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Erschienen in: Cluster Computing 1/2019

05.03.2018

Cryptanalysis of lattice-based key exchange on small integer solution problem and its improvement

verfasst von: Zhengjun Jing, Chunsheng Gu, Zhimin Yu, Peizhong Shi, Chongzhi Gao

Erschienen in: Cluster Computing | Sonderheft 1/2019

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Abstract

Wang et al. introduced a new variant of small integer solution (SIS), namely, bilateral inhomogeneous small integer solution (Bi-ISIS) which is based on lattice cryptography, and constructed a Bi-ISIS-based key exchange (KE) protocol. In this paper, we indicate that Wang et al.’s Bi-ISIS-based KE protocol is not secure because a common shared key can be recovered directly by using linear algebraic methods. Furthermore, we analysis two simple variants of the Bi-ISIS-based KE and show that they are also insecure. To avoid the shared key attack, we present an improvement of the Bi-ISIS-based KE, whose security is reduced to the learning with error problem over modules (M-LWE).

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Literatur
1.
Zurück zum Zitat Li, J., Zhang, Y.H., Cheng, X.F., Yang, X.: Secure attribute-based data sharing for resource-limited users in cloud computing. Comput. Secur. 72(1), 1–12 (2018)CrossRef Li, J., Zhang, Y.H., Cheng, X.F., Yang, X.: Secure attribute-based data sharing for resource-limited users in cloud computing. Comput. Secur. 72(1), 1–12 (2018)CrossRef
2.
Zurück zum Zitat Huang, Z., Liu, S.L., Mao, X.P., Chen, K.F., Li, J.: Insight of the protection for data security under selective opening attacks. Inf. Sci. 413(1), 223–224 (2017)CrossRef Huang, Z., Liu, S.L., Mao, X.P., Chen, K.F., Li, J.: Insight of the protection for data security under selective opening attacks. Inf. Sci. 413(1), 223–224 (2017)CrossRef
3.
Zurück zum Zitat Li, J., Li, J.W., Chen, X.F., Jia, C.F., Lou, W.J.: Identity-based encryption with outsourced revocation in cloud computing. IEEE Trans. Comput. 64(2), 425–437 (2015)MathSciNetMATHCrossRef Li, J., Li, J.W., Chen, X.F., Jia, C.F., Lou, W.J.: Identity-based encryption with outsourced revocation in cloud computing. IEEE Trans. Comput. 64(2), 425–437 (2015)MathSciNetMATHCrossRef
4.
Zurück zum Zitat Stergiou, C., Psannis, K.E., Kim, B.G., Gupta, B.: Secure integration of IoT and cloud computing. Futur. Gener. Comput. Syst. 78(3), 964–975 (2018)CrossRef Stergiou, C., Psannis, K.E., Kim, B.G., Gupta, B.: Secure integration of IoT and cloud computing. Futur. Gener. Comput. Syst. 78(3), 964–975 (2018)CrossRef
5.
Zurück zum Zitat Tewari, A., Gupta, B.B.: Cryptanalysis of a novel ultra-lightweight mutual authentication protocol for IoT devices using RFID tags. J. Supercomput. 73(3), 1085–1102 (2017)CrossRef Tewari, A., Gupta, B.B.: Cryptanalysis of a novel ultra-lightweight mutual authentication protocol for IoT devices using RFID tags. J. Supercomput. 73(3), 1085–1102 (2017)CrossRef
6.
Zurück zum Zitat Gupta, B.B., Gupta, S., Chaudhary, P.: Enhancing the browser-side context-aware sanitization of suspicious HTML5 code for halting the DOM-based XSS vulnerabilities in cloud. Int. J. Cloud Appl. Comput. 7(1), 1–31 (2017) Gupta, B.B., Gupta, S., Chaudhary, P.: Enhancing the browser-side context-aware sanitization of suspicious HTML5 code for halting the DOM-based XSS vulnerabilities in cloud. Int. J. Cloud Appl. Comput. 7(1), 1–31 (2017)
8.
Zurück zum Zitat Joux, A.: A one round protocol for tripartite Diffie-Hellman. In: International Algorithmic Number Theory Symposium (ANTS), pp. 385–394 (2000) Joux, A.: A one round protocol for tripartite Diffie-Hellman. In: International Algorithmic Number Theory Symposium (ANTS), pp. 385–394 (2000)
9.
