Elliptical Curve Digital Signatures Algorithm

Elliptical digital signatures algorithm provides security services for resource constrained embedded devices. The ECDSA level security can be enhanced by several parameters as parameter key size and the security level of ECDSA elementary modules such as hash function, elliptic curve point multiplication on koblitz curve which is used to compute public key and a pseudo-random generator which generates key pair generation. This paper describes novel security approach on authentication schemes as a modification of ECDSA scheme. This paper provides a comprehensive survey of recent developments on elliptic curve digital signatures approaches. The survey of ECDSA involves major issues like security of cryptosystem, RFID-tag authentication, Montgomery multiplication over binary fields, Scaling techniques, Signature generation ,signature verification, point addition and point doubling of the different coordinate system and classification. DOI: 10.17762/ijritcc2321-8169.150318

High Speed Low Power GF(2k) Elliptic Curve Cryptography Processor Architecture

A new elliptic curve cryptographic processor architecture is proposed in this paper. It gives a choice of performance base depending on the importance of speed and/or power consumption. This flexibility is accomplished by utilizing the normal parallelism in the elliptic curve point operations. Scalable multipliers are adopted to compensate for the extra hardware due to parallelism instead of using the conventional parallel multipliers. It is shown in the paper that this parallelism can be exploited either to increase the speed of operation or to reduce power consumption by reducing the frequency of operation

High Speed Low Power GF(2k) Elliptic Curve Cryptography Processor Architecture

A new elliptic curve cryptographic processor architecture is proposed in this paper. It gives a choice of performance base depending on the importance of speed and/or power consumption. This flexibility is accomplished by utilizing the normal parallelism in the elliptic curve point operations. Scalable multipliers are adopted to compensate for the extra hardware due to parallelism instead of using the conventional parallel multipliers. It is shown in the paper that this parallelism can be exploited either to increase the speed of operation or to reduce power consumption by reducing the frequency of operation

Enhancement of Security Architecture for Smartcard Based Authentication Protocols

Currently computer systems and software used by the average user offer less security due to rapid growth of vulnerability techniques. This dissertation presents an approach to increase the level of security provided to users when interacting with otherwise unsafe applications and computing systems. It provides a general framework for constructing and analyzing authentication protocols in realistic models of communication networks. This framework provides a sound formalization for the authentication problem and suggests simple and attractive design principles for general authentication protocols. The general approach uses trusted devices (specifically smartcards) to provide an area of secure processing and storage. The key element in this approach is a modular treatment of the authentication problem in cryptographic protocols; this applies to the definition of security, to the design of the protocols, and to their analysis. The definitions are drawn from previous ideas and formalizations and incorporate several aspects that were previously overlooked. To identify the best cryptographic algorithm suitable for smartcard applications, the dissertation also investigates the implementation of Elliptic Curve encryption techniques and presents performance comparisons based on similar techniques. The findings discovered that the proposed Elliptic Curve Cryptograpluc (ECC) method provides greater efficiency than similar method in terms of computational speed. Specifically, several aspects of authentication protocols were studied, and new definitions of this problem were presented in various settings depending on the underlying network. Further, the thesis shows how to systematically transform solutions that work in a model of idealized authenticated communications into solutions that are secure in the realistic setting of wired communication channels such as access control, and online transactions involving contact communication schemes. As with all software development, good design and engineering practices are important for software quality. Rather than thinking of security as an add-on feature to software systems, security should be designed into the system from the earliest stages of requirements gathering through development, testing, integration, and deployment. In view of this, a new approach for dealing with this problem in an object-oriented approach is presented. Some practical illustrations were analyzed based on the Unified Modeling Language (UML) as it applies to modeling authentication/access control schemes in online transactions. In particular, important issues such as how smartcard applications can be modeled using UML techniques and how UML can be used to sketch the operations for implementing a secure access using smartcard has been addressed

An implementation of the El Gamal elliptic curve cryptosystem over a finite field of characteristic P

