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

Elliptic Curve Cryptography: The Serpentine Course of a Paradigm Shift

Over a period of sixteen years elliptic curve cryptography went from being an approach that many people mistrusted or misunderstood to being a public key technology that enjoys almost unquestioned acceptance. We describe the sometimes surprising twists and turns in this paradigm shift, and compare this story with the commonly accepted Ideal Model of how research and development function in cryptography. We also discuss to what extent the ideas in the literature on social construction of technology can contribute to a better understanding of this history

Developing an Automatic Generation Tool for Cryptographic Pairing Functions

Pairing-Based Cryptography is receiving steadily more attention from industry, mainly because of the increasing interest in Identity-Based protocols. Although there are plenty of applications, efficiently implementing the pairing functions is often difficult as it requires more knowledge than previous cryptographic primitives. The author presents a tool for automatically generating optimized code for the pairing functions which can be used in the construction of such cryptographic protocols. In the following pages I present my work done on the construction of pairing function code, its optimizations and how their construction can be automated to ease the work of the protocol implementer. Based on the user requirements and the security level, the created cryptographic compiler chooses and constructs the appropriate elliptic curve. It identifies the supported pairing function: the Tate, ate, R-ate or pairing lattice/optimal pairing, and its optimized parameters. Using artificial intelligence algorithms, it generates optimized code for the final exponentiation and for hashing a point to the required group using the parametrisation of the chosen family of curves. Support for several multi-precision libraries has been incorporated: Magma, MIRACL and RELIC are already included, but more are possible

第13回数学総合若手研究集会

Katedra české literaturyFaculty of EducationPedagogická fakult