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On Lattice-Based Signatures with Advanced Functionalities

Alkeilani Alkadri, Nabil (2022)
On Lattice-Based Signatures with Advanced Functionalities.
Technische Universität Darmstadt
doi: 10.26083/tuprints-00020793
Ph.D. Thesis, Primary publication, Publisher's Version

Abstract

Lattice-based cryptography is a prominent class of cryptographic systems that has been emerged as one of the main candidates replacing classical cryptography in future computing environments such as quantum computing. Quantum computers exploit quantum mechanical phenomena to solve computational problems, on which the security of currently deployed (classical) cryptographic systems is based. While these computational problems, e.g., factoring integers and computing discrete logarithms, are intractable for conventional (classical) computers, it is meanwhile known that they can be easily solved on quantum computers (Shor 1997). However, lattice problems, such as finding short non-zero vectors, seem to withstand attacks having quantum computing power.

In the last two decades we have seen many cryptographic proposals based on lattices. In particular, lattice-based (ordinary) signature schemes were greatly improved with respect to efficiency and security. This can be observed from the post-quantum standardization process initiated by the National Institute of Standards and Technology (NIST). In fact, from the five signature schemes that have been submitted to this process, there are currently three finalists, where two of them are lattice-based submissions. In this thesis, we are specifically interested in lattice-based signature schemes with advanced functionalities. In addition to the basic security goals that an ordinary signature scheme ensures, i.e., authentication, non-repudiation, and integrity, these schemes provide features that are application-specific. While ordinary signature schemes based on lattices are ready to be deployed in practice, this statement cannot be made for lattice-based signature schemes with advanced functionalities. This thesis makes a significant progress towards deploying the aforementioned type of signature schemes in practice.

With focus on privacy-preserving applications in future computing environments, we particularly facilitate the protection of secret keys in cryptocurrencies such as Bitcoin and Ethereum. We provide practical solutions to anonymous e-cash, anonymous credentials, smart contracts, and e-voting. We believe that our techniques can be used to develop further advanced signature schemes to be deployed in other application scenarios. For instance, in information security systems that perform critical operations such as distributed key generation, anonymization of medical data, and updating reliable routing information.

Item Type: Ph.D. Thesis
Erschienen: 2022
Creators: Alkeilani Alkadri, Nabil
Type of entry: Primary publication
Title: On Lattice-Based Signatures with Advanced Functionalities
Language: English
Referees: Faust, Prof. Dr. Sebastian ; Buchmann, Prof. Dr. Johannes
Date: 2022
Place of Publication: Darmstadt
Publisher: Universitäts- und Landesbibliothek
Collation: viii, 121 Seiten
Refereed: 24 February 2022
DOI: 10.26083/tuprints-00020793
URL / URN: https://tuprints.ulb.tu-darmstadt.de/20793
Abstract:

Lattice-based cryptography is a prominent class of cryptographic systems that has been emerged as one of the main candidates replacing classical cryptography in future computing environments such as quantum computing. Quantum computers exploit quantum mechanical phenomena to solve computational problems, on which the security of currently deployed (classical) cryptographic systems is based. While these computational problems, e.g., factoring integers and computing discrete logarithms, are intractable for conventional (classical) computers, it is meanwhile known that they can be easily solved on quantum computers (Shor 1997). However, lattice problems, such as finding short non-zero vectors, seem to withstand attacks having quantum computing power.

In the last two decades we have seen many cryptographic proposals based on lattices. In particular, lattice-based (ordinary) signature schemes were greatly improved with respect to efficiency and security. This can be observed from the post-quantum standardization process initiated by the National Institute of Standards and Technology (NIST). In fact, from the five signature schemes that have been submitted to this process, there are currently three finalists, where two of them are lattice-based submissions. In this thesis, we are specifically interested in lattice-based signature schemes with advanced functionalities. In addition to the basic security goals that an ordinary signature scheme ensures, i.e., authentication, non-repudiation, and integrity, these schemes provide features that are application-specific. While ordinary signature schemes based on lattices are ready to be deployed in practice, this statement cannot be made for lattice-based signature schemes with advanced functionalities. This thesis makes a significant progress towards deploying the aforementioned type of signature schemes in practice.

