryption with digital signature. In this paper symmetric, asymmetric algorithm and digital signature techniques are proposed to elevate security. ElGamal encryption algorithm, ElGamal digital signature algorithm and IDEA algorithms are employed in the proposed methodology

Development of a certificate less digital signature scheme & implementation in e-cash system

Today’s wireless communication systems having limited computational resources and communication bandwidth find certificate less public-key cryptosystems very attractive and vital to their operations in the sense that they help in reducing a significant amount of data load on the network. To eliminate the need of public key digital certificates Shamir proposed ID based cryptosystems in which the user’s identity (e.g. name or email id) is used as the public key. However this method had a major drawback of the key escrow problem as a result of which certificate less digital signature (CDS) came into light. The main idea behind CDS is that there’s a private key generator (PKG) which generates a partial private key for the user .Then using that key and some of its own private information the user computes its actual private key. PKG’s public parameters and the user’s private key together calculate the user’s public key. Harn, Ren and Lin in 2008 proposed a CDS model which consisted of four generic modules namely PKG, user key generation, signature generation and verification. In this paper, we propose an improvement of the aforesaid CDS scheme in terms of time complexity and signature length and implement the new scheme in an e-cash model proposed by Popescu and Oros. Performance analysis of both the schemes has been carried out in details

A Practical Set-Membership Proof for Privacy-Preserving NFC Mobile Ticketing

To ensure the privacy of users in transport systems, researchers are working on new protocols providing the best security guarantees while respecting functional requirements of transport operators. In this paper, we design a secure NFC m-ticketing protocol for public transport that preserves users' anonymity and prevents transport operators from tracing their customers' trips. To this end, we introduce a new practical set-membership proof that does not require provers nor verifiers (but in a specific scenario for verifiers) to perform pairing computations. It is therefore particularly suitable for our (ticketing) setting where provers hold SIM/UICC cards that do not support such costly computations. We also propose several optimizations of Boneh-Boyen type signature schemes, which are of independent interest, increasing their performance and efficiency during NFC transactions. Our m-ticketing protocol offers greater flexibility compared to previous solutions as it enables the post-payment and the off-line validation of m-tickets. By implementing a prototype using a standard NFC SIM card, we show that it fulfils the stringent functional requirement imposed by transport operators whilst using strong security parameters. In particular, a validation can be completed in 184.25 ms when the mobile is switched on, and in 266.52 ms when the mobile is switched off or its battery is flat

Time stamped Digital Signature Scheme with Message Recovery & Its Application in E-Cash System

We propose a Timestamped signature scheme which can be verified universally using signer’s public parameters. A trusted third party, the Timestamping System provides timestamp to a signature without even knowing the content of the document. The proposed scheme can withstand active attacks, such as forgery attack and chosen cipher text attack. It also provides the message recovery feature, i.e., from the timestamped signature, the message can be recovered by the receiver. Hence, the message need not be sent with the signature. The suggested scheme do not require any hash function and there by reduces the verification cost as compared to existing schemes at the expense of marginal increase in signature generation cost. Further, the scheme is more secured as its security lies in solving three computationally hard assumptions Performance analysis of both the schemes has been carried out in details. We applied the Time-stamped signature scheme with Message recovery in Ecash syste

On the security of the Blockchain Bix Protocol and Certificates

The BIX protocol is a blockchain-based protocol that allows distribution of certificates linking a subject with his public key, hence providing a service similar to that of a PKI but without the need of a CA. In this paper we analyze the security of the BIX protocol in a formal way, in four steps. First, we identify formal security assumptions which are well-suited to this protocol. Second, we present some attack scenarios against the BIX protocol. Third, we provide a formal security proof that some of these attacks are not feasible under our previously established assumptions. Finally, we show how another attack may be carried on.Comment: 16 pages, 1 figur

