Elliptic Curve Cryptography Engineering

Lecture Notes in Computer Science, 2002

We present an implementation of an EC cryptographic library targeting three main objectives: portability, modularity, and ease of use. Our goal is to provide a fully-equipped library of portable source code with clearly separated modules that allows for easy development of EC cryptographic protocols, and which can be readily tailored to suit different requirements and user needs. We discuss several implementation issues regarding the development of the library and report on some preliminary experiments.

Journal of Internet Technology and Secured Transaction, 2012

We present in this paper an important area of information security emerged in the last decades, namely Elliptic Curves Cryptosystems (ECC). Compared to traditional public-key cryptosystems like RSA or Diffie-Hellman, ECC offers equivalent security with smaller key sizes; these result in faster computations, lower power consumption, as well as memory and bandwidth savings. ECC are more and more considered as an attractive public-key cryptosystem for mobile/wireless environments. ECC are especially useful for mobile devices, which are typically limited in terms of their CPU, power and network connectivity. ECC are the next frontier in the use of security mechanisms by providing good security margins with lower computational cost. ECC's domain is an important field emerged in information security. The elliptic curves (EC) are used for conceiving efficient factorization algorithms and for proving the primality. They are used in public key cryptosystems and in pseudorandom bit generators, too. The elliptic curves were also applied in Codes Theory, where they were used to create very good error protected codes. In this paper, our aim is to examine the security, implementation and performance of ECC applications on various mobile devices. Also, our goal is to compare ECC and conventional PKC performances. Doing these, we want to prove that ECC could become the next-generation of PKC.

2005

The main target of this work is to expose the capacities that make elliptic curve cryptography the most suitable one to he implemented in environments with several constraints related to processor speed, bandwidth, security and memory. We have analyzed several elliptic curve cryptosystems with other public key ones. We have made a comparison among different puhlic key cryptosystems (such as ElGamal for encryption and Diffic-Hellman for kcy cxchanging) and thc corresponding ones based on elliptic curve theory; highlighting algorithm speed characteristics.

International Journal of Electrical and Computer Engineering (IJECE), 2011

The paper presents an extensive and careful study of elliptic curve cryptography (ECC) and its applications. This paper also discuss the arithmetic involved in elliptic curve and how these curve operations is crucial in determining the performance of cryptographic systems. It also presents different forms of elliptic curve in various coordinate system , specifying which is most widely used and why. It also explains how isogenenies between elliptic curve provides the secure ECC. Exentended form of elliptic curve i.e hyperelliptic curve has been presented here with its pros and cons. Performance of ECC and HEC is also discussed based on scalar multiplication and DLP.

Cryptologia, 2015

The most popular encryption scheme based on elliptic curves is the Elliptic Curve Integrated Encryption Scheme (ECIES), which is included in ANSI X9.63, IEEE 1363a, ISO/IEC 18033-2, and SECG SEC1. These standards offer many ECIES options, not always compatible, making it difficult to decide what parameters and cryptographic elements to use in a specific deployment scenario. In this work, we show that a secure and practical implementation of ECIES can only be compatible with two of the four previously mentioned standards. In addition to that, we provide the list of functions and options that must be used in such an implementation. Finally, we present the results obtained when testing this ECIES version implemented as a Java application, which allows us to produce some comments and remarks about the performance and feasibility of our proposed solution.

2016

The cryptographic code that runs the Internet is subject to intense manual optimization by elite programmers. Most of the complexity of the optimized code comes from manipulation of integers too large to fit in hardware registers. Perhaps surprisingly, for a change as innocuous as changing an algorithmic parameter to a different prime number, significant pieces of code are rewritten from scratch. Only a handful of experts on the planet are seen as competent enough to do it well, and new implementations (which often include significant amounts of handwritten assembly) tend to take months to code and debug. In this paper, we demonstrate that the work of those experts can be automated while simultaneously increasing our confidence in code correctness. We implemented a framework in the Coq proof assistant for generating efficient code for elliptic curve cryptography (ECC), with proofs of conformance to a whiteboard-level specification in number theory. While some past projects have veri...

Lecture Notes in Computer Science, 2001

introduced a family of binary finite fields which are composite extensions of F2 and on which arithmetic operations can be performed more quickly than on prime extensions of F2 of the same size. We present here a fast approach to elliptic curve cryptography using a distinguished subset of the set of Silverman fields F 2 N = F h n . This approach leads to a theoretical computation speedup over fields of the same size, using a standard point of view (cf. ). We also analyse their security against prime extension fields F2p , where p is prime, following the method of Menezes and Qu . We conclude that our fields do not present any significant weakness towards the solution of the elliptic curve discrete logarithm problem and that often the Weil descent of Galbraith-Gaudry-Hess-Smart (GGHS) does not offer a better attack on elliptic curves defined over F 2 N than on those defined over F2p , with a prime p of the same size as N . A noteworthy example is provided by F 2 226 : a generic elliptic curve Y 2 + XY = X 3 + αX 2 + β defined over F 2 226 is as prone to the GGHS Weil descent attack as a generic curve defined on the NIST field F 2 233 . Elliptic curve cryptography was introduced in 1986 independently by Koblitz [10] and Miller as a rich context where one can apply cryptographic protocols based on the discrete logarithm problem in a multiplicative group G: given a, b ∈ G such that b = a d , find d. However, the rich structure of elliptic curves made possible a wide variety of attacks that must be avoided in the design of elliptic curve ⋆

Internetworking Indonesia, 2009

Vol. 1/No. 1 (2009) INTERNETWORKING INDONESIA JOURNAL 29 Abstract—This work discusses issues in implementing Elliptic Curve Cryptography (ECC). It provides a brief explanation about ECC basic theory, implementation, and also provides guidance for further reading by ...

