Error exponents of typical random codes

We define the error exponent of the typical random code as the long-block limit of the negative normalized expectation of the logarithm of the error probability of the random code, as opposed to the traditional random coding error exponent, which is the limit of the negative normalized logarithm of the expectation of the error probability. For the ensemble of uniformly randomly drawn fixed composition codes, we provide exact error exponents of typical random codes for a general discrete memoryless channel (DMC) and a wide class of (stochastic) decoders, collectively referred to as the generalized likelihood decoder (GLD). This ensemble of fixed composition codes is shown to be no worse than any other ensemble of independent codewords that are drawn under a permutation--invariant distribution (e.g., i.i.d. codewords). We also present relationships between the error exponent of the typical random code and the ordinary random coding error exponent, as well as the expurgated exponent for the GLD. Finally, we demonstrate that our analysis technique is applicable also to more general communication scenarios, such as list decoding (for fixed-size lists) as well as decoding with an erasure/list option in Forney's sense.Comment: 26 pages, submitted for publicatio

Algorithms for Determining the Order of the Group of Points on an EllipticCurve with Application in Cryptography

Eliptické křivky jsou rovinné křivky, jejíž body vyhovují Weierstrassově rovnici. Jejich hlavní využití je v kryptografii, kde představují důležitý nástroj k tvorbě těžko rozluštitelných kódů bez znalosti klíče, který je v porovnání s ostatními šifrovacími systémy krátký. Díky těmto přednostem jsou hojně využívány. Abychom mohli kódovat a dekódovat zprávy v systému eliptických křivek, musíme znát řád dané eliptické křivky. K jeho získání se mimo jiné používá Shanksův algoritmus a jeho vylepšená varianta, Mestreho algoritmus.The elliptic curves are plane curves whose points satisfy the Weierstrass equation. Their main application is in the cryptography, where they represent an important device for creating code which is hard to break without knowing the key and which is short in comparison with other encoding methods. The elliptic curves are widely used thanks to these advantages. To be able to code and decode in the elliptic curve cryptography we must know the order of the given elliptic curve. The Shank's algorithm and its improved version, the Mestre's algorithm, are used for its determining.

Polar Coding for Secret-Key Generation

Practical implementations of secret-key generation are often based on sequential strategies, which handle reliability and secrecy in two successive steps, called reconciliation and privacy amplification. In this paper, we propose an alternative approach based on polar codes that jointly deals with reliability and secrecy. Specifically, we propose secret-key capacity-achieving polar coding schemes for the following models: (i) the degraded binary memoryless source (DBMS) model with rate-unlimited public communication, (ii) the DBMS model with one-way rate-limited public communication, (iii) the 1-to-m broadcast model and (iv) the Markov tree model with uniform marginals. For models (i) and (ii) our coding schemes remain valid for non-degraded sources, although they may not achieve the secret-key capacity. For models (i), (ii) and (iii), our schemes rely on pre-shared secret seed of negligible rate; however, we provide special cases of these models for which no seed is required. Finally, we show an application of our results to secrecy and privacy for biometric systems. We thus provide the first examples of low-complexity secret-key capacity-achieving schemes that are able to handle vector quantization for model (ii), or multiterminal communication for models (iii) and (iv).Comment: 26 pages, 9 figures, accepted to IEEE Transactions on Information Theory; parts of the results were presented at the 2013 IEEE Information Theory Worksho

The Quantum Frontier

The success of the abstract model of computation, in terms of bits, logical operations, programming language constructs, and the like, makes it easy to forget that computation is a physical process. Our cherished notions of computation and information are grounded in classical mechanics, but the physics underlying our world is quantum. In the early 80s researchers began to ask how computation would change if we adopted a quantum mechanical, instead of a classical mechanical, view of computation. Slowly, a new picture of computation arose, one that gave rise to a variety of faster algorithms, novel cryptographic mechanisms, and alternative methods of communication. Small quantum information processing devices have been built, and efforts are underway to build larger ones. Even apart from the existence of these devices, the quantum view on information processing has provided significant insight into the nature of computation and information, and a deeper understanding of the physics of our universe and its connections with computation. We start by describing aspects of quantum mechanics that are at the heart of a quantum view of information processing. We give our own idiosyncratic view of a number of these topics in the hopes of correcting common misconceptions and highlighting aspects that are often overlooked. A number of the phenomena described were initially viewed as oddities of quantum mechanics. It was quantum information processing, first quantum cryptography and then, more dramatically, quantum computing, that turned the tables and showed that these oddities could be put to practical effect. It is these application we describe next. We conclude with a section describing some of the many questions left for future work, especially the mysteries surrounding where the power of quantum information ultimately comes from.Comment: Invited book chapter for Computation for Humanity - Information Technology to Advance Society to be published by CRC Press. Concepts clarified and style made more uniform in version 2. Many thanks to the referees for their suggestions for improvement

