Efficient algorithms for pairing-based cryptosystems

We describe fast new algorithms to implement recent cryptosystems based on the Tate pairing. In particular, our techniques improve pairing evaluation speed by a factor of about 55 compared to previously known methods in characteristic 3, and attain performance comparable to that of RSA in larger characteristics.We also propose faster algorithms for scalar multiplication in characteristic 3 and square root extraction over Fpm, the latter technique being also useful in contexts other than that of pairing-based cryptography

Efficient implementation of elliptic curve cryptography.

Elliptic Curve Cryptosystems (ECC) were introduced in 1985 by Neal Koblitz and Victor Miller. Small key size made elliptic curve attractive for public key cryptosystem implementation. This thesis introduces solutions of efficient implementation of ECC in algorithmic level and in computation level. In algorithmic level, a fast parallel elliptic curve scalar multiplication algorithm based on a dual-processor hardware system is developed. The method has an average computation time of n3 Elliptic Curve Point Addition on an n-bit scalar. The improvement is n Elliptic Curve Point Doubling compared to conventional methods. When a proper coordinate system and binary representation for the scalar k is used the average execution time will be as low as n Elliptic Curve Point Doubling, which makes this method about two times faster than conventional single processor multipliers using the same coordinate system. In computation level, a high performance elliptic curve processor (ECP) architecture is presented. The processor uses parallelism in finite field calculation to achieve high speed execution of scalar multiplication algorithm. The architecture relies on compile-time detection rather than of run-time detection of parallelism which results in less hardware. Implemented on FPGA, the proposed processor operates at 66MHz in GF(2 167) and performs scalar multiplication in 100muSec, which is considerably faster than recent implementations.Dept. of Electrical and Computer Engineering. Paper copy at Leddy Library: Theses & Major Papers - Basement, West Bldg. / Call Number: Thesis2004 .A57. Source: Masters Abstracts International, Volume: 44-03, page: 1446. Thesis (M.A.Sc.)--University of Windsor (Canada), 2005

Cryptographic Key Distribution In Wireless Sensor Networks Using Bilinear Pairings

It is envisaged that the use of cheap and tiny wireless sensors will soon bring a third wave of evolution in computing systems. Billions of wireless senor nodes will provide a bridge between information systems and the physical world. Wireless nodes deployed around the globe will monitor the surrounding environment as well as gather information about the people therein. It is clear that this revolution will put security solutions to a great test. Wireless Sensor Networks (WSNs) are a challenging environment for applying security services. They differ in many aspects from traditional fixed networks, and standard cryptographic solutions cannot be used in this application space. Despite many research efforts, key distribution in WSNs still remains an open problem. Many of the proposed schemes suffer from high communication overhead and storage costs, low scalability and poor resilience against different types of attacks. The exclusive usage of simple and energy efficient symmetric cryptography primitives does not solve the security problem. On the other hand a full public key infrastructure which uses asymmetric techniques, digital signatures and certificate authorities seems to be far too complex for a constrained WSN environment. This thesis investigates a new approach to WSN security which addresses many of the shortcomings of existing mechanisms. It presents a detailed description on how to provide practical Public Key Cryptography solutions for wireless sensor networks. The contributions to the state-of-the-art are added on all levels of development beginning with the basic arithmetic operations and finishing with complete security protocols. This work includes a survey of different key distribution protocols that have been developed for WSNs, with an evaluation of their limitations. It also proposes Identity- Based Cryptography (IBC) as an ideal technique for key distribution in sensor networks. It presents the first in-depth study of the application and implementation of Pairing- Based Cryptography (PBC) to WSNs. This is followed by a presentation of the state of the art on the software implementation of Elliptic Curve Cryptography (ECC) on typical WSNplatforms. New optimized algorithms for performing multiprecision multiplication on a broad range of low-end CPUs are introduced as well. Three novel protocols for key distribution are proposed in this thesis. Two of these are intended for non-interactive key exchange in flat and clustered networks respectively. A third key distribution protocol uses Identity-Based Encryption (IBE) to secure communication within a heterogeneous sensor network. This thesis includes also a comprehensive security evaluation that shows that proposed schemes are resistant to various attacks that are specific to WSNs. This work shows that by using the newest achievements in cryptography like pairings and IBC it is possible to deliver affordable public-key cryptographic solutions and to apply a sufficient level of security for the most demanding WSN applications

Design and analysis of efficient and secure elliptic curve cryptoprocessors

Elliptic Curve Cryptosystems have attracted many researchers and have been included in many standards such as IEEE, ANSI, NIST, SEC and WTLS. The ability to use smaller keys and computationally more efficient algorithms compared with earlier public key cryptosystems such as RSA and ElGamal are two main reasons why elliptic curve cryptosystems are becoming more popular. They are considered to be particularly suitable for implementation on smart cards or mobile devices. Power Analysis Attacks on such devices are considered serious threat due to the physical characteristics of these devices and their use in potentially hostile environments. This dissertation investigates elliptic curve cryptoprocessor architectures for curves defined over GF(2m) fields. In this dissertation, new architectures that are suitable for efficient computation of scalar multiplications with resistance against power analysis attacks are proposed and their performance evaluated. This is achieved by exploiting parallelism and randomized processing techniques. Parallelism and randomization are controlled at different levels to provide more efficiency and security. Furthermore, the proposed architectures are flexible enough to allow designers tailor performance and hardware requirements according to their performance and cost objectives. The proposed architectures have been modeled using VHDL and implemented on FPGA platform