In Eurocrypt 2009, Hofheinz and Kiltz proposed a practical chosen ciphertext (CCA) secure public key encryption under factoring assumption based on Rabin trapdoor one-way permutation. We show that when the modulus is special such that Z * N has semismooth order, the instantiation of Hofheinz-Kiltz 09 scheme (HK09) over a much smaller subgroup of quadratic residue group (Semi-smooth Subgroup) is CCA secure as long as this type of modulus is hard to be factored. Since the exponent domain of this instantiation is much smaller than the original one, the efficiency is substantially improved. In addition, we show how to construct a practical CCA secure encryption scheme from ElGamal trapdoor one-way function under factoring assumption. When instantiated over Semi-smooth Subgroup, this scheme has even better decryption efficiency than HK09 instantiation.
We present a secure backpropagation neural network training model (SecureBP), which allows a neural network to be trained while retaining the confidentiality of the training data, based on the homomorphic encryption scheme. We make two contributions. The first one is to introduce a method to find a more accurate and numerically stable polynomial approximation of functions in a certain interval. The second one is to find a strategy of refreshing ciphertext during training, which keeps the order of magnitude of noise at O˜e33.
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