Zurück zum Zitat Ran, C., Krawczyk, H.: Analysis of key-exchange protocols and their use for building secure channels. In: International Conference on the Theory and Applications of Cryptographic Techniques (EUROCRYPT 2001), pp.453-474 (2001) Ran, C., Krawczyk, H.: Analysis of key-exchange protocols and their use for building secure channels. In: International Conference on the Theory and Applications of Cryptographic Techniques (EUROCRYPT 2001), pp.453-474 (2001)
10.
Zurück zum Zitat Shor, P.W.: Polynomial-time algorithms for prime factorization and discrete logarithms on a quantum computer. SIAM Rev. 41(2), 303–332 (1999)MathSciNetMATHCrossRef Shor, P.W.: Polynomial-time algorithms for prime factorization and discrete logarithms on a quantum computer. SIAM Rev. 41(2), 303–332 (1999)MathSciNetMATHCrossRef
11.
Zurück zum Zitat Buchmann, J.A., Butin, D., G¨opfert, F., Petzoldt, A.: Post-Quantum cryptography: state of the art. In: The New Codebreakers, pp. 88–108 (2016) Buchmann, J.A., Butin, D., G¨opfert, F., Petzoldt, A.: Post-Quantum cryptography: state of the art. In: The New Codebreakers, pp. 88–108 (2016)
12.
Zurück zum Zitat Ajtai, M.: Generating hard instances of lattice problems. In: Proceedings of the Twenty-Eighth Annual ACM Symposium on Theory of Computing, pp. 99–108 (1996) Ajtai, M.: Generating hard instances of lattice problems. In: Proceedings of the Twenty-Eighth Annual ACM Symposium on Theory of Computing, pp. 99–108 (1996)
13.
Zurück zum Zitat Regev, O.: On lattices, learning with errors, random linear codes, and cryptography. In: Proceedings of the Thirty-Seventh Annual ACM Symposium on Theory of Computing (STOC’05), pp. 84–93 (2005) Regev, O.: On lattices, learning with errors, random linear codes, and cryptography. In: Proceedings of the Thirty-Seventh Annual ACM Symposium on Theory of Computing (STOC’05), pp. 84–93 (2005)
14.
Zurück zum Zitat Gentry, C.: Fully homomorphic encryption using ideal lattices. In: Proceedings of the Forty-First Annual ACM Symposium on Theory of Computing (STOC’09), pp. 169–178 (2009) Gentry, C.: Fully homomorphic encryption using ideal lattices. In: Proceedings of the Forty-First Annual ACM Symposium on Theory of Computing (STOC’09), pp. 169–178 (2009)
15.
Zurück zum Zitat Garg, S., Gentry, C., Halevi, S.: Candidate multilinear maps from ideal lattices. In: Annual International Conference on the Theory and Applications of Cryptographic Techniques (EUROCRYPT 2013), pp. 1–17 (2013) Garg, S., Gentry, C., Halevi, S.: Candidate multilinear maps from ideal lattices. In: Annual International Conference on the Theory and Applications of Cryptographic Techniques (EUROCRYPT 2013), pp. 1–17 (2013)
16.
Zurück zum Zitat Dan, B., Freeman, D.: Homomorphic signatures for polynomial functions. In: Annual International Conference on the Theory and Applications of Cryptographic Techniques (EUROCRYPT 2011), pp. 149–168 (2011) Dan, B., Freeman, D.: Homomorphic signatures for polynomial functions. In: Annual International Conference on the Theory and Applications of Cryptographic Techniques (EUROCRYPT 2011), pp. 149–168 (2011)
17.
Zurück zum Zitat Zhang, J., Zhang, Z.F., Ding, J.T., Snook, M.: Authenticated key exchange from ideal lattices. In: Annual International Conference on the Theory and Applications of Cryptographic Techniques (EUROCRYPT 2015), pp. 719–751 (2015) Zhang, J., Zhang, Z.F., Ding, J.T., Snook, M.: Authenticated key exchange from ideal lattices. In: Annual International Conference on the Theory and Applications of Cryptographic Techniques (EUROCRYPT 2015), pp. 719–751 (2015)
18.
Zurück zum Zitat Peikert, C.: Lattice cryptography for the Internet. In: International Workshop on Post-quantum Cryptography (PQCrypto), pp. 197–219 (2014) Peikert, C.: Lattice cryptography for the Internet. In: International Workshop on Post-quantum Cryptography (PQCrypto), pp. 197–219 (2014)
20.
Zurück zum Zitat Wang, S.B., Zhu, Y., Ma, D., Feng, R.Q.: Lattice-based key exchange on small integer solution problem. Sci. China Inf. Sci. 57(11), 1–12 (2014)MathSciNetMATH Wang, S.B., Zhu, Y., Ma, D., Feng, R.Q.: Lattice-based key exchange on small integer solution problem. Sci. China Inf. Sci. 57(11), 1–12 (2014)MathSciNetMATH
