History of Cryptographic Key Sizes

International audienc

Cryptography for Big Data Security

As big data collection and analysis becomes prevalent in today’s computing environments there is a growing need for techniques to ensure security of the collected data. To make matters worse, due to its large volume and velocity, big data is commonly stored on distributed or shared computing resources not fully controlled by the data owner. Thus, tools are needed to ensure both the confidentiality of the stored data and the integrity of the analytics results even in untrusted environments. In this chapter, we present several cryptographic approaches for securing big data and discuss the appropriate use scenarios for each. We begin with the problem of securing big data storage. We first address the problem of secure block storage for big data allowing data owners to store and retrieve their data from an untrusted server. We present techniques that allow a data owner to both control access to their data and ensure that none of their data is modified or lost while in storage. However, in most big data applications, it is not sufficient to simply store and retrieve one’s data and a search functionality is necessary to allow one to select only the relevant data. Thus, we present several techniques for searchable encryption allowing database- style queries over encrypted data. We review the performance, functionality, and security provided by each of these schemes and describe appropriate use-cases. However, the volume of big data often makes it infeasible for an analyst to retrieve all relevant data. Instead, it is desirable to be able to perform analytics directly on the stored data without compromising the confidentiality of the data or the integrity of the computation results. We describe several recent cryptographic breakthroughs that make such processing possible for varying classes of analytics. We review the performance and security characteristics of each of these schemes and summarize how they can be used to protect big data analytics especially when deployed in a cloud setting. We hope that the exposition in this chapter will raise awareness of the latest types of tools and protections available for securing big data. We believe better understanding and closer collaboration between the data science and cryptography communities will be critical to enabling the future of big data processing

Connecting Legendre with Kummer and Edwards

Scalar multiplication on Legendre form elliptic curves can be speeded up in two ways. One can perform the bulk of the computation either on the associated Kummer line or on an appropriate twisted Edwards form elliptic curve. This paper provides details of moving to and from between Legendre form elliptic curves and associated Kummer line and moving to and from between Legendre form elliptic curves and related twisted Edwards form elliptic curves. Further, concrete twisted Edwards form elliptic curves are identified which correspond to known Kummer lines at the 128-bit security level which provide very fast scalar multiplication on modern architectures supporting SIMD operations

Some remarks on fair exchange protocol

Abstract. Fair exchange turns out to be an increasingly importanttopic due to the rapid growth of electronic commerce. An exchange is deemed to be fair if at the end of exchange, either each party receives the expected item or neither party receives any useful information about the other's item. Several protocols for fair exchange have been proposed in recent years. In this paper, we rst examine a newly published fair exchange protocol and point out its aws and weaknesses. We then put forward a more e cient and secure protocol and give an informal analysis

Security of Ubiquitous Computing Systems

The chapters in this open access book arise out of the EU Cost Action project Cryptacus, the objective of which was to improve and adapt existent cryptanalysis methodologies and tools to the ubiquitous computing framework. The cryptanalysis implemented lies along four axes: cryptographic models, cryptanalysis of building blocks, hardware and software security engineering, and security assessment of real-world systems. The authors are top-class researchers in security and cryptography, and the contributions are of value to researchers and practitioners in these domains. This book is open access under a CC BY license

Enhancing Privacy Protection:Set Membership, Range Proofs, and the Extended Access Control

Privacy has recently gained an importance beyond the field of cryptography. In that regard, the main goal behind this thesis is to enhance privacy protection. All of the necessary mathematical and cryptographic preliminaries are introduced at the start of this thesis. We then show in Part I how to improve set membership and range proofs, which are cryptographic primitives enabling better privacy protection. Part II shows how to improve the standards for Machine Readable Travel Documents (MRTDs), such as biometric passports. Regarding set membership proofs, we provide an efficient protocol based on the Boneh-Boyen signature scheme. We show that alternative signature schemes can be used and we provide a general protocol description that can be applied for any secure signature scheme. We also show that signature schemes in our design can be replaced by cryptographic accumulators. For range proofs, we provide interactive solutions where the range is divided in a base u and the u-ary digits are handled by one of our set membership proofs. A general construction is also provided for any set membership proof. We additionally explain how to handle arbitrary ranges with either two range proofs or with an improved solution based on sumset representation. These efficient solutions achieve, to date, the lowest asymptotical communication load. Furthermore, this thesis shows that the first efficient non-interactive range proof is insecure. This thesis thus provides the first efficient and secure non-interactive range proof. In the case of MRTDs, two standards exist: one produced by the International Civil Aviation Organization (ICAO) and the other by the European Union, which is called the Extended Access Control (EAC). Although this thesis focuses on the EAC, which is supposed to solve all privacy concerns, it shows that both standards fail to provide complete privacy protection. Lastly, we provide several solutions to improve them

