Efficient Lattice based (H)IB-DRE

In CCS’04, Diament etc al. presented special kind of public key encryption called Dual Receiver Encryption (DRE). In DRE, sender encrypts the plaintext using public keys of two independent re-ceivers. Both independent receivers can decrypt the ciphertext into the same plaintext using their own private keys. This new cryptography primitive has applications in construction of complete non-malleability and plaintext-awareness public key encryption, for a secure management of data that is to be disseminated to distributed processors, for ubiquitous and mobile computing applications. Daode Zhang et. al. constructed lattice-based IB-DRE scheme which is secure against stronger security notion i.e. adaptive-ID. We present hierarchical identity based dual encryption (HIB-DRE) scheme under LWE assumption. To the best of our knowledge, this gives the first provably secure HIB-DRE scheme in the lattice based setting. Independent work by Naccache[1] and Chatterjee-Sarkar[2] presented a variant of Waters’s identity based encryption scheme to reduce Public Param-eters. They have considered an identity of l-bits as l′ chunks where size of each chunk is l/l′ . This reduces the Public Parameter (PP) size from l to l′ n ×m matrices. This idea was named as blocking technique[3]. We have used blocking technique to reduce the size of PP. Daode Zhang et. al.[4] presented adaptive secure IB-DRE scheme. This scheme[4] contains l + 1, n × m matrices as PPs, where l denotes the number of the bits in identity. Using blocking technique we have reduced the size of PP by around factor β . Because of this the size of prime number q in field Zq is increased by 2β which results in increase in computation cost. We have shown that compared to Daode Zhang et. al.scheme the size of the PP can be decreased approximately by 80% and the time complexity is increased by only 1.40% for a suitably chosen β .