21.
Zurück zum Zitat Gupta, D.S., Biswas, G.P.: Cryptanalysis of Wang et al’.s lattice-based key exchange protocol. Perspect. Sci. 8(1), 228–230 (2016)CrossRef Gupta, D.S., Biswas, G.P.: Cryptanalysis of Wang et al’.s lattice-based key exchange protocol. Perspect. Sci. 8(1), 228–230 (2016)CrossRef
22.
Zurück zum Zitat Mao, S.W., Zhang, P., Wang, H.Z.: Cryptanalysis of a lattice based key exchange protocol. Sci China Inf. Sci. 60(2), 1–3 (2017)CrossRef Mao, S.W., Zhang, P., Wang, H.Z.: Cryptanalysis of a lattice based key exchange protocol. Sci China Inf. Sci. 60(2), 1–3 (2017)CrossRef
23.
Zurück zum Zitat Langlois, A., Stehl´e, D.: Worst-case to average-case reductions for module lattices. Des. Codes Cryptogr. 75(3), 565–599 (2015) Langlois, A., Stehl´e, D.: Worst-case to average-case reductions for module lattices. Des. Codes Cryptogr. 75(3), 565–599 (2015)
24.
Zurück zum Zitat Micciancio, D., Regev, O.: Worst-case to average-case reductions based on Gaussian measures. SIAM J. Comput. 37(1), 267–302 (2007)MathSciNetMATHCrossRef Micciancio, D., Regev, O.: Worst-case to average-case reductions based on Gaussian measures. SIAM J. Comput. 37(1), 267–302 (2007)MathSciNetMATHCrossRef
26.
Zurück zum Zitat Applebaum, B., Cash, D., Peikert, C., Sahai, A.: Fast cryptographic primitives and circular secure encryption based on hard learning problems. In: Advances in Cryptology—CRYPTO 2009, pp. 595–618 (2009) Applebaum, B., Cash, D., Peikert, C., Sahai, A.: Fast cryptographic primitives and circular secure encryption based on hard learning problems. In: Advances in Cryptology—CRYPTO 2009, pp. 595–618 (2009)
27.
Zurück zum Zitat Micciancio, D., Regev, O.: Lattice-based cryptography. In: Post Quantum Cryptography, pp. 147–191 (2009) Micciancio, D., Regev, O.: Lattice-based cryptography. In: Post Quantum Cryptography, pp. 147–191 (2009)
28.
29.
Zurück zum Zitat Brakerski, Z., Gentry, C., Vaikuntanathan, V.: (Leveled) fully homomorphic encryption without bootstrapping. ACM Trans. Comput. Theory 6(3), 309–325 (2013)MathSciNetMATH Brakerski, Z., Gentry, C., Vaikuntanathan, V.: (Leveled) fully homomorphic encryption without bootstrapping. ACM Trans. Comput. Theory 6(3), 309–325 (2013)MathSciNetMATH
30.
Zurück zum Zitat Li, J., Chen, X.F., Li, M.Q., Li, J.W., Lee, P., Lou, W.J.: Secure deduplication with efficient and reliable convergent key management. IEEE Trans. Parallel Distrib. Syst. 25(6), 1615–1625 (2014)CrossRef Li, J., Chen, X.F., Li, M.Q., Li, J.W., Lee, P., Lou, W.J.: Secure deduplication with efficient and reliable convergent key management. IEEE Trans. Parallel Distrib. Syst. 25(6), 1615–1625 (2014)CrossRef
31.
Zurück zum Zitat Li, P., Li, J., Huang, Z.G., Li, T., Gao, C.Z., Yiu, S.M., Chen, K.: Multi-key privacy-preserving deep learning in cloud computing. Fut. Gener. Comput. Syst. 74(1), 76–85 (2017)CrossRef Li, P., Li, J., Huang, Z.G., Li, T., Gao, C.Z., Yiu, S.M., Chen, K.: Multi-key privacy-preserving deep learning in cloud computing. Fut. Gener. Comput. Syst. 74(1), 76–85 (2017)CrossRef
32.
Zurück zum Zitat Li, J., Liu, Z.L., Chen, X.F., Fatos, X., Tan, X., Wong, D.S.: L-EncDB: a lightweight framework for privacy-preserving data queries in cloud computing. Knowl. Syst. 79(1), 18–26 (2015)CrossRef Li, J., Liu, Z.L., Chen, X.F., Fatos, X., Tan, X., Wong, D.S.: L-EncDB: a lightweight framework for privacy-preserving data queries in cloud computing. Knowl. Syst. 79(1), 18–26 (2015)CrossRef
Metadaten
Titel
Cryptanalysis of lattice-based key exchange on small integer solution problem and its improvement
verfasst von
Zhengjun Jing
Chunsheng Gu
Zhimin Yu
Peizhong Shi
Chongzhi Gao
Publikationsdatum
05.03.2018
Verlag
Springer US
Erschienen in
Cluster Computing / Ausgabe Sonderheft 1/2019
Print ISSN: 1386-7857
Elektronische ISSN: 1573-7543
DOI
https://doi.org/10.1007/s10586-018-2293-x

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