An Improvement on Shimada's Public-Key Cryptosystem

The difficulty of breaking Rabin's cryptosystem is the same as that of factoring its public key. So far, this has been proven to be very difficult. However the disadvantage of Rabin's cryptosystem is that the deciphering function cannot produce a unique plaintext. Many modified Rabin's cryptosystems have been proposed. Recently, an excellent scheme modified from Rabin's cryptosystem has been proposed by Shimada. Using Shimada's scheme, we can obtain the desired plaintext without any information additional to the ciphertext itself. Here we propose an improvement to this scheme to simplify the decryption process. Our effort makes the implementation of Shimada's public key cryptosystem more efficient.