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[1]陈和风*,马文平,张成丽.缺损函数簇的新构造[J].厦门大学学报(自然科学版),2017,56(01):106-110.[doi:10.6043/j.issn.0438-0479.201604018]
 CHEN Hefeng*,MA Wenping,ZHANG Chengli.New Construction of Lossy Function Families[J].Journal of Xiamen University(Natural Science),2017,56(01):106-110.[doi:10.6043/j.issn.0438-0479.201604018]
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《厦门大学学报(自然科学版)》[ISSN:0438-0479/CN:35-1070/N]

卷:
56卷
期数:
2017年01期
页码:
106-110
栏目:
研究论文
出版日期:
2017-01-23

文章信息/Info

Title:
New Construction of Lossy Function Families
文章编号:
0438-0479(2017)01-0106-05
作者:
陈和风12*马文平1张成丽1
1.西安电子科技大学综合业务网理论及关键技术国家重点实验室,陕西 西安 710071; 2.集美大学计算机工程学院,福建 厦门 361021
Author(s):
CHEN Hefeng12*MA Wenping1ZHANG Chengli1
1.State Key Laboratory of Integrated Service Networks,Xidian University,Xi’an 710071,China; 2.Computer Engineering College,Jimei University,Xiamen 361021,China
关键词:
缺损函数簇 同态加密 纠错码
Keywords:
lattice lossy function family homomorphic encryption error correcting codes
分类号:
TP 309
DOI:
10.6043/j.issn.0438-0479.201604018
文献标志码:
A
摘要:
缺损陷门函数簇是一个重要的密码原型,可应用于抗碰撞杂凑函数、选择密文安全的加密方案和不经意传输等密码原型的黑盒构造.现有方法大多基于数论中的困难假设实现,基于理想格上小主理想问题和最近向量问题的困难假设,设计一个具有加同态性质的加密方案,在此基础上结合纠错码,针对Micciancio和Peikert在CRYPTO 2013上提出的缺损函数簇的推广定义,给出一个新的构造方法,得到均匀输入分布下不可区分的不可逆陷门函数簇和抗第二原像损耗函数簇,其函数索引仅用一个矩阵表示,具有较短的长度,这有利于构造高效的密码方案,也表明理论上的可行性.
Abstract:
Lossy trapdoor functions are powerful cryptographic primitive.Theycan be primarily applied to the black-box constructions of collision-resistant hash functions,chosen-ciphertext secure encryption,oblivious transfer,among others.The existing Lossy trapdoor functions are realized from a variety of number-theoretic assumptions.In view of the general definition of lossy function families,which is formalized by Micciancio and Peikert at CRYPTO 2013,based on small principal ideal problem and closest vector problem in ideal lattices,we propose an additive homomorphic encryption scheme at first.Then,combining with error correcting codes,we present a new construction of un-invertible functions and second pre-image resistant functions whose distributions are indistinguishable under uniform input distribution.The lossy function shown here enjoy short function descriptions(only consists of one matrix),which in turn yield more efficient cryptographic schemes.It exhibits certain theoretical values.

参考文献/References:

[1] PEIKERT C,WATERS B.Lossy trapdoor functions and their applications [C]∥STOC 2008.Victoria:British Columbia,2008:187-196.
[2] ROSEN A,SEGEV G.Efficient lossy trapdoor functions based on the composite residuosity assumption[C]∥TCC2009.San Francisco:LNCS,2009:419-436.
[3] DAMGARD I,JURIK M.A generalization,a simplification and some applications of Paillier’s probabilistic public-key system [C]∥PKC 2001.Cheju Island:LNCS,2001:119-136.
[4] ALWEN J,KRENN S,PIETRZAK K.Learning with rounding,Revisited [C]∥CRYPTO 2013,UCSB.[S.l.]:LNCS,2013:57-74.
[5] MICCIANCIO D,PEIKERT C.Hardness of SIS and LWE with small parameters [C]∥CRYPTO 2013,UCSB.[S.l.]:LNCS,2013:21-39.
[6] SMART N P,VERCAUTEREN F.Fully homomorphic encryption with relatively small key and ciphertext sizes [C]∥PKC 2010.Paris:LNCS,2010:420-443.
[7] LIDL R,NIEDIRRITER H,COHN P M.Finite fields[M].Cambridge:Cambridge University Press,1997:36.
[8] GENTRY C.Fully homomorphic encryption using ideal lattices[C]∥STOC 2009.New York:ACM,2009:169-178.
[9] BELLARE M,KILTZ E,PEIKERT C.Identity-based(lossy)trapdoor functions and applications [C]∥EUROCRYPT 2012.Cambridge:LNCS,2012:228-245.

备注/Memo

备注/Memo:
收稿日期:2016-04-11 录用日期:2016-09-20
基金项目:国家自然科学基金(61072140,61373171); 高等学校博士学科点专项科研基金(20100203110003)
*通信作者:chenhefeng1118@163.com
更新日期/Last Update: 1900-01-01