A Verifiable Multi-Recipient Encryption Scheme from Multilinear Maps

Multi-recipient encryption is an important public key cryptosystem, which can be applied for a variety of purposes, such as broadcasting data. In order to design an secure multi-recipient public key encryption (MRPKE) in post-quantum era, in this paper, we construct a novel MRPKE scheme base on Garg-Gentry-Halevi (GGH) framework which is a graded algebras analogue of multilinear maps from ideal lattice. Under the grade decisional Diffie-Hellman (GDDH) assumption of GGH, the proposed scheme has semantically safety against chosen plaintext attack (CPA). At the same time, each recipient, without first decrypting, can verify whether the message to be received is from a legitimate sender. Furthermore, the encryption and decryption only involves the polynomial modular addition and multiplication in polynomial ring, so the efficiency of the proposed scheme is higher.