An Approach Towards Rebalanced RSA-CRT with Short Public Exponent

Based on the Chinese Remainder Theorem (CRT), Quisquater and Couvreur proposed an RSA variant, RSA-CRT, to speedup RSA decryption. According to RSA-CRT, Wiener suggested another RSA variant, Rebalanced RSA-CRT, to further speedup RSA-CRT decryption by shifting decryption cost to encryption cost. However, such an approach will make RSA encryption very time-consuming because the public exponent e in Rebalanced RSA-CRT will be of the same order of magnitude as φ(N). In this paper we study the following problem: does there exist any secure variant of Rebalanced RSA-CRT, whose public exponent e is much shorter than φ(N)? We solve this problem by designing a variant of Rebalanced RSA-CRT with dp and dq of 198 bits. This variant has the public exponent e = 2 + 1 such that its encryption is about 3 times faster than that of the original Rebalanced RSA-CRT.