Efficient software implementation of elliptic curves and bilinear pairings

Orientador: Júlio César Lopez HernándezTese (doutorado) - Universidade Estadual de Campinas, Instituto de ComputaçãoResumo: O advento da criptografia assimétrica ou de chave pública possibilitou a aplicação de criptografia em novos cenários, como assinaturas digitais e comércio eletrônico, tornando-a componente vital para o fornecimento de confidencialidade e autenticação em meios de comunicação. Dentre os métodos mais eficientes de criptografia assimétrica, a criptografia de curvas elípticas destaca-se pelos baixos requisitos de armazenamento para chaves e custo computacional para execução. A descoberta relativamente recente da criptografia baseada em emparelhamentos bilineares sobre curvas elípticas permitiu ainda sua flexibilização e a construção de sistemas criptográficos com propriedades inovadoras, como sistemas baseados em identidades e suas variantes. Porém, o custo computacional de criptossistemas baseados em emparelhamentos ainda permanece significativamente maior do que os assimétricos tradicionais, representando um obstáculo para sua adoção, especialmente em dispositivos com recursos limitados. As contribuições deste trabalho objetivam aprimorar o desempenho de criptossistemas baseados em curvas elípticas e emparelhamentos bilineares e consistem em: (i) implementação eficiente de corpos binários em arquiteturas embutidas de 8 bits (microcontroladores presentes em sensores sem fio); (ii) formulação eficiente de aritmética em corpos binários para conjuntos vetoriais de arquiteturas de 64 bits e famílias mais recentes de processadores desktop dotadas de suporte nativo à multiplicação em corpos binários; (iii) técnicas para implementação serial e paralela de curvas elípticas binárias e emparelhamentos bilineares simétricos e assimétricos definidos sobre corpos primos ou binários. Estas contribuições permitiram obter significativos ganhos de desempenho e, conseqüentemente, uma série de recordes de velocidade para o cálculo de diversos algoritmos criptográficos relevantes em arquiteturas modernas que vão de sistemas embarcados de 8 bits a processadores com 8 coresAbstract: The development of asymmetric or public key cryptography made possible new applications of cryptography such as digital signatures and electronic commerce. Cryptography is now a vital component for providing confidentiality and authentication in communication infra-structures. Elliptic Curve Cryptography is among the most efficient public-key methods because of its low storage and computational requirements. The relatively recent advent of Pairing-Based Cryptography allowed the further construction of flexible and innovative cryptographic solutions like Identity-Based Cryptography and variants. However, the computational cost of pairing-based cryptosystems remains significantly higher than traditional public key cryptosystems and thus an important obstacle for adoption, specially in resource-constrained devices. The main contributions of this work aim to improve the performance of curve-based cryptosystems, consisting of: (i) efficient implementation of binary fields in 8-bit microcontrollers embedded in sensor network nodes; (ii) efficient formulation of binary field arithmetic in terms of vector instructions present in 64-bit architectures, and on the recently-introduced native support for binary field multiplication in the latest Intel microarchitecture families; (iii) techniques for serial and parallel implementation of binary elliptic curves and symmetric and asymmetric pairings defined over prime and binary fields. These contributions produced important performance improvements and, consequently, several speed records for computing relevant cryptographic algorithms in modern computer architectures ranging from embedded 8-bit microcontrollers to 8-core processorsDoutoradoCiência da ComputaçãoDoutor em Ciência da Computaçã

Name service and routing for traffic anonymizing networks

Orientador: Julio Cesar Lopez HernandezDissertação (mestrado) - Universidade Estadual de Campinas, Instituto de ComputaçãoResumo: Em diversos cenários, é desejável que não apenas o conteúdo de uma comunicação seja preservado, mas também a identidade dos seus participantes. Satisfazer esta propriedade requer mecanismos diferentes dos comumente utilizados para fornecer sigilo e autenticidade. Neste trabalho, a problemática da comunicação anônima na Internet é abordada a partir do projeto e implementação de componentes específicos para este fim. Em particular, são apresentados um componente para roteamento anônimo eficiente em sistemas peer-to-peer estruturados e um serviço de nomes para facilitar a publicação de serviços anonimizados. As principais contribuições deste trabalho são: (i) estudo de definições, métricas e técnicas relacionadas a anonimato computacional; (ii) estudo do paradigma de Criptografia de Chave Pública Sem Certificados; (iii) projeto de uma rede de anonimização completa, adequada tanto para comunicação genérica como para funcionalidade específica; (iv) estudo e projeto de esquemas de roteamento em ambientes anônimos; (v) projeto de um serviço de nomes que aplica técnicas criptográficas avançadas para fornecer suporte a serviços anonimizados; (vi) implementação em software dos conceitos apresentadosAbstract: In several scenarios, it¿s desirable to protect not only the content of a communication, but the identities of its participants. To satisfy this property, different techniques from those used to support confidentiality and authentication are commonly required. In this work, the problem of anonymous communication on the Internet is explored through the design and implementation of specific components with this function. In particular, a name service and a routing component for anonymous environments are presented. The main contributions of this work are: (i) the study of definitions, metrics and techniques related to computational anonymity; (ii) the study of Certificateless Public Key Cryptography, a new model of public key cryptography; (iii) the design of a complete anonymization network, suitable for both generic communication and dedicated functionality; (iv) the study and design of routing schemes for anonymous communication; (v) the design of a name service to support location-hidden services in the anonymous network; (vi) the implementation of the concepts presented.MestradoCriptografia e Segurança ComputacionalMestre em Ciência da Computaçã

2DT-GLS: Faster and exception-free scalar multiplication in the GLS254 binary curve

