Towards Efficient Hardware Implementation of Elliptic and Hyperelliptic Curve Cryptography

Implementation of elliptic and hyperelliptic curve cryptographic algorithms has been the focus of a great deal of recent research directed at increasing efficiency. Elliptic curve cryptography (ECC) was introduced independently by Koblitz and Miller in the 1980s. Hyperelliptic curve cryptography (HECC), a generalization of the elliptic curve case, allows a decreasing field size as the genus increases. The work presented in this thesis examines the problems created by limited area, power, and computation time when elliptic and hyperelliptic curves are integrated into constrained devices such as wireless sensor network (WSN) and smart cards. The lack of a battery in wireless sensor network limits the processing power of these devices, but they still require security. It was widely believed that devices with such constrained resources cannot incorporate a strong HECC processor for performing cryptographic operations such as elliptic curve scalar multiplication (ECSM) or hyperelliptic curve divisor multiplication (HCDM). However, the work presented in this thesis has demonstrated the feasibility of integrating an HECC processor into such devices through the use of the proposed architecture synthesis and optimization techniques for several inversion-free algorithms. The goal of this work is to develop a hardware implementation of binary elliptic and hyperelliptic curves. The focus is on the modeling of three factors: register allocation, operation scheduling, and storage binding. These factors were then integrated into architecture synthesis and optimization techniques in order to determine the best overall implementation suitable for constrained devices. The main purpose of the optimization is to reduce the area and power. Through analysis of the architecture optimization techniques for both datapath and control unit synthesis, the number of registers was reduced by an average of 30%. The use of the proposed efficient explicit formula for the different algorithms also enabled a reduction in the number of read/write operations from/to the register file, which reduces the processing power consumption. As a result, an overall HECC processor requires from 1843 to 3595 slices for a Xilinix XC4VLX200 and the total computation time is limited to between 10.08 ms to 15.82 ms at a maximum frequency of 50 MHz for a varity of inversion-free coordinate systems in hyperelliptic curves. The value of the new model has been demonstrated with respect to its implementation in elliptic and hyperelliptic curve crypogrpahic algorithms, through both synthesis and simulations. In summary, a framework has been provided for consideration of interactions with synthesis and optimization through architecture modeling for constrained enviroments. Insights have also been presented with respect to improving the design process for cryptogrpahic algorithms through datapath and control unit analysis

Studies on high-speed hardware implementation of cryptographic algorithms

Cryptographic algorithms are ubiquitous in modern communication systems where they have a central role in ensuring information security. This thesis studies efficient implementation of certain widely-used cryptographic algorithms. Cryptographic algorithms are computationally demanding and software-based implementations are often too slow or power consuming which yields a need for hardware implementation. Field Programmable Gate Arrays (FPGAs) are programmable logic devices which have proven to be highly feasible implementation platforms for cryptographic algorithms because they provide both speed and programmability. Hence, the use of FPGAs for cryptography has been intensively studied in the research community and FPGAs are also the primary implementation platforms in this thesis. This thesis presents techniques allowing faster implementations than existing ones. Such techniques are necessary in order to use high-security cryptographic algorithms in applications requiring high data rates, for example, in heavily loaded network servers. The focus is on Advanced Encryption Standard (AES), the most commonly used secret-key cryptographic algorithm, and Elliptic Curve Cryptography (ECC), public-key cryptographic algorithms which have gained popularity in the recent years and are replacing traditional public-key cryptosystems, such as RSA. Because these algorithms are well-defined and widely-used, the results of this thesis can be directly applied in practice. The contributions of this thesis include improvements to both algorithms and techniques for implementing them. Algorithms are modified in order to make them more suitable for hardware implementation, especially, focusing on increasing parallelism. Several FPGA implementations exploiting these modifications are presented in the thesis including some of the fastest implementations available in the literature. The most important contributions of this thesis relate to ECC and, specifically, to a family of elliptic curves providing faster computations called Koblitz curves. The results of this thesis can, in their part, enable increasing use of cryptographic algorithms in various practical applications where high computation speed is an issue

Recent Application in Biometrics

In the recent years, a number of recognition and authentication systems based on biometric measurements have been proposed. Algorithms and sensors have been developed to acquire and process many different biometric traits. Moreover, the biometric technology is being used in novel ways, with potential commercial and practical implications to our daily activities. The key objective of the book is to provide a collection of comprehensive references on some recent theoretical development as well as novel applications in biometrics. The topics covered in this book reflect well both aspects of development. They include biometric sample quality, privacy preserving and cancellable biometrics, contactless biometrics, novel and unconventional biometrics, and the technical challenges in implementing the technology in portable devices. The book consists of 15 chapters. It is divided into four sections, namely, biometric applications on mobile platforms, cancelable biometrics, biometric encryption, and other applications. The book was reviewed by editors Dr. Jucheng Yang and Dr. Norman Poh. We deeply appreciate the efforts of our guest editors: Dr. Girija Chetty, Dr. Loris Nanni, Dr. Jianjiang Feng, Dr. Dongsun Park and Dr. Sook Yoon, as well as a number of anonymous reviewers

