Image encryption scheme in public key cryptography based on cubic pells quadratic case

Abstract

Cryptography systems face new threats with the transformation of time and technology. Each innovation tries to contest challenges posed by the previous system by analyzing approaches that are able to provide impressive outcomes. The prime aim of this work is to urge ways in which the concept of Pell’s equation can be used in Public key Cryptography techniques.The main aim of this approach is secure and can be computed very fast. Using Cubic Pell’s equation defined in Quadratic Case, a secure public key technique for Key generation process is showcased. The paper highlights that a key generation time of proposed scheme using Pell’s Quadratic case equation is fast compared to existing methods.The strength and quality of the proposed method is proved and analyzed by obtaining the results of entropy, differential analysis, correlation analysis and avalanche effect. The superiority of the proposed method over the conventional AES and DES is confirmed by a 50% increase in the execution speed and shows that Standard diviation and Entropy analysis of proposed scheme gives immunity to guess the encryption key and also it is hard to deduce the private key from public key using Diffrential analysis.

Linear equation for text cryptography using letters' coordinates

“…Consequently, the experimental results have been demonstrated that it is difficult to discover the used key. Figure 3 explains the cryptosystem of the algorithm has been divided into two modules [28], [29], which are; i) data encryption module and ii) data decryption module.…”

Elliptical curve cryptography image encryption scheme with aid of optimization technique using gravitational search algorithm

“…Where 𝐶 𝑗 (𝑡) is the cost function of the jth node at the iteration instant of t. 𝐶 𝑗 𝑤𝑜𝑟𝑠𝑒 (𝑡) represents the worst cost function and 𝐶 𝑗 𝑏𝑒𝑠𝑡 (𝑡) represents the best cost function. The mass and acceleration of the jth node are given by ( 10) and (11).…”

“…The public keys are distributed to all people, and only the person who is participating in the conversation recognizes the private key. ECC, unlike secret key cryptography, is ideal for systems where a protected channel to relay the private key is not available [11], [12]. ECC is a nearly modern public key cryptosystem that offers higher thresholds, lower mathematical difficulty, smaller key sizes, and greater computational efficiency [13], [14].…”

Key Generation Using Generalized Pell’s Equation in Public Key Cryptography Based on the Prime Fake Modulus Principle to Image Encryption and Its Security Analysis

“…Further, they analyzed cryptanalysis of Fermat's attack [28,29], Weiner's continued fraction [30] and extended Euclidean method and these are compared along with RSA using numerical examples. A novel public key cryptography technique is proposed by R a g h u n a n d a n et al [31] which makes use of using Pell's quadratic case for key generation process and these are compared along with RSA using numerical examples. R a g h u n a n d a n et al [32] also introduces the concept of fake modulus which is to overcome the limitations of Integer factorization attack.…”