Security Improvement in Elliptic Curve Cryptography

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.

Text Encryption with Improved Elliptic Curve Cryptography

“…The elliptic curve equation used was y 2 = x 3 + x + 1 mod 277. That is E 277 (1,1). Generated all the points of the elliptic curve using the conventional elliptic curve arithmetic, and created a mapping table for encryption/decryption operation.…”

“…Decryption is the opposite of encryption, which is the conversion of an encrypted file into its original format. Elliptic Curve Cryptography (ECC) is a public key cryptography that uses two set of keys for its operation, a private key and a public key [1]. The private key is usually an integer while the public key is usually a point on the elliptic curve.…”

A Proposed Algorithm for Encrypted Data Hiding in Video Stream Based on Frame Random Distribution

“…Elliptic curves have been studied by a number theorists for about a century, not for applications in mathematics or computing science, but because of their intrinsic mathematical beauty and interest [12,13]. An elliptic curve over a prime field is defined by ( ) Where the elliptic curve group consists of all points that satisfy the elliptic curve [7].…”

iTrust—A Trustworthy and Efficient Mapping Scheme in Elliptic Curve Cryptography

“…The crucial advantage associated with mapping points to an elliptic curve stems from an exploitation of the elliptic curve discrete logarithm problem (ECDLP) [17], which constitutes the base of ECC. However, if a message M, encrypted using ECC, did not map to an elliptic curve (i.e., the x value of M has no corresponding y), then it is necessary to increment x and recalculate until y is found [18][19][20]. However, the increment to x changes M, thereby resulting in the wrong decoding phase for the retrieval of M. Thus, to secure messages in the encoding and decoding phases, certain bits should be concatenated to mapping points to avoid changing the original message.…”