Efficient Cryptographic Algorithms and Protocols for Mobile Ad Hoc Networks

As the next evolutionary step in digital communication systems, mobile ad hoc networks (MANETs) and their specialization like wireless sensor networks (WSNs) have been attracting much interest in both research and industry communities. In MANETs, network nodes can come together and form a network without depending on any pre-existing infrastructure and human intervention. Unfortunately, the salient characteristics of MANETs, in particular the absence of infrastructure and the constrained resources of mobile devices, present enormous challenges when designing security mechanisms in this environment. Without necessary measures, wireless communications are easy to be intercepted and activities of users can be easily traced. This thesis presents our solutions for two important aspects of securing MANETs, namely efficient key management protocols and fast implementations of cryptographic primitives on constrained devices. Due to the tight cost and constrained resources of high-volume mobile devices used in MANETs, it is desirable to employ lightweight and specialized cryptographic primitives for many security applications. Motivated by the design of the well-known Enigma machine, we present a novel ultra-lightweight cryptographic algorithm, referred to as Hummingbird, for resource-constrained devices. Hummingbird can provide the designed security with small block size and is resistant to the most common attacks such as linear and differential cryptanalysis. Furthermore, we also present efficient software implementations of Hummingbird on 4-, 8- and 16-bit microcontrollers from Atmel and Texas Instruments as well as efficient hardware implementations on the low-cost field programmable gate arrays (FPGAs) from Xilinx, respectively. Our experimental results show that after a system initialization phase Hummingbird can achieve up to 147 and 4.7 times faster throughput for a size-optimized and a speed-optimized software implementation, respectively, when compared to the state-of-the-art ultra-lightweight block cipher PRESENT on the similar platforms. In addition, the speed optimized Hummingbird encryption core can achieve a throughput of 160.4 Mbps and the area optimized encryption core only occupies 253 slices on a Spartan-3 XC3S200 FPGA device. Bilinear pairings on the Jacobians of (hyper-)elliptic curves have received considerable attention as a building block for constructing cryptographic schemes in MANETs with new and novel properties. Motivated by the work of Scott, we investigate how to use efficiently computable automorphisms to speed up pairing computations on two families of non-supersingular genus 2 hyperelliptic curves over prime fields. Our findings lead to new variants of Miller's algorithm in which the length of the main loop can be up to 4 times shorter than that of the original Miller's algorithm in the best case. We also generalize Chatterjee et al.'s idea of encapsulating the computation of the line function with the group operations to genus 2 hyperelliptic curves, and derive new explicit formulae for the group operations in projective and new coordinates in the context of pairing computations. Efficient software implementation of computing the Tate pairing on both a supersingular and a non-supersingular genus 2 curve with the same embedding degree of k = 4 is investigated. Combining the new algorithm with known optimization techniques, we show that pairing computations on non-supersingular genus 2 curves over prime fields use up to 55.8% fewer field operations and run about 10% faster than supersingular genus 2 curves for the same security level. As an important part of a key management mechanism, efficient key revocation protocol, which revokes the cryptographic keys of malicious nodes and isolates them from the network, is crucial for the security and robustness of MANETs. We propose a novel self-organized key revocation scheme for MANETs based on the Dirichlet multinomial model and identity-based cryptography. Firmly rooted in statistics, our key revocation scheme provides a theoretically sound basis for nodes analyzing and predicting peers' behavior based on their own observations and other nodes' reports. Considering the difference of malicious behaviors, we proposed to classify the nodes' behavior into three categories, namely good behavior, suspicious behavior and malicious behavior. Each node in the network keeps track of three categories of behavior and updates its knowledge about other nodes' behavior with 3-dimension Dirichlet distribution. Based on its own analysis, each node is able to protect itself from malicious attacks by either revoking the keys of the nodes with malicious behavior or ceasing the communication with the nodes showing suspicious behavior for some time. The attack-resistant properties of the resulting scheme against false accusation attacks launched by independent and collusive adversaries are also analyzed through extensive simulations. In WSNs, broadcast authentication is a crucial security mechanism that allows a multitude of legitimate users to join in and disseminate messages into the networks in a dynamic and authenticated way. During the past few years, several public-key based multi-user broadcast authentication schemes have been proposed in the literature to achieve immediate authentication and to address the security vulnerability intrinsic to μTESLA-like schemes. Unfortunately, the relatively slow signature verification in signature-based broadcast authentication has also incurred a series of problems such as high energy consumption and long verification delay. We propose an efficient technique to accelerate the signature verification in WSNs through the cooperation among sensor nodes. By allowing some sensor nodes to release the intermediate computation results to their neighbors during the signature verification, a large number of sensor nodes can accelerate their signature verification process significantly. When applying our faster signature verification technique to the broadcast authentication in a 4×4 grid-based WSN, a quantitative performance analysis shows that our scheme needs 17.7%~34.5% less energy and runs about 50% faster than the traditional signature verification method

Performance of HECC coprocessors using inversion-free formulae

The HyperElliptic Curve Cryptosystem (HECC) was quite extensively studied during the recent years. In the open literature one can find results on how to improve the group operations of HECC as well as teh implementations for various types of processors. There have also been some efforts to implement HECC on hardware devices, like for instance FPGAs. Only one of these works, however, deals with the inversion-free formulae to compute the group operations of HECC. We present inversion-free group operations for the HEC y^2 + xy = x^5 + f1x + f0 and we target characteristic-two fields. The reason is that of allowing a fair comparison with hardware architectures using the affine case. In the main part of the paper we use these results to investigate various hardware architectures for a HECC VLSI coprocessor. If area constraints are not considered, scalar multiplication can be performed in 19,769 clock cycles using three field multipliers (of type D = 32), one field adder and one field squarer, where D indicates the digit-size of the multiplier. However, the optimal solution in terms of latency and area uses two multipliers (of type D = 4), one addition and one squaring. The main finding of the present contribution is that coprocessors based on the inversion-free formulae should be preferred compared to those using group operations containing inversion. This holds despite the fact that one field inversion in the affine HECC group operation is traded by up to 24 field multiplications in the inversion-free case