Short-Exponent RSA
In some applications, a short private exponent d is chosen to improve the decryption or signing process for RSA public key cryptosystem. However. in a typical RSA, if the private exponent d is selected first, the public exponent e should be of the same order Of magnitude as phi(N). Sun et al. devised three RSA variants Using unbalanced prime factors p and q 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 primes p and q are more insecure than the instances with balanced p and q. This investigation focuses on designing a new RSA variant with balanced p and q, and short exponents d and e, 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 which p and q are balanced, and a trade-off between the lengths of d and e is enable. In addition, We provide the security analysis and feasibility analysis of the proposed schemes.
rsa encryption digital signature public-key cryptosystem