We revisit and improve performance of arithmetic in the binary GLS254 curve by introducing the 2DT-GLS scalar multiplication algorithm. The algorithm includes theoretical and practice-oriented contributions of potential independent interest: (i) for the first time, a proof that the GLS scalar multiplication algorithm does not incur exceptions, such that faster incomplete formulas can be used; (ii) faster dedicated atomic formulas that alleviate the cost of precomputation; (iii) a table compression technique that reduces the storage needed for precomputed points; (iv) a refined constant-time scalar decomposition algorithm that is more robust to rounding. We also present the first GLS254 implementation for Armv8. With our contributions, we set new speed records for constant-time scalar multiplication by $34.5\%$ and $6\%$ on 64-bit Arm and Intel platforms, respectively

MOSFHET: Optimized Software for FHE over the Torus

Homomorphic encryption is one of the most secure solutions for processing sensitive information in untrusted environments, and there have been many recent advances towards its efficient implementation for the evaluation of linear functions and approximated arithmetic. However, the practical performance when evaluating arbitrary (nonlinear) functions is still a major challenge for HE schemes. The TFHE scheme [Chillotti et al., 2016] is the current state-of-the-art for the evaluation of arbitrary functions, and, in this work, we focus on improving its performance. We divide this paper into two parts. First, we review and implement the main techniques to improve performance or error behavior in TFHE proposed so far. For many, this is the first practical implementation. Then, we introduce novel improvements to several of them and new approaches to implement some commonly used procedures. We also show which proposals can be suitably combined to achieve better results. We provide a single library containing all the reviewed techniques as well as our original contributions. Our implementation is up to 1.2 times faster than previous ones with a similar optimization level, and our novel techniques provide speedups of up to 2.83 times on algorithms such as the Full-Domain Functional Bootstrap (FDFB)

Laconic Private Set-Intersection From Pairings

Private set-intersection (PSI) is one of the most practically relevant special-purpose secure multiparty computation tasks, as it is motivated by many real-world applications. In this paper we present a new private set-intersection protocol which is laconic, meaning that the protocol only has two rounds and that the first message is independent of the set sizes. Laconic PSI can be useful in applications, where servers with large sets would like to learn the intersection of their set with smaller sets owned by resource-constrained clients and where multiple rounds of interactions are not possible. Previously, practically relevant laconic PSI protocols were only known from factoring-type assumptions. The contributions of this work are twofold: 1) We present the first laconic PSI protocol based on assumptions over pairing-friendly elliptic curves; and 2) For the first time we provide empirical evaluation of any laconic PSI protocol by carefully implementing and optimising both our and previous protocols. Our experimental results shows that our protocol outperforms prior laconic PSI protocols

Faster Unbalanced Private Set Intersection

Protocols for Private Set Intersection (PSI) are important cryptographic primitives that perform joint operations on datasets in a privacy-preserving way. They allow two parties to compute the intersection of their private sets without revealing any additional information beyond the intersection itself. Unfortunately, PSI implementations in the literature do not usually employ the best possible cryptographic implementation techniques. This results in protocols presenting computational and communication complexities that are prohibitive, particularly in the case when one of the participants is a low-powered device and there are bandwidth restrictions. This paper builds on modern cryptographic engineering techniques and proposes optimizations for a promising one-way PSI protocol based on public-key cryptography. For the case when one of the parties holds a set much smaller than the other (a realistic assumption in many scenarios) we show that our improvements and optimizations yield a protocol that outperforms the communication complexity and the run time of previous proposals by around one thousand times

Improved Threshold Signatures, Proactive Secret Sharing, and Input Certification from LSS Isomorphisms

In this paper we present a series of applications steming from a formal treatment of linear secret-sharing isomorphisms, which are linear transformations between different secret-sharing schemes defined over vector spaces over a field $\mathbb{F}$ and allow for efficient multiparty conversion from one secret-sharing scheme to the other. This concept generalizes the folklore idea that moving from a secret-sharing scheme over $\mathbb{F}_{p}$ to a secret sharing ``in the exponent\u27\u27 can be done non-interactively by multiplying the share unto a generator of e.g., an elliptic curve group. We generalize this idea and show that it can also be used to compute arbitrary bilinear maps and in particular pairings over elliptic curves. We include the following practical applications originating from our framework: First we show how to securely realize the Pointcheval-Sanders signature scheme (CT-RSA 2016) in MPC. Second we present a construction for dynamic proactive secret-sharing which outperforms the current state of the art from CCS 2019. Third we present a construction for MPC input certification using digital signatures that we show experimentally to outperform the previous best solution in this area

Verifiable Mix-Nets and Distributed Decryption for Voting from Lattice-Based Assumptions

Cryptographic voting protocols have recently seen much interest from practitioners due to their (planned) use in countries such as Estonia, Switzerland, France, and Australia. Practical protocols usually rely on tested designs such as the mixing-and-decryption paradigm. There, multiple servers verifiably shuffle encrypted ballots, which are then decrypted in a distributed manner. While several efficient protocols implementing this paradigm exist from discrete log-type assumptions, the situation is less clear for post-quantum alternatives such as lattices. This is because the design ideas of the discrete log-based voting protocols do not carry over easily to the lattice setting, due to specific problems such as noise growth and approximate relations. In this work, we propose a new verifiable secret shuffle for BGV ciphertexts and a compatible verifiable distributed decryption protocol. The shuffle is based on an extension of a shuffle of commitments to known values which is combined with an amortized proof of correct re-randomization. The verifiable distributed decryption protocol uses noise drowning, proving the correctness of decryption steps in zero-knowledge. Both primitives are then used to instantiate the mixing-and-decryption electronic voting paradigm from lattice-based assumptions. We give concrete parameters for our system, estimate the size of each component and provide implementations of all important sub-protocols. Our experiments show that the shuffle and decryption protocol is suitable for use in real-world e-voting schemes