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Improved lattice-based CCA2-secure PKE in the standard model

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Abstract

Based on the identity-based encryption (IBE) from lattices by Agrawal et al. (Eurocrypt’10), Micciancio and Peikert (Eurocrypt’12) presented a CCA1-secure public-key encryption (PKE), which has the best known efficiency in the standard model and can be used to obtain a CCA2-secure PKE from lattices by using the generic BCHK transform (SIAM J Comput, 2006) with a cost of introducing extra overheads to both computation and storage for the use of other primitives such as signatures and commitments. In this paper, we propose a more efficient standard model CCA2-secure PKE from lattices by carefully combining a different message encoding (which encodes the message into the most significant bits of the LWE’s “secret term”) with several nice algebraic properties of the tag-based lattice trapdoor and the LWE problem (such as unique witness and additive homomorphism). Compared to the best known lattice-based CCA1-secure PKE in the standard model due to Micciancio and Peikert (Eurocrypt’12), we not only directly achieve the CCA2-security without using any generic transform (and thus do not use signatures or commitments), but also reduce the noise parameter roughly by a factor of 3. This improvement makes our CCA2-secure PKE more efficient in terms of both computation and storage. In particular, when encrypting a 256-bit (respectively, 512-bit) message at 128-bit (respectively, 256-bit) security, the ciphertext size of our CCA2-secure PKE is even 33%–44% (respectively, 36%–46%) smaller than that of their CCA1-secure PKE.

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Acknowledgements

Jiang ZHANG is supported by National Key Research and Development Program of China (Grant Nos. 2017YFB0802005, 2018YFB0804105), National Natural Science Foundation of China (Grant No. 61602046), Young Elite Scientists Sponsorship Program by CAST (Grant No. 2016QNRC001), and Opening Project of Guangdong Provincial Key Laboratory of Data Security and Privacy Protection (Grant No. 2017B030301004). Yu YU is supported by National Natural Science Foundation of China (Grant Nos. 61872236, 61572192), National Cryptography Development Fund (Grant No. MMJJ20170209), and Anhui Initiative in Quantum Information Technologies (Grant No. AHY150100). Shuqin FAN is supported by National Key Research and Development Program of China (Grant No. 2017YFB0802005). Zhenfeng ZHANG is supported by National Key Research and Development Program of China (Grant No. 2017YFB0802005) and National Natural Science Foundation of China (Grant No. U1536205).

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Authors and Affiliations

  1. State Key Laboratory of Cryptology, P.O. Box 5159, Beijing, 100878, China

    Jiang Zhang & Shuqin Fan

  2. Guangdong Provincial Key Laboratory of Data Security and Privacy Protection, Jinan University, Guangzhou, 510632, China

    Jiang Zhang

  3. Department of Computer Science and Engineering, Shanghai Jiao Tong University, Shanghai, 200240, China

    Yu Yu

  4. Trusted Computing and Information Assurance Laboratory, Institute of Software, Chinese Academy of Sciences, Beijing, 100190, China

    Zhenfeng Zhang

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  1. Jiang Zhang
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Correspondence to Jiang Zhang.

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Zhang, J., Yu, Y., Fan, S. et al. Improved lattice-based CCA2-secure PKE in the standard model. Sci. China Inf. Sci. 63, 182101 (2020). https://doi.org/10.1007/s11432-019-9861-3

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