一种基于身份的全同态加密体制
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摘要
全同态加密在云计算安全领域具有重要应用价值。公钥尺寸较大是现有全同态加密体制普遍存在的缺点。为解决这一问题,文章将基于身份加密的思想和全同态加密体制相结合,利用近似特征向量方法,无需生成运算密钥,构造了一种真正意义上基于身份的全同态加密体制。采用更有效的陷门生成算法,将文献[13]中基于身份的全同态加密的体制参数由m≥5nlogq减小至m≈2nlogq。本体制的安全性在随机喻示模型下归约到容错学习问题难解性。
Fully homomorphic encryption is of great value in cloud computing. The public key of the existing fully homomorphic encryption has generally oversized. Using the approximate eigenvector method and taking the advantages of no evaluate keys,this paper constructs an identity-based fully homomorphic encryption which compromises the merits of both kinds of encryption. Using the new effective trapdoor generation algorithm,the parameter m≥5nlogq in paper [13]has reduced to m≈2nlogq. In the random oracle model,the security of the scheme strictly reduces to the hardness of decisional learning with error problems.
Fully homomorphic encryption is of great value in cloud computing. The public key of the existing fully homomorphic encryption has generally oversized. Using the approximate eigenvector method and taking the advantages of no evaluate keys,this paper constructs an identity-based fully homomorphic encryption which compromises the merits of both kinds of encryption. Using the new effective trapdoor generation algorithm,the parameter m≥5nlogq in paper [13]has reduced to m≈2nlogq. In the random oracle model,the security of the scheme strictly reduces to the hardness of decisional learning with error problems.
引文
[1]Gentry C.Fully homomorphic encryption using ideal lattices[C]//STOC.2009:169-178.
[2]Van Dijk M,Gentry C,Halevi S,et al.Fully homomorphic encryption over the integers[C]//Advances in Cryptology-EUROCRYPT 2010.2010:24-43.
[3]Coron J S,Mandal A,Naccache D,et al.Fully homomorphic encryption over the integers with shorter public keys[C]//Advances in Cryptology-CRYPTO 2011.2011:487-504.
[4]Coron J S,Naccache D,Tibouchi M.Public key compression and modulus switching for fully homomorphic encryption over theintegers[C]//Advances in Cryptology-EUROCRYPT 2012.2012:446-464.
[5]Brakerski Z,Vaikuntanathan V.Efficient fully homomorphic encryption from(standard)LWE[J].SIAM Journal on Computing,2014,43(2):831-871.
[6]Brakerski Z,Gentry C,Vaikuntanathan V.(Leveled)fully homomorphic encryption without bootstrapping[C]//Proceedings of the 3rd Innovations in Theoretical Computer Science Conference.2012:309-325.
[7]Gentry C,Halevi S,Smart N P.Fully homomorphic encryption with polylog overhead[C]//Advances in Cryptolog-EUROCRYPT 2012.2012:465-482.
[8]Gentry C,Halevi S,Smart N P.Better bootstrapping in fully homomorphic encryption[C]//Public Key Cryptography-PKC2012.2012:1-16.
[9]Naccache D.Is theoretical cryptography any good in practice[J].Talk given at CHES,2010:81-106.
[10]Gentry C,Halevi S,Vaikuntanathan V.A simple BGN-type cryptosystem from LWE[C]//Advances in Cryptology-EUROCRYPT 2010.2010:506-522.
[11]光焱,祝跃飞,费金龙,等.利用容错学习问题构造基于身份的全同态加密体制[J].通信学报,2014,35(2):111-117.
[12]Brakerski Z.Fully homomorphic encryption without modulus switching from classical Gap SVP[C]//CRYPTO.2012:868-886.
[13]Craig Gentry,Sahai A,Waters B.Homomorphic encryption from learning with errors:Conceptually-simpler,asymptoticallyfaster,attribute-based[C]//Advances in Cryptology-CRYPTO 2013.2013:75-92.
[14]Gentry C,Peikert C,Vaikuntanathan V.Trapdoors for hard lattices and new cryptographic constructions[C]//Proceedings of the fortieth annual ACM symposium on Theory of computing.2008:197-206.
[15]Regev O.On lattices,learning with errors,random linear codes,and cryptography[C]//Proceedings of 37rd ACM Symposium on Theory of Computing(STOC2005).2005:84-93.
[16]Peikert C.Public-key cryptosystems from the worst-case shortest vector problem[C]//Proceedings of the forty-first annual ACM symposium on Theory of computing.2009:333-342.
[17]Micciancio D,Peikert C.Trapdoors for lattices:Simpler,tighter,faster,smaller[C]//Advances in Cryptology-EUROCRYPT 2012.2012:700-718.
[2]Van Dijk M,Gentry C,Halevi S,et al.Fully homomorphic encryption over the integers[C]//Advances in Cryptology-EUROCRYPT 2010.2010:24-43.
[3]Coron J S,Mandal A,Naccache D,et al.Fully homomorphic encryption over the integers with shorter public keys[C]//Advances in Cryptology-CRYPTO 2011.2011:487-504.
[4]Coron J S,Naccache D,Tibouchi M.Public key compression and modulus switching for fully homomorphic encryption over theintegers[C]//Advances in Cryptology-EUROCRYPT 2012.2012:446-464.
[5]Brakerski Z,Vaikuntanathan V.Efficient fully homomorphic encryption from(standard)LWE[J].SIAM Journal on Computing,2014,43(2):831-871.
[6]Brakerski Z,Gentry C,Vaikuntanathan V.(Leveled)fully homomorphic encryption without bootstrapping[C]//Proceedings of the 3rd Innovations in Theoretical Computer Science Conference.2012:309-325.
[7]Gentry C,Halevi S,Smart N P.Fully homomorphic encryption with polylog overhead[C]//Advances in Cryptolog-EUROCRYPT 2012.2012:465-482.
[8]Gentry C,Halevi S,Smart N P.Better bootstrapping in fully homomorphic encryption[C]//Public Key Cryptography-PKC2012.2012:1-16.
[9]Naccache D.Is theoretical cryptography any good in practice[J].Talk given at CHES,2010:81-106.
[10]Gentry C,Halevi S,Vaikuntanathan V.A simple BGN-type cryptosystem from LWE[C]//Advances in Cryptology-EUROCRYPT 2010.2010:506-522.
[11]光焱,祝跃飞,费金龙,等.利用容错学习问题构造基于身份的全同态加密体制[J].通信学报,2014,35(2):111-117.
[12]Brakerski Z.Fully homomorphic encryption without modulus switching from classical Gap SVP[C]//CRYPTO.2012:868-886.
[13]Craig Gentry,Sahai A,Waters B.Homomorphic encryption from learning with errors:Conceptually-simpler,asymptoticallyfaster,attribute-based[C]//Advances in Cryptology-CRYPTO 2013.2013:75-92.
[14]Gentry C,Peikert C,Vaikuntanathan V.Trapdoors for hard lattices and new cryptographic constructions[C]//Proceedings of the fortieth annual ACM symposium on Theory of computing.2008:197-206.
[15]Regev O.On lattices,learning with errors,random linear codes,and cryptography[C]//Proceedings of 37rd ACM Symposium on Theory of Computing(STOC2005).2005:84-93.
[16]Peikert C.Public-key cryptosystems from the worst-case shortest vector problem[C]//Proceedings of the forty-first annual ACM symposium on Theory of computing.2009:333-342.
[17]Micciancio D,Peikert C.Trapdoors for lattices:Simpler,tighter,faster,smaller[C]//Advances in Cryptology-EUROCRYPT 2012.2012:700-718.