With focus on privacy-preserving applications in future computing environments, we particularly facilitate the protection of secret keys in cryptocurrencies such as Bitcoin and Ethereum. We provide practical solutions to anonymous e-cash, anonymous credentials, smart contracts, and e-voting. We believe that our techniques can be used to develop further advanced signature schemes to be deployed in other application scenarios. For instance, in information security systems that perform critical operations such as distributed key generation, anonymization of medical data, and updating reliable routing information.

Alternative Abstract:
Alternative abstract Language

Gitterbasierte Kryptografie ist eine prominente Klasse kryptografischer Systeme, die sich als einer der Hauptkandidaten herausgestellt hat, die die klassische Kryptografie in der Gegenwart von Quantencomputern ersetzen. Quantencomputer nutzen quantenmechanische Phänomene zur Lösung von Rechenproblemen, auf denen die Sicherheit derzeit eingesetzter (klassischer) kryptografischer Systeme basiert. Während diese Rechenprobleme, z.B. das Faktorisieren ganzer Zahlen und das Berechnen diskreter Logarithmen, für herkömmliche (klassische) Computer unlösbar sind, ist mittlerweile bekannt, dass sie auf Quantencomputern leicht gelöst werden können (Shor 1997). Allerdings scheinen Gitterprobleme, wie das Auffinden kurzer und nicht trivialer Vektoren, Angriffen mit Quantenrechenleistung standzuhalten.

In den letzten zwei Jahrzehnten haben wir viele kryptografische Verfahren gesehen, die auf Gittern basieren. Insbesondere gitterbasierte (gewöhnliche) Signaturverfahren wurden hinsichtlich Effizienz und Sicherheit stark verbessert. Dies lässt sich anhand des vom National Institute of Standards and Technology (NIST) initiierten Post-Quanten-Standardisierungsprozesses beobachten. In der Tat gibt es von den fünf Signaturverfahren, die bei diesem Prozess eingereicht wurden, derzeit drei Finalisten, von denen zwei gitterbasierte Einreichungen sind. In dieser Arbeit interessieren wir uns speziell für gitterbasierte Signaturverfahren mit erweiterten Funktionalitäten. Zusätzlich zu den grundlegenden Sicherheitszielen, die ein gewöhnliches Signaturverfahren gewährleistet, d.h. Authentifizierung, Nichtabstreitbarkeit und Integrität, bieten diese Verfahren Merkmale, die anwendungsspezifisch sind. Während gewöhnliche, gitterbasierte Signaturverfahren bereit sind, in der Praxis eingesetzt zu werden, kann diese Aussage nicht für gitterbasierte Signaturverfahren mit erweiterten Funktionalitäten gemacht werden. Diese Arbeit macht einen bedeutenden Fortschritt in Richtung des Einsatzes der oben genannten Art von Signaturverfahren in der Praxis. Mit Fokus auf datenschutzfreundliche Anwendungen in zukünftigen Rechensystemen, wie z.B. Quantencomputern, erleichtern wir insbesondere den Schutz geheimer Schlüssel in Kryptowährungen wie Bitcoin und Ethereum. Wir bieten praktische Lösungen für anonymes E-Cash, anonyme Berechtigungsnachweise (Credentials), Smart Contracts und E-Voting. Wir glauben, dass unsere Techniken verwendet werden können, um weitere fortgeschrittene Signaturverfahren zu entwickeln, die in anderen Anwendungsszenarien eingesetzt werden können. Beispielsweise in Informationssicherheitssystemen, die kritische Operationen wie die Generierung verteilter Schlüssel, die Anonymisierung medizinischer Daten und die Aktualisierung zuverlässiger Routing-Informationen durchführen.

German
Status: Publisher's Version
URN: urn:nbn:de:tuda-tuprints-207938
Classification DDC: 000 Generalities, computers, information > 004 Computer science
500 Science and mathematics > 510 Mathematics
Divisions: 20 Department of Computer Science
20 Department of Computer Science > Angewandte Kryptographie
20 Department of Computer Science > Theoretical Computer Science - Cryptography and Computer Algebra
Date Deposited: 03 Mar 2022 13:47
Last Modified: 24 Jun 2022 06:39
PPN:
Referees: Faust, Prof. Dr. Sebastian ; Buchmann, Prof. Dr. Johannes
Refereed / Verteidigung / mdl. Prüfung: 24 February 2022
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