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基于整数近似GCD的全同态加密方案 被引量：2

Fully homomorphic encryption based on approximate integer GCD
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摘要 设计了基于整数近似GCD问题新的全同态加密方案。跟随Gentry设计模式,构造somewhat同态加密方案,并归约其安全性到整数近似GCD;引入稀疏子集和难度假设来压缩解密电路,使其具有自举性;最后转换somewhat同态加密方案到全同态加密方案。与文献[1]方案相比,提出的somewhat同态加密方案更接近于文献[2]中公钥加密方案。 This paper desiged a fully homomorphic encryption（ FHE） scheme based on approximate integer GCD problem.Following Gentry＇s scheme,firstly,it construced a somewhat homomorphic encryption（SHE） scheme,and reduced its security to approximate integer GCD. Then it squashed decryption circuit to achieve bootstrapping by applying SSSP assumption. Finally,it transfered SHE into FHE. The SHE is closer to the public key scheme in literature[2]than [1].
作者 于志敏 古春生 景征骏
机构地区 江苏理工学院计算机工程学院 中国科学技术大学计算机科学与技术学院 南京邮电大学计算机学院
出处 《计算机应用研究》 CSCD 北大核心 2014年第7期2105-2108,共4页 Application Research of Computers
基金 国家自然科学基金资助项目(61142007) 江苏省普通高校研究生科研创新计划资助项目(CXZZ13_0493) 江苏省属高校自然科学基金资助项目(13KJB520005) "青蓝工程"资助项目
关键词 近似整数最大公因数 公钥方案 全同态加密 稀疏子集和问题 approximate integer GCD public key cryptosystem FHE SSSP
分类号 TP309.7 [自动化与计算机技术—计算机系统结构]
  • 相关文献

参考文献18

  • 1Van DIJK M, GENTRY C, HALEVI S, et al. Fully homomorphic encryption over the integers [ C ]//LNCS, vol 6110. Berlin : Springer, 2010:24-43.
  • 2REGEV O. New lattice-based cryptographic constructions[ J]. Jour- nal of the ACM ,2004,51 (6) :899-942.
  • 3RIVEST R,ADLEMAN L,DERTOUZOS M. On data banks and pri- vacy homomorphisms [ J ]. Foundations of Secure Computation, 1978,7( 1 ) :169-177.
  • 4GENTRY C. A fully homomorphic encryption scheme[ D ]. Stanford: Stanford University, 2009.
  • 5GENTRY C. Fully homomorphic encryption using ideal lattices [ C ]// Proc of STOC. New York:ACM Press,2009:169-178.
  • 6GENTRY C, HALEVI S. Implementing gentry' s fully-homomorphic encryption scheme [ C ]//LNCS, vol 6632. Berlin :Springer,2011 : 129- 148.
  • 7SMART N P, VERCAUTEREN F. Fully homomorphic encryption with relatively small key and ciphertext sizes [ C ]//LNCS, vol 6056. Ber- lin : Springer, 2010:420 - 443.
  • 8BRAKERSKI Z, VAIKUNTANATHAN V. Efficient fully homomor- phic encryption from (standard) LWE[ EB/OL]. (2011-08-04). ht- tp ://eprint. iacr. org/2011/344.
  • 9REGEV O. On lattices, learning with errors, random linear codes, and cryptography[ C ]//Proc of STOC. New York : ACM Press ,2005 : 84-93.
  • 10GENTRY C, HALEVI S. Fully homomorphic encryption without squashing using depth- 3 arithmetic circuits [ EB/OL ]. ( 2011- 09- 14). http ://eprint. iacr. org/2011/279.

二级参考文献45

  • 1Rivest R L, Adleman L, Dertouzos M L.On data banks and privacy homomorphisms[Z].Foundations of Secure Computation, 1978.
  • 2Gentry C.Fully homomorphic encryption using ideal lattices[C]//STOC' 09,2009 : 169-178.
  • 3Gentry C.A fully homomorphic encryption scheme[D/OL]. Stanford University , 2009.http : //crypto.stanford.edu/craig.
  • 4van Dijk M, Gentry C, Halevi S, et al.Fully homomorphic encryption over the integers[C]//Volume 6110 of LNCS : Proc of Eurocrypt, 2010 : 24-43.
  • 5Smart N P, Vercauteren F.Fully homomorphic encryption with relatively small key and ciphertext sizes[C]// Volume 6056 of Lecture Notes in Computer Science: Public Key Cryptography-PKC' 10, Springer, 2010.
  • 6Stehle D, Steinfeld R.Faster fully homomorphic encryption, Cryptology ePrint Archive, Report 2010/299[EB/OL]. (2010).http://eprint.iacr.org/.
  • 7Howgrave-Graham N.Approximate integer common divisors[C]//Volume 2146 of Lecture Notes in Computer Science: CaLC' 01.[S.l.] : Springer, 2001 : 51-66.
  • 8Rivest R, Adleman L, Dertouzos M. On Data Banks and Privacy Homomorphisms[M]. [S. 1.]: Academic Press, 1978: 169-177.
  • 9Lipton B. Searching for Elements in Black Box Fields and Applications[C]//Proc. of Cryptology-Crypto'96. [S. 1.]: Springer- Verlag, 1996: 283-297.
  • 10Domingo-Ferrer J. A Provably Secure Additive and Multiplicative Privacy Homomorphism[C]//Proc. of the 5th International Conference on Information Security. [S. 1.]: Springer-Verlag, 2002: 471-483.

共引文献49

同被引文献26

  • 1向广利,陈莘萌,马捷,张俊红.实数范围上的同态加密机制[J].计算机工程与应用,2005,41(20):12-14. 被引量：18
  • 2Gentry C. A fully homomorphic encryption scheme [ D ]. Stanford: Stanford University ,2009.
  • 3Gentry C, Halevi S. Implementing gentry' s fully-homomorphic en- cryption scheme [ C ]//Proc of EUROCRYPT. Berlin : Springer-Ver- lag,2011 : 129-148.
  • 4Smart N P, Vercauteren F, Fully homomorphic encryption with rela- tively small key and ciphertext sizes [ C]//Proc of PKC. Berlin: Springer-Verlag,2010 : 420 - 443.
  • 5Van Dijk M, Gentry C, Halevi S, et al. Fully homomorphic encryp- tion over the integers [ C ]//Proc of the 29th Annum International Conference on Theory and Applications of Cryptograhic Techniques. Berlin : Springer-Verlag, 2010 : 24 - 43.
  • 6Coron J S, Mandal A, Naccache D, et al. Fully homomorphic en- cryption over the integers with shorter public keys [ C ]//Proc of CRYPTO. Berlin : Springer-Verlag, 2011:487-504.
  • 7Coron J S, Naccahe D, Tibouchi M. Public-key compression and modulus switching for fully homomorphic encryption over the integers[ C]//Proc of Eurocrypto. 2012:450-460.
  • 8Coron J S, L~point T, Tibouchi M,et al. Batch fully homomorphic en- cryption over the integers [ C ]//Proc of EUROCRYPT. 2013 : 315- 335.
  • 9Brakerski Z, Vaikuntanathan V. Efficient fully homomorphie encryp- tion from (standard) LWE [ C ]//Proe of FOCS. 2011.
  • 10Brakerski Z, Vaikuntanathan V. Fully homomorphie eneryption from ring-LWE and security for key dependent messages [ C ]//Pine of CRYPTO. Berlin : Springer-Verlag, 2011 : 505- 524.

引证文献2

二级引证文献18

计算机应用研究
2014年 第7期

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