Individual verifiability in electronic voting

This PhD Thesis is the fruit of the job of the author as a researcher at Scytl Secure Electronic Voting, as well as the collaboration with Paz Morillo, from the Department of Applied Mathematics at UPC and Alex Escala, PhD student. In her job at Scytl, the author has participated in several electronic voting projects for national-level binding elections in different countries. The participation of the author covered from the protocol design phase, to the implementation phase by providing support to the development teams. The thesis focuses on studying the mechanisms that can be provided to the voters, in order to examine and verify the processes executed in a remote electronic voting system. This work has been done as part of the tasks of the author at the electronic voting company Scytl. Although this thesis does not talk about system implementations, which are interesting by themselves, it is indeed focused on protocols which have had, or may have, an application in the real world. Therefore, it may surprise the reader by not using state of the art cryptography such as pairings or lattices, which still, although providing very interesting properties, cannot be efficiently implemented and used in a real system. Otherwise, the protocols presented in this thesis use standard and well-known cryptographic primitives, while providing new functionalities that can be applied in nowadays electronic voting systems. The thesis has the following contents: A survey on electronic voting systems which provide voter verification functionalities. Among these systems we can find the one used in the Municipal and Parliamentary Norwegian elections of 2011 and 2013, and the system used in the Australian State of New South Wales for the General State Elections in 2015, in which the author has had an active participation in the design of their electronic voting protocols. A syntax which can be used for modeling electronic voting systems providing voter verifiability. This syntax is focused on systems characterized by the voter confirming the casting of her vote, after verifying some evidences provided by the protocol. Along with this syntax, definitions for the security properties required for such schemes are provided. A description of the electronic voting protocol and system which has been used in 2014 and 2015 elections in the Swiss Canton of Neuchâtel, which has individual verification functionalities, is also provided in this thesis, together with a formal analysis of the security properties of the scheme and further extensions of the protocol. Finally, two new protocols which provide new functionalities respect to those from the state of the art are proposed: A new protocol providing individual verifiability which allows voters to defend against coertion by generating fake proofs, and a protocol which makes a twist to individual verifiability by ensuring that all the processes executed by the voting device and the remote server are correct, without requiring an active verification from the voter. A formal analysis of the security properties of both protocols is provided, together with examples of implementation in real systems.Aquesta tesi és fruit de la feina de l'autora com a personal de recerca a la empresa Scytl Secure Electtronic Voting, així com de la col·laboració amb la Paz Morillo, del departament de matemàtica aplicada a la UPC, i el Alex Escala, estudiant de doctorat. A la feina a Scytl, l'autora ha participat a varis projectes de vot electrònic per a eleccions vinculants a nivell nacional, que s'han efectuat a varis països. La participació de la autora ha cobert tant la fase de disseny del protocol, com la fase de implementació, on ha proveït suport als equips de desenvolupament. La tesi estudia els mecanismes que es poden proporcionar als votants per a poder examinar i verificar els processos que s'executen en sistemes de vot electrònic. Tot i que la tesi no parla de la implementació dels sistemes de vot electrònic, sí que s'enfoca en protocols que han tingut, o poden tenir, una aplicació pràctica actualment. La tesi té els continguts següents: Un estudi en sistemes de vot electrònic que proporcionen funcionalitats per a que els votants verifiquin els processos. Entre aquests sistemes, trobem el que es va utilitzar a les eleccions municipals i parlamentàries a Noruega als anys 2011 i 2013, així com el sistema utilitzat a l'estat Australià de New South Wales, per a les eleccions generals de 2015, sistemes en els que l'autora ha participat directament en el diseny dels seus protocols criptogràfics. La tesi també conté una sintaxi que es pot utilizar per modelar sistemes de vot electrònic que proporcionen verificabilitat individual (on verifica el votant). Aquesta sintaxi s'enfoca en sistemes caracteritzats pel fet de que el votant confirma la emissió del seu vot un cop ha verificat unes evidències sobre ell, proporcionades pel protocol. A més de la sintaxi, es proporcionen definicions de les propietats de seguretat d'aquestts sistemes. La tesi també conté una descripció del sistema i protocol de vot electrònic que s'utilitza al cantó Suís de Neuchâtel a partir del 2014, el qual té funcionalitats per a que els votants verifiquin certs processos del sistema. La tesi a més conté un anàlisi de la seguretat de l'esquema, així com possibles extensions del protocol. Finalment, la tesi inclou dos protocols nous que proporcionen noves característiques i funcionalitats respecte als existents a l'estat de l'art de la tècnica. El primer permet a un votant defendre's de un coaccionador generant proves falses, i el segon fa un canvi de paradigma de la verificabilitat individual, de forma que el votant no ha de verificar certs processos per a saber que s'han efectuant correctament. La tesi inclou un anàlisi formal de les propietats de seguretat dels dos protocols, així com exemples de com podrien ser implementats en un escenari real.Postprint (published version