Cryptography with anonymity in mind

Advances in information technologies gave a rise to powerful ubiquitous com- puting devices, and digital networks have enabled new ways of fast communication, which immediately found tons of applications and resulted in large amounts of data being transmitted. For decades, cryptographic schemes and privacy-preserving protocols have been studied and researched in order to offer end users privacy of their data and implement useful functionalities at the same time, often trading security properties for cryptographic assumptions and efficiency. In this plethora of cryptographic constructions, anonymity properties play a special role, as they are important in many real-life scenarios. However, many useful cryptographic primitives lack anonymity properties or imply prohibitive costs to achieve them. In this thesis, we expand the territory of cryptographic primitives with anonymity in mind. First, we define Anonymous RAM, a generalization of a single- user Oblivious RAM to multiple mistrusted users, and present two constructions thereof with different trade-offs between assumptions and efficiency. Second, we define an encryption scheme that allows to establish chains of ciphertexts anony- mously and verify their integrity. Furthermore, the aggregatable version of the scheme allows to build a Parallel Anonymous RAM, which enhances Anonymous RAM by supporting concurrent users. Third, we show our technique for construct- ing efficient non-interactive zero-knowledge proofs for statements that consist of both algebraic and arithmetic statements. Finally, we show our framework for constructing efficient single secret leader election protocols, which have been recently identified as an important component in proof-of-stake cryptocurrencies.Fortschritte in der Informationstechnik haben leistungsstarke allgegenwärtige Rechner hervorgerufen, während uns digitale Netzwerke neue Wege für die schnelle Kommunikation ermöglicht haben. Durch die Vielzahl von Anwendungen führte dies zur Übertragung von riesigen Datenvolumen. Seit Jahrzehnten wurden bereits verschiedene kryptographische Verfahren und Technologien zum Datenschutz erforscht und analysiert. Das Ziel ist die Privatsphäre der Benutzer zu schützen und gleichzeitig nützliche Funktionalität anzubieten, was oft mit einem Kompromiss zwischen Sicherheitseigenschaften, kryptographischen Annahmen und Effizienz verbunden ist. In einer Fülle von kryptographischen Konstruktionen spielen Anonymitätseigenschaften eine besondere Rolle, da sie in vielen realistischen Szenarien sehr wichtig sind. Allerdings fehlen vielen kryptographischen Primitive Anonymitätseigenschaften oder sie stehen im Zusammenhang mit erheblichen Kosten. In dieser Dissertation erweitern wir den Bereich von kryptographischen Prim- itiven mit einem Fokus auf Anonymität. Erstens definieren wir Anonymous RAM, eine Verallgemeinerung von Einzelbenutzer-Oblivious RAM für mehrere misstraute Benutzer, und stellen dazu zwei Konstruktionen mit verschiedenen Kompromissen zwischen Annahmen und Effizienz vor. Zweitens definieren wir ein Verschlüsselungsverfahren, das es erlaubt anonym eine Verbindung zwischen Geheimtexten herzustellen und deren Integrität zu überprüfen. Darüber hinaus bietet die aggregierbare Variante von diesem Verfahren an, Parallel Anonymous RAM zu bauen. Dieses verbessert Anonymous RAM, indem es mehrere Benutzer in einer parallelen Ausführung unterstützen kann. Drittens zeigen wir eine Meth- ode für das Konstruieren effizienter Zero-Knowledge-Protokolle, die gleichzeitig aus algebraischen und arithmetischen Teilen bestehen. Zuletzt zeigen wir ein Framework für das Konstruieren effizienter Single-Leader-Election-Protokolle, was kürzlich als ein wichtiger Bestandteil in den Proof-of-Stake Kryptowährungen erkannt worden ist

Privacy-Preserving Observation in Public Spaces

One method of privacy-preserving accounting or billing in cyber-physical systems, such as electronic toll collection or public transportation ticketing, is to have the user present an encrypted record of transactions and perform the accounting or billing computation securely on them. Honesty of the user is ensured by spot checking the record for some selected surveyed transactions. But how much privacy does that give the user, i.e. how many transactions need to be surveyed? It turns out that due to collusion in mass surveillance all transactions need to be observed, i.e. this method of spot checking provides no privacy at all. In this paper we present a cryptographic solution to the spot checking problem in cyber-physical systems. Users carry an authentication device that authenticates only based on fair random coins. The probability can be set high enough to allow for spot checking, but in all other cases privacy is perfectly preserved. We analyze our protocol for computational efficiency and show that it can be efficiently implemented even on plat- forms with limited computing resources, such as smart cards and smart phones