<abstract xmlns="http://www.w3.org/1999/xhtml">

<p>RSA is one among the most popular public key cryptographic algorithm for security systems. It is explored in the results that RSA is prone to factorization problem, since it is sharing common modulus and public key exponent. In this paper the concept of fake modulus and generalized Pell’s equation is used for enhancing the security of RSA. Using generalized Pell’s equation it is explored that public key exponent depends on several parameters, hence obtaining private key parameter itself is a big challenge. Fake modulus concept eliminates the distribution of common modulus, by replacing it with a prime integer, which will reduce the problem of factorization. It also emphasizes the algebraic cryptanalysis methods by exploring Fermat’s factorization, Wiener’s attack, and Trial and division attacks.</p>
</abstract>

RSA is one among the most popular public key cryptographic algorithm for security systems. It is explored in the results that RSA is prone to factorization problem, since it is sharing common modulus and public key exponent. In this paper the concept of fake modulus and generalized Pell’s equation is used for enhancing the security of RSA. Using generalized Pell’s equation it is explored that public key exponent depends on several parameters, hence obtaining private key parameter itself is a big challenge. Fake modulus concept eliminates the distribution of common modulus, by replacing it with a prime integer, which will reduce the problem of factorization. It also emphasizes the algebraic cryptanalysis methods by exploring Fermat’s factorization, Wiener’s attack, and Trial and division attacks.

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

Department of Computer Science and Engineering, N.M.A.M Institute of Technology

Nitte, Affiliated to Visvesaraya Technological University

Department of Electronics and Communications Shri Madhwa Vadiraja Institute of Technology and Management

Bantakal, Udupi, Affiliated to Visvesaraya Technological University

Department of Mathematics, N.M.A.M Institute of Technology

Cybernetics and Information Technologies

This work is licensed under the Creative Commons Attribution-NonCommercial-NoDerivatives 4.0 International License.

RSA is one among the most popular public key cryptographic algorithm for security systems. It is explored in the results that RSA is prone to factorization...

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

Published Online: Sep 13, 2020

Page range: 86 - 101

Received: Jan 25, 2020

Accepted: Jun 29, 2020

DOI: https://doi.org/10.2478/cait-2020-0030

Keywords
Public Key Cryptography, Fermat’s Factorization, Standard Deviation, Pell’s Equation, Wiener’s Attack, Trial and Division

© 2020 K. R. Raghunandan et al., published by Sciendo

This work is licensed under the Creative Commons Attribution-NonCommercial-NoDerivatives 4.0 International License.

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

Published Online: Sep 13, 2020

Page range: 86 - 101

Received: Jan 25, 2020

Accepted: Jun 29, 2020

DOI: https://doi.org/10.2478/cait-2020-0030

KeywordsPublic Key Cryptography, Fermat’s Factorization, Standard Deviation, Pell’s Equation, Wiener’s Attack, Trial and Division

© 2020 K. R. Raghunandan et al., published by Sciendo

This work is licensed under the Creative Commons Attribution-NonCommercial-NoDerivatives 4.0 International License.

Keywords
Public Key Cryptography, Fermat’s Factorization, Standard Deviation, Pell’s Equation, Wiener’s Attack, Trial and Division