Elliptic Curve Cryptography Services for Mobile Operating Systems

Mobile devices as smartphones, tablets and laptops, are nowadays considered indispensable objects by most people in developed countries. A s personal and work assistant s , some of th e s e devices store , process and transmit sensitive and private data. Naturally , the number of mobile applications with integrated cryptographic mechanisms or offering security services has been significantly increasing in the last few years. Unfortunately, not all of those applications are secure by design, while other may not implement the cryptographic primitives correctly. Even the ones that implement them correctly may suffer from longevity problems, since cryptographic primitives that are considered secure nowadays may become obsolete in the next few years. Rivest, Shamir and Adleman (RSA) is an example of an widely used cryptosystem that may become depleted shorty . While the security issues in the mobile computing environment may be of median severity for casual users, they may be critical for several professional classes, namely lawyers, journalists and law enforcement agents. As such, it is important to approach these problems in a structured manner. This master’s program is focused on the engineering and implementation of a mobile application offering a series of security services. The application was engineered to be secure by design for the Windows Phone 8.1 Operating System (OS) which, at the time of writing this dissertation, was the platform with the most discreet offer in terms of applications of this type. The application provides services such as secure exchange of a cryptographic secret, encryption and digital signature of messages and files, management of contacts and encryption keys and secure password generation and storage. Part of the cryptographic primitives used in this work are from the Elliptic Curve Cryptography (ECC) theory, for which the discrete logarithm problem is believed to be harder and key handling is easier. The library defining a series of curves and containing the procedures and operations supporting the ECC primitives was implemented from scratch, since there was none available, comprising one of the contributions of this work. The work evolved from the analysis of the state-of-the-art to the requirements analysis and software engineering phase, thoroughly described herein, ending up with the development of a prototype. The engineering of the application included the definition of a trust model for the exchange of public keys and the modeling of the supporting database. The most visible outcomes of this master’s program are the fully working prototype of a mobile application offering the aforementioned security services, the implementation of an ECC library for the .NET framework, and this dissertation. The source code for the ECC library was made available online on GitHub with the name ECCryptoLib [Ana15]. Its development and improvement was mostly dominated by unit testing. The library and the mobile application were developed in C?. The level of security offered by the application is guaranteed via the orchestration and combination of state-of-the-art symmetric key cryptography algorithms, as the Advanced Encryption Standard (AES) and Secure Hash Algorithm 256 (SHA256) with the ECC primitives. The generation of passwords is done by using several sensors and inputs as entropy sources, which are fed to a cryptographically secure hash function. The passwords are stored in an encrypted database, whose encryption key changes every time it is opened, obtained using a Password-Based Key Derivation Function 2 (PBKDF2) from a master password. The trust model for the public keys designed in the scope of this work is inspired in Pretty Good Privacy (PGP), but granularity of the trust levels is larger.Dispositivos móveis como computadores portáteis, smartphones ou tablets, são, nos dias de hoje, considerados objectos indispensáveis pela grande maioria das pessoas residentes em países desenvolvidos. Por serem utilizados como assistentes pessoais