We design a provably secure public-key encryption scheme based on modular squaring (Rabin's public-key encryption scheme [28]) over Z_N, where N = P~dq (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 = p~dq [31]. Takagi's method uses Chinese Remainder Theorem (CRT), whereas our decryption requires no CRT-like computation. We also compare our scheme to existing factoringbased schemes including RSA-OAEP Rabin-SAEP and Rabin-SAEP+. Furthermore, we consider the (future) hardness of the integer-factoring: N = p~dq vs. N = pq for large size of N.
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