Abstract
This paper proposed different approaches to enhance the performance of the Elliptic Curve Cryptography (ECC) algorithm. ECC is vulnerable to attacks by exploiting the public parameters of ECC to solve Discrete Logarithm Problem (DLP). Therefore, these public parameters should be selected safely to obviate all recognized attacks. This paper presents a new generator function to produce the domain parameters for creating the elliptic curve; a secure mechanism is used in the proposed function to avoid all possible known attacks that attempts to solve the Elliptic Curve Discrete Logarithm Problem (ECDLP). Moreover, an efficient algorithm has been proposed for choosing two base points from the curve in order to generate two subgroups in a secure manner. The purpose of the aforementioned algorithm is to offer more confidence for the user since it is not built upon a hidden impairment that it could be subsequently utilized to retrieve user’s private key. The Elliptic Curve Diffie Hellman (ECDH) algorithm is implemented to exchange a session key between the communicating parties in a secure manner. Beside, a preprocessing operation is performed on the message to enhance the diffusion property and consequently leads to increase the strength against cryptanalysis attack. Finally, the dual encryption/decryption algorithm is implemented using different session keys in each stage of the encryption to boost immunity against any attack on the digital audio transmission. The gained results show the positive effect of the dual elliptic curve system in terms of speed and confidentiality without needing any extra time for encryption.
Highlights
Elliptic curves were suggested by Neal Koblitz and VictorMiller independently in 1985 to design a public-key cryptographic system [1]
The Elliptic Curve Cryptography (ECC) offers more security compared to the RSA algorithm since it is based on Discrete Logarithm Problem (DLP), while the latest algorithm based on the prime number factorization problem [2], [3]
The layout of this paper is composed of the following sections: the related work of elliptic curve cryptography is introduced in Section II, Section III describes the concepts of the advanced encryption standard and cryptographic hash function, the linear congruential generator is presented in Section IV, Section V clarifies the password based key derivation function, Section VI discusses the proposed system followed by the experimental results and discussion in Section VII, and Section VIII presents the conclusions
Summary
The Elliptic Curve Cryptography (ECC) is a public-key cryptosystem which playing an important role in cryptography world. The ECC offers more security compared to the RSA algorithm since it is based on DLP, while the latest algorithm based on the prime number factorization problem [2], [3]. ) , addition a with times and it is performed over an elliptic curve. The definition of elliptic curve is based on the equation, two variables and two coefficients; the values of variables and coefficients are limited to elements of a finite field [1]. The elliptic curve over the prime field is considered. A. Mathematics of ECC Over Finite Field In general, an elliptic curve E over prime field ( ). The coefficients must satisfy (2), where Δ denoted to the discriminant of E
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