Since the earliest times, individuals and groups of individuals have been interested in communicating sensitive information in a manner which would guarantee that such information could not be arbitrarily received. Further, such information was to be received by select recipients and this required that a means of secure information transmission be found and employed. To these ends, methods of information encryption have ever since been sought and employed. The entire study and practice of this activity, cryptology, the science of message encryption and decryption, provides a framework for this thesis. In particular, the development of cryptology has been influenced by some specific areas of mathematics, employing abstract mathematical concepts and utilizing algebraic structures known as elliptic curves. It is with respect to these structures and their utilization in specific cryptosystems, called elliptic curve cryptosystems on which this thesis focuses. More specifically, this thesis is concerned with the implementation of such a cryptosystem and is a demonstration of that implementation. Additional pertinent examples, illustrations and supporting computer programs are included to present a self-contained work

A microcoded elliptic curve cryptographic processor.

Leung Ka Ho.Thesis (M.Phil.)--Chinese University of Hong Kong, 2001.Includes bibliographical references (leaves [85]-90).Abstracts in English and Chinese.Abstract --- p.iAcknowledgments --- p.iiiList of Figures --- p.ixList of Tables --- p.xiChapter 1 --- Introduction --- p.1Chapter 1.1 --- Motivation --- p.1Chapter 1.2 --- Aims --- p.3Chapter 1.3 --- Contributions --- p.3Chapter 1.4 --- Thesis Outline --- p.4Chapter 2 --- Cryptography --- p.6Chapter 2.1 --- Introduction --- p.6Chapter 2.2 --- Foundations --- p.6Chapter 2.3 --- Secret Key Cryptosystems --- p.8Chapter 2.4 --- Public Key Cryptosystems --- p.9Chapter 2.4.1 --- One-way Function --- p.10Chapter 2.4.2 --- Certification Authority --- p.10Chapter 2.4.3 --- Discrete Logarithm Problem --- p.11Chapter 2.4.4 --- RSA vs. ECC --- p.12Chapter 2.4.5 --- Key Exchange Protocol --- p.13Chapter 2.4.6 --- Digital Signature --- p.14Chapter 2.5 --- Secret Key vs. Public Key Cryptography --- p.16Chapter 2.6 --- Summary --- p.18Chapter 3 --- Mathematical Background --- p.19Chapter 3.1 --- Introduction --- p.19Chapter 3.2 --- Groups and Fields --- p.19Chapter 3.3 --- Finite Fields --- p.21Chapter 3.4 --- Modular Arithmetic --- p.21Chapter 3.5 --- Polynomial Basis --- p.21Chapter 3.6 --- Optimal Normal Basis --- p.22Chapter 3.6.1 --- Addition --- p.23Chapter 3.6.2 --- Squaring --- p.24Chapter 3.6.3 --- Multiplication --- p.24Chapter 3.6.4 --- Inversion --- p.30Chapter 3.7 --- Summary --- p.33Chapter 4 --- Literature Review --- p.34Chapter 4.1 --- Introduction --- p.34Chapter 4.2 --- Hardware Elliptic Curve Implementation --- p.34Chapter 4.2.1 --- Field Processors --- p.34Chapter 4.2.2 --- Curve Processors --- p.36Chapter 4.3 --- Software Elliptic Curve Implementation --- p.36Chapter 4.4 --- Summary --- p.38Chapter 5 --- Introduction to Elliptic Curves --- p.39Chapter 5.1 --- Introduction --- p.39Chapter 5.2 --- Historical Background --- p.39Chapter 5.3 --- Elliptic Curves over R2 --- p.40Chapter 5.3.1 --- Curve Addition and Doubling --- p.41Chapter 5.4 --- Elliptic Curves over Finite Fields --- p.44Chapter 5.4.1 --- Elliptic Curves over Fp with p>〉3 --- p.44Chapter 5.4.2 --- Elliptic Curves over F2n --- p.45Chapter 5.4.3 --- Operations of Elliptic Curves over F2n --- p.46Chapter 5.4.4 --- Curve Multiplication --- p.49Chapter 5.5 --- Elliptic Curve Discrete Logarithm Problem --- p.51Chapter 5.6 --- Public Key Cryptography --- p.52Chapter 5.7 --- Elliptic Curve Diffie-Hellman Key Exchange --- p.54Chapter 5.8 --- Summary --- p.55Chapter 6 --- Design Methodology --- p.56Chapter 6.1 --- Introduction --- p.56Chapter 6.2 --- CAD Tools --- p.56Chapter 6.3 --- Hardware Platform --- p.59Chapter 6.3.1 --- FPGA --- p.59Chapter 6.3.2 --- Reconfigurable Hardware Computing --- p.62Chapter 6.4 --- Elliptic Curve Processor Architecture --- p.63Chapter 6.4.1 --- Arithmetic Logic Unit (ALU) --- p.64Chapter 6.4.2 --- Register File --- p.68Chapter 6.4.3 --- Microcode --- p.69Chapter 6.5 --- Parameterized Module Generator --- p.72Chapter 6.6 --- Microcode Toolkit --- p.73Chapter 6.7 --- Initialization by Bitstream Reconfiguration --- p.74Chapter 6.8 --- Summary --- p.75Chapter 7 --- Results --- p.76Chapter 7.1 --- Introduction --- p.76Chapter 7.2 --- Elliptic Curve Processor with Serial Multiplier (p = 1) --- p.76Chapter 7.3 --- Projective verses Affine Coordinates --- p.78Chapter 7.4 --- Elliptic Curve Processor with Parallel Multiplier (p > 1) --- p.79Chapter 7.5 --- Summary --- p.80Chapter 8 --- Conclusion --- p.82Chapter 8.1 --- Recommendations for Future Research --- p.83Bibliography --- p.85Chapter A --- Elliptic Curves in Characteristics 2 and3 --- p.91Chapter A.1 --- Introduction --- p.91Chapter A.2 --- Derivations --- p.91Chapter A.3 --- "Elliptic Curves over Finite Fields of Characteristic ≠ 2,3" --- p.92Chapter A.4 --- Elliptic Curves over Finite Fields of Characteristic = 2 --- p.94Chapter B --- Examples of Curve Multiplication --- p.95Chapter B.1 --- Introduction --- p.95Chapter B.2 --- Numerical Results --- p.9