ou de trabalho, alguns destes dispositivos guardam, processam e transmitem dados sensíveis ou privados. Naturalmente, o número de aplicações móveis com mecanismos criptográficos integrados ou que oferecem serviços de segurança, tem vindo a aumentar de forma significativa nos últimos anos. Infelizmente, nem todas as aplicações são seguras por construção, e outras podem não implementar as primitivas criptográficas corretamente. Mesmo aquelas que as implementam corretamente podem sofrer de problemas de longevidade, já que primitivas criptográficas que são hoje em dia consideradas seguras podem tornar-se obsoletas nos próximos anos. O Rivest, Shamir and Adleman (RSA) constitui um exemplo de um sistema criptográfico muito popular que se pode tornar obsoleto a curto prazo. Enquanto que os problemas de segurança em ambientes de computação móvel podem ser de média severidade para utilizadores casuais, estes são normalmente críticos para várias classes profissionais, nomeadamente advogados, jornalistas e oficiais da justiça. É, por isso, importante, abordar estes problemas de uma forma estruturada. Este programa de mestrado foca-se na engenharia e implementação de uma aplicação móvel que oferece uma série de serviços de segurança. A aplicação foi desenhada para ser segura por construção para o sistema operativo Windows Phone 8.1 que, altura em que esta dissertação foi escrita, era a plataforma com a oferta mais discreta em termos de aplicações deste tipo. A aplicação fornece funcionalidades como trocar um segredo criptográfico entre duas entidades de forma segura, cifra, decifra e assinatura digital de mensagens e ficheiros, gestão de contactos e chaves de cifra, e geração e armazenamento seguro de palavras-passe. Parte das primitivas criptográficas utilizadas neste trabalho fazem parte da teoria da criptografia em curvas elípticas, para a qual se acredita que o problema do logaritmo discreto é de mais difícil resolução e para o qual a manipulação de chaves é mais simples. A biblioteca que define uma série de curvas, e contendo os procedimentos e operações que suportam as primitivas criptográficas, foi totalmente implementada no âmbito deste trabalho, dado ainda não existir nenhuma disponível no seu início, compreendendo assim uma das suas contribuições. O trabalho evoluiu da análise do estado da arte para o levantamento dos requisitos e para a fase de engenharia de software, aqui descrita detalhadamente, culminando no desenvolvimento de um protótipo. A engenharia da aplicação incluiu a definição de um sistema de confiança para troca de chaves públicas e também modelação da base de dados de suporte. Os resultados mais visíveis deste programa de mestrado são o protótipo da aplicação móvel, completamente funcional e disponibilizando as funcionalidades de segurança acima mencionadas, a implementação de uma biblioteca Elliptic Curve Cryptography (ECC) para framework .NET, e esta dissertação. O código fonte com a implementação da biblioteca foi publicada online. O seu desenvolvimento e melhoramento foi sobretudo dominado por testes unitários. A biblioteca e a aplicação móvel foram desenvolvidas em C?. O nível de segurança oferecido pela aplicação é garantido através da orquestração e combinação de algoritmos da criptografia de chave simétrica atuais, como o Advanced Encryption Standard (AES) e o Secure Hash Algorithm 256 (SHA256), com as primitivas ECC. A geração de palavras-passe é feita recorrendo utilizando vários sensores e dispoitivos de entrada como fontes de entropia, que posteriormente são alimentadas a uma função de hash criptográfica. As palavras-passe são guardadas numa base de dados cifrada, cuja chave de cifra muda sempre que a base de dados é aberta, sendo obtida através da aplicação de um Password-Based Key Derivation Function 2 (PBKDF2) a uma palavrapasse mestre. O modelo de confiança para chaves públicas desenhado no âmbito deste trabalho é inspirado no Pretty Good Privacy (PGP), mas a granularidade dos níveis de confiança é superior

Biometric Cryptosystems : Authentication, Encryption and Signature for Biometric Identities