IEEE Transactions on Very Large Scale Integration (VLSI) Systems, 2000

This paper presents a method for producing hardware designs for elliptic curve cryptography (ECC) systems over the finite field GF(2 ), using the optimal normal basis for the representation of numbers. Our field multiplier design is based on a parallel architecture containing multiple -bit serial multipliers; by changing the number of such serial multipliers, designers can obtain implementations with different tradeoffs in speed, size and level of security. A design generator has been developed which can automatically produce a customised ECC hardware design that meets user-defined requirements. To facilitate performance characterization, we have developed a parametric model for estimating the number of cycles for our generic ECC architecture. The resulting hardware implementations are among the fastest reported: for a key size of 270 bits, a point multiplication in a Xilinx XC2V6000 FPGA at 35 MHz can run over 1000 times faster than a software implementation on a Xeon computer at 2.6 GHz.

2013

Elliptic curve cryptography is an asymmetric key cryptography. The points on two dimensional elliptic curve are used for declaration of data encryption & decryption. It include public key generation on the elliptic curve and private key generation to decrypt the data. The present paper deals with an overview of Elliptic curve cryptography (ECC) and its implementation through coordinate geometry for data encryption. We introduce a new approach in the form of cardan's method to find points on X axis at elliptic curve over finite field and form public key cryptographic system and finally we define two dimensional alphabetic table and description in the form of algorithm to use it for plain text encryption.

Proceedings of the Second International Conference on Cryptology in India Progress in Cryptology, 2001

introduced a family of binary finite fields which are composite extensions of F2 and on which arithmetic operations can be performed more quickly than on prime extensions of F2 of the same size. We present here a fast approach to elliptic curve cryptography using a distinguished subset of the set of Silverman fields F 2 N = F h n . This approach leads to a theoretical computation speedup over fields of the same size, using a standard point of view (cf. ). We also analyse their security against prime extension fields F2p , where p is prime, following the method of Menezes and Qu . We conclude that our fields do not present any significant weakness towards the solution of the elliptic curve discrete logarithm problem and that often the Weil descent of Galbraith-Gaudry-Hess-Smart (GGHS) does not offer a better attack on elliptic curves defined over F 2 N than on those defined over F2p , with a prime p of the same size as N . A noteworthy example is provided by F 2 226 : a generic elliptic curve Y 2 + XY = X 3 + αX 2 + β defined over F 2 226 is as prone to the GGHS Weil descent attack as a generic curve defined on the NIST field F 2 233 . Elliptic curve cryptography was introduced in 1986 independently by Koblitz [10] and Miller as a rich context where one can apply cryptographic protocols based on the discrete logarithm problem in a multiplicative group G: given a, b ∈ G such that b = a d , find d. However, the rich structure of elliptic curves made possible a wide variety of attacks that must be avoided in the design of elliptic curve ⋆

International Journal of Electrical and Computer Engineering (IJECE), 2024

The elliptic curve cryptosystem (ECC) has several applications in Information Security, especially in cryptography with two main activities including encrypting and decrypting. There were several solutions of different research teams which propose various forms of the elliptic curve cryptosystem on cryptographic sector. In the paper, we proposed a solution for applying the elliptic curve on cryptography which is based on these proposals as well as basic idea about the elliptic curve cryptosystem. We also make comparison between our proposal and other listed solution in the same application of the elliptic curve for designing encryption and decryption algorithms. The comparison results are based on parameters such as time consumption (t), RAM consumption (MB), source code size (Bytes), and computational complexity.

2010

This paper is intended to set up a strategy for design of elliptic curve (EC) operations in order to design an EC cryptoprocessor to be used in cryptographic applications using new modern technologies (e.g. FPGA) that provide integrated chip emulation. Also, we present the strategy for evaluating and certification of the developed product.

1997

The security of many cryptographic protocols depends on the di culty of solving the so-called \discrete logarithm" problem, in the multiplicative group of a nite eld. Although, in the general case, there are no polynomial time algorithms for this problem, constant improvements are being made { with the result that the use of these protocols require much larger key sizes, for a given level of security, than may be convenient.

2006

Public key cryptography systems are based on sound mathematical foundations that are designed to make the problem hard for an intruder to break into the system. The major approaches that since 1976 have withstood intruder attacks, are the discrete logarithm Mr. Raja Ghosal PhD Student, Auto-ID Lab, ADELAIDE School of Electrical and Electronics Engineering, The University of Adelaide Prof. Peter H. Cole Research Director, Auto-ID Lab, ADELAIDE School of Electrical and Electronics Engineering, The University of Adelaide Contact: [email protected] or [email protected]. Internet: www.autoidlabs.org