支持同态算术运算的数据加密方案算法研究

doi:10.11959/j.issn.1000-436x.2015019

Abstract

Abstract:

An efficient homomorphic encryption scheme called CESIL was proposed to meet the requirements of operating on encrypted data when protecting users' privacy in computing services.CESIL included key generation algorithm,encryption algorithm,decryption algorithm and calculation algorithm.In CESIL,a polynomial coefficient vector ring was established by defining addition and multiplication using polynomial ring; by using ideal lattice,the vector ring was partitioned into many residue classes to produce a quotient ring and its representative set; the plaintext was encrypted by mapping it to a representative and replacing the representative with another element in the same residue class.The features of operations in quotient ring ensured CESIL operate on encrypted data.Furthermore,the fast Fourier transform (FFT) algorithm was used to increase the efficiency and decrease the length of key.Theoretical analysis and experimental results show that CESIL is semantically secure,and can do addition and multiplication operations on encrypted data homomorphically in a specific scope.Comparing to some existing homomorphic encryption schemes,the CESIL runs efficiently,and has shorter length in key and ciphertext.Thus,the CESIL fits the practical applications better.

Key words: homomorphic encryption, privacy-preserving, ideal lattice, representative, computing service

ANGPan Y,UIXiao-lin G,AOJing Y,INJian-cai L,IANFeng T,HANGXue-jun Z. Research on algorithms of data encryption scheme that supports homomorphic arithmetical operations[J]. Journal on Communications, 2015, 36(1): 167-178.

Figures/Tables 9

符号	意义
A ^m×n	由集合A中元素构成的m×n矩阵
A^m	A上的m维列矩阵或列向量
x←y	将y的值赋给x
x←_RA	从集合A中随机选取一个值赋给x
$\cdot$	四舍五入取整，若·代表一个矩阵，则?·?是对矩阵中的每个元素四舍五入取整
(a)	交换环中元素a生成的理想，如A为交换环，a∈A，则(a)={a·r\|?r∈A}
b]	元素 b 所在的剩余类，如对于商环 A/(a),b∈A，则[b]={b+a·r\|?r∈A}∈A/(a)
b]a	b]的代表元，所有商环A/(a)中元素的代表元构成A/(a)的代表元集合

References 20

[1]	RIVEST R L , ADLEMAN L , DERTOUZOS M L . On data banks and privacy homomorphisms[A]. DeMillo RA Foundations of Secure Computation[C]. NY,USA: Academic Press, 1978. 169-180.
[2]	PAILLIER P . Public-key cryptosystems based on composite degree residuosity classes[A]. Proc of the Advances in Cryptology (EUROCRYPT'99)[C]. Prague,Czech Republic, 1999. 223-238.
[3]	GOLDWASSER S , MICALI S . Probabilistic encryption[J]. Journal of Computer and System Sciences, 1984,28(2): 270-299.
[4]	RIVEST R L , SHAMIR A , ADLEMAN L . A method for obtaining digital signatures and public-key cryptosystems[J]. Communications of the ACM, 1978,21(2): 120-126.
[5]	ELGAMAL T . A public-key cryptosystem and a signature scheme based on discrete logarithms[J]. IEEE Transactions on Information Theory, 1985,31(4): 469-472.
[6]	BONEH D , GOH E J , NISSIM K . Evaluating 2-DNF formulas on ciphertexts[A]. Second Theory of Cryptography Conference (TTC 2005)[C]. Cambridge,MA,USA, 2005. 325-341.
[7]	GENTRY C . A Fully Homomorphic Encryption Scheme[D]. California,USA: Stanford University, 2009.
[8]	GENTRY C . Fully homomorphic encryption using ideal lattices[A]. Proc of the 41st ACM Symposium on Theory of Computing(STOC' 09)[C]. Bethesda,Maryland,USA, 2009. 169-178.
[9]	SMART P N , VERCAUTEREN F . Fully homomorphic encryption with relatively small key and ciphertext sizes[A]. Proc of the Public Key Cryptography (PKC 2010)[C]. Paris,France, 2010. 420-443.
[10]	DIJK V M , GENTRY C , HALEVI S , et al. Fully homomorphic encryption over the integers[A]. Proc of the Advances in Cryptology (EUROCRYPT 2010)[C]. Riviera,France, 2010. 24-43.
[11]	CORON J , MANDAL A , NACCACHE D , et al. Fully homomorphic encryption over the integers with shorter public keys[A]. Proc of the Advances in Cryptology (CRYPTO 2011)[C]. Santa Barbara,California,USA, 2011. 487-504.
[12]	BRAKERSKI Z , VAIKUNTANATHAN V . Fully homomorphic encryption from ring-lwe and security for key dependent messages[A]. Proc of the Advances in Cryptology (CRYPTO 2011)[C]. Santa Barbara,California,USA, 2011. 505-524.
[13]	GENTRY C , HALEVI S . Implementing Gentry's fully-homomorphic encryption scheme[A]. Proc of the Advances in Cryptology (EUROCRYPT 2011)[C]. Tallinn,Estonia, 2011. 129-148.
[14]	BRAKERSKI Z , GENTRY C , VAIKUNTANATHAN V . Fully homomorphic encryption without bootstrapping[J]. Computer and Information Science, 2011,111(111): 1-12.
[15]	GENTRY C , HALEVI S . Fully homomorphic encryption without squashing using depth-3 arithmetic circuits[A]. Proc of the 2011 IEEE 52nd Annual Symposium on Foundations of Computer Science[C]. Palm Springs,CA,USA, 2011. 107-109.
[16]	黄汝维，桂小林，余思等．云环境中支持隐私保护的可计算加密方法[J]．计算机学报， 2011,34(12):2391-2402. HUANG R W , GUI X L , YU S , et al. Privacy-preserving computable encryption scheme of cloud computing[J]. Chinese Journal of Computers, 2011,34(12):2391-2402.
[17]	冯登国．信息安全中的数学方法与技术[M]．北京：清华大学出版社， 2009. FENG D G . Mathematical Methods and Techniques for Information Security[M]. Beijing: Tsinghua University Press, 2009.
[18]	HOFFSTEIN J , PIPHER J , SILVERMAN J H . NTRU:a ring-based public key cryptosystem[A]. Proceedings of the Third International Symposium on Algorithmic Number Theory[C]. Portland,Orgeon,USA, 1998. 267-288.
[19]	MICCIANCIO D . Improving lattice based cryptosystems using the hermite normal form[A]. Proc of the Cryptography and Lattices Conference[C]. Rhode Island,USA, 2001. 126-145.
[20]	DAVIS P J . Circulant Matrices[M]. New York: Jonh Wiley ＆ Sons, 1979. 85-91.

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n	密钥长度/kbyte			明文或密文长度/kbyte
n	CESIL	CESVMC	明文	CESIL	CVO	CVM
8	0.125	1	1	64	64	512
16	0.25	4	2	128	128	2048
32	0.5	16	4	256	256	8192
64	1	64	8	512	512	32768

o_p	+	×	?	/	+×
URSA	×	√	×	×	×
Paillier	√	×	×	×	×
CESVMC	√	1次	√	1次	×
CESIL	√	√	＞1次	可除	√

Research on algorithms of data encryption scheme that supports homomorphic arithmetical operations

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