Efficient software implementation of elliptic curves and bilinear pairings

Author(s)

Diego de Freitas Aranha

• Document type: Doctoral Thesis
• Press: Campinas, SP.
• Institution: Universidade Estadual de Campinas (UNICAMP). Instituto de Computação
• Defense date: 2011-08-26

Examining board members

Julio César López Hernández; Anderson Clayton Alves Nascimento; Paulo Sergio Licciardi Messeder Barreto; Marco Aurelio Amaral Henriques; Ricardo Dahab

• Advisor: Julio César López Hernández

Abstract

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 processors (AU)

• FAPESP's process: 07/06950-0 - Efficient Implementation of Cryptographic Algorithms in Modern Architectures
• Grantee: Diego de Freitas Aranha
• Support Opportunities: Scholarships in Brazil - Doctorate