Lattice Based Efficient Threshold Public Key Encryption Scheme

A (t,u)threshold public key encryption (TPKE) is a public key encryption where a private key is splitted among u decryption servers (insiders) and at least t decryption servers (insiders) are required to decrypt the ciphertext but no group of t− 1 or less malicious insiders can decrypt the message. Bendlin and Damgard [1] presented first lattice based threshold public key encryption scheme based on Regev’s LWE based encryption system [2]. We propose efficient lattice based threshold public key encryption scheme based on [3]. We have reduced size of the public key from (n2+1)log n×‖Zq‖ to (n2 +1)×‖Zq‖ with the same ciphertext size where ‖Zq‖ is the number of bits required to represent an element of Zq. Resplittable threshold public key encryption (RTPKE) was introduced by Hanaoka et al [4] in a generic construction of CCA secure uni-directional proxy re-encryption scheme. RTPKE is a threshold public key encryption with an additional randomized algorithm Tsplit. Based on our efficient threshold scheme, we have constructed efficient resplittable threshold public key encryption scheme.