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IEICE Transactions on Fundamentals of Electronics, Communications and Computer Sciences

Abstract

In some applications, a short private exponentd is chosen to improve the decryption or signing process for RSA public key cryptosystem. However, in a typical RSA, if the private exponentd is selected first, the public exponente should be of the same order of magnitude asφ(N). Sun et al. devised three RSA variants using unbalanced prime factorsp andq to lower the computational cost. Unfortunately, Durfee & Nguyen broke the illustrated instances of the first and third variants by solving small roots to trivariate modular polynomial equations. They also indicated that the instances with unbalanced primesp andq are more insecure than the instances with balancedp andq. This investigation focuses on designing a new RSA variant with balancedp andq, and short exponentsd ande, to improve the security of an RSA variant against the Durfee & Nguyen's attack, and the other existing attacks. Furthermore, the proposed variant (Scheme A) is also extended to another RSA variant (Scheme B) in whichp andq are balanced, and a trade-off between the lengths ofd ande is enable. In addition, we provide the security analysis and feasibility analysis of the proposed schemes.

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