To lower the sizes of keys, a certificateless encryption scheme is put forward by using a trapdoor sampling algorithm over a selected NTRU lattice to extract partial private keys and using Ring Learning With Errors (RLWE) problem to generate public keys. Its security is based on both assumptions of the decisional ring learning with errors problem and the decisional Small Polynomial Ratio (SPR) problem. To further improve efficiency, a certificateless parallel encryption scheme with more efficient algorithms only using arithmetic in integers is also given by respectively using the Chinese Remainder Theorem (CRT) to decompose the enlarged plaintext space into the product of distinct prime ideals and to break down the ring, over which encryption operations work, for obtaining the Chinese Remainder basis. The given results show that the proposed schemes are characterized by low computation complexity and small communication complexity.
GENTRY C, PEIKERT C, and VAIKUNTANATHAN V. Trapdoors for hard lattices and new cryptographic constructions[C]. Proceedings of the 40th ACM Symposium on Theory of Computing (STOC08), Victoria, Canada, 2008: 197-206. doi: 10.1145/1374376.1374407.
[2]
AGRAWAL S, BONEH D, and BOYEN X. Lattice basis delegation in fixed dimension and shorter-ciphertext hierarchical IBE[J]. LNCS, 2010, 6223: 98-115. doi: 10.1007 /978-3-642-14623-7_6.
[3]
DUCAS L, LYUBASHEVSKY V, and PREST T. Efficient identity-based encryption over NTRU lattices[J]. LNCS, 2014, 8874: 22-41. doi: 10.1007/978-3-662-45608-8_2.
[4]
BRAKERSKI Z, GENTRY C, and VAIKUNTANATHAN V. Fully homomorphic encryption without Bootstrapping[C]. Proceedings of the 3rd Innovations in Theoretical Computer Science (ITCS) Conference, Cambridge, Massachusetts, 2012: 309-325.
[5]
LOPEZ-ALT A, TROMER E, and VAIKUNTANATHAN V. On-the-fly multiparty computation on the cloud via multikey fully homomorphic encryption[C]. Proceedings of the 44th ACM Symposium on Theory of Computing (STOC12), New York, USA, 2012: 1219-1234. doi: 10.1145/2213977.2214086.
[6]
BRAKERSKI?Z and VAIKUNTANATHAN V.? Lattice- based? FHE?as?secure?as?PKE[C]. Proceedings of the 5rd Innovations in Theoretical Computer Science (ITCS) Conference, Princeton, New Jersey, 2014: 1-12.
[7]
MICCIANCIO D and PEIKERT C. Trapdoor for lattices: simpler, tighter, faster, smaller[J]. LNCS, 2012, 7237: 738-755.
[8]
JARVIS K and NEVINS M. ETRU: NTRU over the Eisenstein integers[J]. Designs, Codes and Cryptography, 2015, 74(1): 219-242.
[9]
BI J G and CHENG Q. Lower bounds of shortest vector lengths in random NTRU lattices[J]. Theoretical Computer Science, 2014, 560(2): 121-130. doi: 10.1007/978-3-642- 29952-0_18.
[10]
SEPAHI R, STEINFELD R, and PIEPRZYK J. Lattice- based certificateless public-key encryption in the standard model[J]. International Journal of Information Security, 2014,?13(4):?315-333. doi: 10.1007/s10207-013-0215-8.
[11]
JIANG Mingming, HU Yupu, LEI Hao, et al. Lattice-based certificateless encryption scheme[J]. Frontiers of Computer Science, 2014,?8(5):?828-836. doi: 10.1007/s11704-014-3187-6.
[12]
AL-RIYAMI S S and PATERSON K G. Certificateless public key cryptography[J]. LNCS, 2003, 2894: 452-473.
[13]
DENT A. A survey of Certificateless encryption schemes and security models[J]. International Journal of Information Security, 2008,?7(5):?347-377. doi: 10.1007/s10207-008-0055-0.
