中文摘要：

E-mail： laiqiqi2006@ 126.com Qiqi Lai is a PhD student in Xidian University. He received his MS in cryptography from Xidian University, China in 2011 and his BS in information security from Information Engineering University, China in 2008. His research interests include public-key cryptography and provable security. Yuan Chen is a researcher at the State Key Laboratory of Integrated Service Networks （ISN）, Xidian University, China. Her main interests are in cryptography, especially, provable security of public-key encryptions. Yupu Hu is a professor and PhD supervisor of the School of Telecommunications Engineering, Xidian University, China. He received his PhD in cryptography from Xidian University, China in 1999, and received his MS and BS in mathematics from Xidian University, China in 1999 and 1987, respectively. His main research interests include public key cryptography based on lattices and the analysis and application of fully homomorphic encryption schemes. Baocang Wang is an associate professor and MS supervisor of the School of Telecommunications Engineering, Xidian University, China. He received his PhD in cryptography from Xidian University, China in 2006, and received his MS and BS in mathematics from Xidian University in 2004 and 2001, respectively. His main research interestsinclude public-key cryptography and wireless network security. Mingming Jiang is a PhD student in Xidian University, China. He received his MS and BS in cryptography from Huaibei Normal University, China in 2010 and 2007, respectively. His research interests include public- key cryptography based on lattices and provable security.