Biometrics have been used for secure identification and authentication for more than two decades since biometric data is unique, non-transferable, unforgettable, and always with us. Recently, biometrics has pervaded other aspects of security applications that can be listed under the topic of ``Biometric Cryptosystems''. Although the security of some of these systems is questionable when they are utilized alone, integration with other technologies such as digital signatures or Identity Based Encryption (IBE) schemes results in cryptographically secure applications of biometrics. It is exactly this field of biometric cryptosystems that we focused in this thesis. In particular, our goal is to design cryptographic protocols for biometrics in the framework of a realistic security model with a security reduction. Our protocols are designed for biometric based encryption, signature and remote authentication. We first analyze the recently introduced biometric remote authentication schemes designed according to the security model of Bringer et al.. In this model, we show that one can improve the database storage cost significantly by designing a new architecture, which is a two-factor authentication protocol. This construction is also secure against the new attacks we present, which disprove the claimed security of remote authentication schemes, in particular the ones requiring a secure sketch. Thus, we introduce a new notion called ``Weak-identity Privacy'' and propose a new construction by combining cancelable biometrics and distributed remote authentication in order to obtain a highly secure biometric authentication system. We continue our research on biometric remote authentication by analyzing the security issues of multi-factor biometric authentication (MFBA). We formally describe the security model for MFBA that captures simultaneous attacks against these systems and define the notion of user privacy, where the goal of the adversary is to impersonate a client to the server. We design a new protocol by combining bipartite biotokens, homomorphic encryption and zero-knowledge proofs and provide a security reduction to achieve user privacy. The main difference of this MFBA protocol is that the server-side computations are performed in the encrypted domain but without requiring a decryption key for the authentication decision of the server. Thus, leakage of the secret key of any system component does not affect the security of the scheme as opposed to the current biometric systems involving cryptographic techniques. We also show that there is a tradeoff between the security level the scheme achieves and the requirement for making the authentication decision without using any secret key. In the second part of the thesis, we delve into biometric-based signature and encryption schemes. We start by designing a new biometric IBS system that is based on the currently most efficient pairing based signature scheme in the literature. We prove the security of our new scheme in the framework of a stronger model compared to existing adversarial models for fuzzy IBS, which basically simulates the leakage of partial secret key components of the challenge identity. In accordance with the novel features of this scheme, we describe a new biometric IBE system called as BIO-IBE. BIO-IBE differs from the current fuzzy systems with its key generation method that not only allows for a larger set of encryption systems to function for biometric identities, but also provides a better accuracy/identification of the users in the system. In this context, BIO-IBE is the first scheme that allows for the use of multi-modal biometrics to avoid collision attacks. Finally, BIO-IBE outperforms the current schemes and for small-universe of attributes, it is secure in the standard model with a better efficiency compared to its counterpart. Another contribution of this thesis is the design of biometric IBE systems without using pairings. In fact, current fuzzy IBE schemes are secure under (stronger) bilinear assumptions and the decryption of each message requires pairing computations almost equal to the number of attributes defining the user. Thus, fuzzy IBE makes error-tolerant encryption possible at the expense of efficiency and security. Hence, we design a completely new construction for biometric IBE based on error-correcting codes, generic conversion schemes and weakly secure anonymous IBE schemes that encrypt a message bit by bit. The resulting scheme is anonymous, highly secure and more efficient compared to pairing-based biometric IBE, especially for the decryption phase. The security of our generic construction is reduced to the security of the anonymous IBE scheme, which is based on the Quadratic Residuosity assumption. The binding of biometric features to the user's identity is achieved similar to BIO-IBE, thus, preserving the advantages of its key generation procedure

The Einstein Toolkit: A Community Computational Infrastructure for Relativistic Astrophysics

We describe the Einstein Toolkit, a community-driven, freely accessible computational infrastructure intended for use in numerical relativity, relativistic astrophysics, and other applications. The Toolkit, developed by a collaboration involving researchers from multiple institutions around the world, combines a core set of components needed to simulate astrophysical objects such as black holes, compact objects, and collapsing stars, as well as a full suite of analysis tools. The Einstein Toolkit is currently based on the Cactus Framework for high-performance computing and the Carpet adaptive mesh refinement driver. It implements spacetime evolution via the BSSN evolution system and general-relativistic hydrodynamics in a finite-volume discretization. The toolkit is under continuous development and contains many new code components that have been publicly released for the first time and are described in this article. We discuss the motivation behind the release of the toolkit, the philosophy underlying its development, and the goals of the project. A summary of the implemented numerical techniques is included, as are results of numerical test covering a variety of sample astrophysical problems.Comment: 62 pages, 20 figure

Austrian High-Performance-Computing meeting (AHPC2020)

This booklet is a collection of abstracts presented at the AHPC conference