Design and Analysis of Fast Provably Secure Public-Key Cryptosystems Based on a Modular Squaring

We design a provably secure public-key encryption scheme based on modular squaring (Rabin's public-key encryption scheme [28]) over ZN, where N = pdq (p and q are prime integers, and d > 1), and we show that this scheme is extremely faster than the existing provably secure schemes. Security of our scheme is enhanced by the original OAEP padding scheme [3]. While Boneh presents two padding schemes that are simplified OAEP, and applies them to design provably secure Rabin-based schemes (Rabin-SAEP, Rabin-SAEP+), no previous works explores Rabin-OAEP. We gives the exact argument of security of our OAEP-based scheme. For speeding up our scheme, we develop a new technique of fast decryption, which is a modification of Takagi's method for RSA-type scheme with N = pdq [31]. Takagi's method uses Chinese Remainder Theorem (CRT), whereas our decryption requires no CRT-like computation. We also compare our scheme to existing factoring-based schemes including RSA-OAEP, Rabin-SAEP and Rabin-SAEP+. Furthermore, we consider the (future) hardness of the integer-factoring: N = pdq vs. N = pq for large size of N.

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