Fast 160-Bits GF (P) Elliptic Curve Crypto Hardware of High-Radix Scalable Multipliers

In this paper, a fast hardware architecture for elliptic curve cryptography computation in Galois Field GF(p) is proposed. The architecture is implemented for 160-bits, as its data size to handle. The design adopts projective coordinates to eliminate most of the required GF(p) inversion calculations replacing them with several multiplication operations. The hardware is intended to be scalable, which allows the hardware to compute long precision numbers in a repetitive way. The design involves four parallel scalable multipliers to gain the best speed. This scalable design was implemented in different versions depending on the area and speed. All scalable implementations were compared with an available FPGA design. The proposed scalable hardware showed interesting results in both area and speed. It also showed some area-time flexibility to accommodate the variation needed by different crypto applications

Efficient utilization of scalable multipliers in parallel to compute GF(p) elliptic curve cryptographic operations

This paper presents the design and implementation of an elliptic curve cryptographic core to realize point scalar multiplication operations used for the GF(p) elliptic curve encryption/decryption and the elliptic curve digital signature algorithm (ECDSA). The design makes use of projective coordinates together with scalable Montgomery multipliers for data size of up to 256-bits. We propose using four multiplier cores together with the ordinary projective coordinates which outperform implementations with Jacobean coordinates typically believed to perform better. The proposed architecture is particularly attractive for elliptic curve cryptosystems when hardware area optimization is the key concern