Towards an Efficient Public Key Cryptosystem

2013

Abstract. The basic operation in elliptic curve cryptosystem is scalar multiplication. It is the computation of integer multiple of a given point on the curve. Computation of scalar multiple is faster by using signed binary representation as compared to binary representation. In this paper ‘Direct Recoding Method ’ a new modified algorithm for computation of signed binary representation is proposed. Our proposed method is efficient when compared to other standard methods such as NAF, MOF and complementary recoding method.

International Journal of Advances in Applied Sciences (IJAAS), 2024

The idea of an addition chain can be applied to scalar multiplication involving huge number operations in elliptic curve cryptosystems. In this article, initially, we study the taxonomy of the addition chain problem to build up an understanding of the problem. We then examine the mathematics behind an optimal addition chain that includes the theoretical boundary for the upper limit and lower limit which laid the foundation for experimentation hereafter. In the following, we examine different addition chain solutions that were used to increase efficiency in scalar multiplication. To avoid any possible confusion, we intentionally separated the discussion into two modules called integer recoding method and chain generator based on the heuristics method. These methods were developed by considering various aspects such as the space within which the operation is executed, the curve that is selected, the formulation to express the original equation, and the choices of operation and arithmetic, all together to improve operational efficiency.

Advances in Cryptology-ASIACRYPT …, 2005

Abstract. In this paper, we propose a efficient and secure point mul-tiplication algorithm, based on double-base chains. This is achieved by taking advantage of the sparseness and the ternary nature of the so-called double-base number system (DBNS). The speed-ups are the re- ...

International Journal of Computer Applications, 2018

The purpose of this research is to enhance the cryptographic system called the Elliptic Curve. Elliptic Curve cryptosystem (ECC) is a technique of public-key encryption, which is rooted on the arithmetical construction of elliptic curves over finite fields. Elliptic Curve Cryptographic System necessitates smaller keys compared to non-ECC cryptography to offer equal security. The security of RSA is based on the computational task of considering extensive numbers leading to an increase in encryption computation time, slower connection of the SSL handshake and increase in CPU usage during handshakes. Therefore, there should be a new way of solving this problem, which is ECC encryption. Elliptic curves are effective for digital signatures, key agreement, generators, pseudo-random and other related tasks. The first phase of the project involves understanding the key exchange of Diffie-Hellman and applying the properties of the Elliptic Curves. It is terminated with key facts that the Elliptic Curve Cryptography has a shorter key length, saves bandwidth, which facilitates key generation during the encryption/decryption of data, also the assurance of faster encryption and decryption, and notwithstanding its efficiency and efficacy in small devices.

2013 11th International Symposium on Programming and Systems (ISPS), 2013

ABSTRACT Sensor nodes have limited computing power and memory sizes. Sometimes, they are used in applications that require sending rapidly secure data to a remote control center. Therefore, they require lightweight techniques to accomplish this task. In this paper, we used Elliptical Curve Cryptography (ECC) for data encryption because ECC could create smaller and more efficient cryptographic keys compared to other cryptographic techniques such as RSA. We used specific algorithms to improve scalar multiplication time in spite of energy consumption. Moreover, we proposed a distributed scheme to enhance more the data delivery time from a source node to the base station by involving neighbors in the calculation. The results of experiments on TelosB motes showed considerable improvement of data delivery time.

2005

Among the various arithmetic operations required in implementing public key cryptographic algorithms, the elliptic curve point multiplication has probably received the maximum atten- tion from the research community in the last decade. Many methods for ecient and secure implementation of point multiplication have been proposed. The eciency of these methods mainly depends on the representation one uses for the scalar multiplier. In the current work we propose an ecient algorithm based on the so-called double-base number system. We introduce the new concept of double-base chains which, if manipulated with care, can significantly reduce the complexity of scalar multiplication on elliptic curves. Besides we have adopted some other measures to further reduce the operation count. Our algorithm compares favorably against classical and other similar approaches.

2015

Elliptic curve cryptosystem (ECC) is being used nowadays more than ever to fulfill the need for public key cryptosystem because of its ability to use shorter keys lengths and computationally more efficient algorithms than anther public key cryptosystems such as Rivest-Shamir- Adleman (RSA), Digital Signature Algorithm (DSA) and ElGamal. The most time consuming operation in ECC is elliptic curve scalar multiplication (ECSM). Many research have been carried out to accelerate this operation. The structure of the ECSM involves three mathematical levels: finite field arithmetic, point arithmetic and scalar arithmetic. The purpose of this work is to study different issues that arise in the efficient implementation of ECSM over prime field, specifically targeting the point and scalar arithmetic levels over elliptic curve. At the point arithmetic level, we introduce the 4- dimensional Jacobian coordinates system (4 - DJC), where a point (X; Y;Z; T) with Z 6= 0 and T = Z2, corresponds to aff...

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.

International Journal of Computer Applications, 2014

Elliptic curve scalar multiplication is the operation of successively adding a point along an elliptic curve to itself k times. It is used in elliptic curve cryptography (ECC) as a means of producing a trapdoor function. In this paper, algorithms to compute the elliptic curve scalar multiplication using a special form for integers will introduce, and then two types of signed digit representation will use. The signed digit form of the scalar is calculated by many types of algorithms such as binary , non adjacent form and direct recoding. The results indicate that the proposed methods perform better to compute the scalar multiplication on elliptic curves and it is more efficient than the existing methods.

International Journal of Advanced Computer Science, 2014

Since the inception of elliptic curve cryptography by Koblitz [1] and Miller [2] for implementing public-key protocols as the Diffie-Hellman key agreement, elliptic curve cryptography has become one of the most researched area for providing one stop reliable and secure solution in the field of cryptography. The ECC covers all relevant asymmetric cryptographic primitives like digital signature (ECDSA), key exchange and agreement protocols. Point multiplication serves as the basic building block in all ECC primitives and is the computationally most expensive operation and our analysis revolves around this concept. This paper gives an introduction to Elliptic Curve Cryptography and deals with evaluation of fast scalar multiplication with parallelization of field operation and point addition/multiplication. Elliptic curve cryptography offers best optimized solution with minimum resources like Low memory, High Throughput, low power consumption and minimum key length for the same level of security as compared to its counterpart like RSA, DSA etc. in public key cryptography domain. The work is based on the extensive research work done by Julio Lopez, Ricardo Dahab, Montgomery and other pioneer scientists and academicians in the field of elliptic curve cryptography. Given the importance of Scalar multiplication , we focused ourselves on the Fast Multiplication on Elliptic Curves over finite Binary field GF(2 m) without Pre-computation whose background is set by Julio Lopez et al. in [1], because the finite field operations can be implemented very efficiently in hardware and software.