The Distributed Decryption Schemes for Somewhat Homomorphic Encryption

We propose distributed decryption schemes for somewhat homomorphic encryption (SHE). The proposed schemes are constructed based on the encryption scheme by Brakerski and Vaikuntanathan. In SHE, homomorphic multiplication increases the number of elements in a ciphertext. The proposed scheme can decrypt a ciphertext containing more than two elements with k out of N parties. The distributed decryption scheme introduced by Damgard, Pastro, Smart and Zakarias needs a trusted third party for decrypting a ciphertext that has more than two elements with N out of N parties. We present a distributed decryption scheme in which the parties can decrypt ciphertexts of any size without a trusted third party. In addition, we evaluate the errors of the proposed schemes.