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– 288.
[2]Regev O. On lattices£¬learning with errors£¬ran-
dom linear codes£¬and cryptography[C]. In Pro-
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ceedings of STOC£¬2005£¬pp. 113 – 117. [3]Gentry C£¬Peikert C£¬and Vaikuntanathan V.
Trapdoors for hard lattices and new cryptographic constructions[C]. STOC¡¯08£¬Victoria£¬BC£¬ Canada£¬ACM£¬2008: 197 – 206.
[4]Peikert C. Public – key cryptosystems from the worst – case shortest vector problem[C]. STOC¡¯ 09£¬Maryland£¬USA£¬ACM£¬2009: 333 – 342.
[5]LYUBASHEVSHY V£¬PEIKERT C£¬REGEV O.
¡¤49¡¤ On ideal lattice and learning with errors over rings
[C]. In Eurocrypt 2010£¬LNCS 6110£¬Spring – Verlag£¬2010: 1 – 23.
[6]ÕŽ¨º½£¬ºØ½¡£¬ºúÓèå§. »ùÓÚ R – LWE µÄÐÂÐÍ NTRU ¼ÓÃÜ·½°¸[J]. µç×ӿƼ¼. 2012. 5. 15. [7]ÀîÐÂÉ磬ÕÅÓ¯£¬ºúÓèå§. Ò»ÖÖ NTRU ½âÃÜʧ°ÜÑÐ
¾¿·½°¸µÄ·ÖÎöºÍ¸Ä½ø[J]. Ó¦ÓÃÊýѧѧ±¨. 2008 Äê 7 ÔÂ. µÚ 31 ¾í£¬µÚ 4 ÆÚ.
A New Public – key Cryptosystem Based on R – LWE
Bai Jian1£¬2 Liu Hui1£¬2 Zhang Ruoqing1£¬2 Yang Yatao2
1. Beijing Electronic Science and Technology Institute£¬Beijing 100070£¬China
2. School of Telecommunication Engineering£¬Xi’dian University£¬Xi’an£¬710071£¬China Abstract: Public – key cryptosystems based on lattice is post – quantum cryptography and the efficiency is high£¬which now becomes a hot topic. Public – key cryptosystem is designed based on the learning with errors over ring in lattice. We give the choice of parameters and how to generate the keys£¬encrypt
theplaintextanddecryptthecipertextindetails. Andalso£¬thesecurityofthispublic-keycryptosys- tem and the analysis of efficiency are discussed. In the end£¬we compare the public – key cryptosystem with NTRU.
Keywords: Cryptography; Post – quantum Cryptosystem; Public – key Cryptosystem Based on Lattice; R – LWE ( Learning with Errors over Rings) ; Public – key Cryptosystem Based on R – LWE
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