Abstract
Despite the importance of preimage sampling algorithm in lattice-based cryptography, its low efficiency limits its applications. In this study, we propose a family of gadget-based trapdoors on NTRU lattice. Our construction is compatible with existing efficient preimage sampling algorithms and offer compact secret. Comparison with two trapdoor schemes of [10], the hash-and-sign signature scheme based on our trapdoor scheme has better security and the sizes of secret and signature are reduced. In the first scheme, the sizes of public key and secret key are 6.25 kB and 5.0 kB for an estimation of 63.95-bit security. In the second one, they are 6.25 kB and 5.0 kB for an estimation of 75.92-bit security. Our proof-of-concept shows that the sizes of secret key and public key can be reduced to 0.88 kB and 3.06 kB for an estimation of 86.72-bit security.
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References
Gentry, C.: Fully homomorphic encryption using ideal lattices. In: STOC, pp. 169–178. ACM (2009)
Cheon, J.H., Kim, D., Kim, T., Son, Y.: A new trapdoor over module-NTRU lattice and its application to ID-based encryption. IACR Cryptology ePrint Archive, 2019/1468 (2019)
Gentry, C., Peikert, C., V aikuntanathan, V.: Trapdoors for hard lattices and new cryptographic constructions. In: STOC, pp. 197–206. ACM (2008)
Ajtai, M.: Generating hard instances of lattice problems. Quaderni di Matematica 13, 1–32 (2004)
Chen, Y., Genise, N., Mukherjee, P.: Approximate trapdoors for lattices and smaller hash-and-sign signatures. In: Galbraith, S.D., Moriai, S. (eds.) ASIACRYPT 2019. LNCS, vol. 11923, pp. 3–32. Springer, Cham (2019). https://doi.org/10.1007/978-3-030-34618-8_1
Micciancio, D., Peikert, C.: Trapdoors for lattices: simpler, tighter, faster, smaller. In: Pointcheval, D., Johansson, T. (eds.) EUROCRYPT 2012. LNCS, vol. 7237, pp. 700–718. Springer, Heidelberg (2012). https://doi.org/10.1007/978-3-642-29011-4_41
Ducas, L., Prest, T.: Fast fourier orthogonalization. In: ISSAC, pp. 191–198. ACM (2016)
Jia, H., Hu, Y., Tang, C.: Lattice-based hash-and-sign signatures using approximate trapdoor, revisited. IET Inf. Secur. 16(1), 41–50 (2022)
Genise, N., Micciancio, D.: Faster gaussian sampling for trapdoor lattices with arbitrary modulus. In: Nielsen, J.B., Rijmen, V. (eds.) EUROCRYPT 2018. LNCS, vol. 10820, pp. 174–203. Springer, Cham (2018). https://doi.org/10.1007/978-3-319-78381-9_7
Genise, N., Li, B.: Gadget-based iNTRU lattice trapdoors. In: Bhargavan, K., Oswald, E., Prabhakaran, M. (eds.) INDOCRYPT 2020. LNCS, vol. 12578, pp. 601–623. Springer, Cham (2020). https://doi.org/10.1007/978-3-030-65277-7_27
Lyubashevsky, V.: Lattice signatures without trapdoors. In: Pointcheval, D., Johansson, T. (eds.) EUROCRYPT 2012. LNCS, vol. 7237, pp. 738–755. Springer, Heidelberg (2012). https://doi.org/10.1007/978-3-642-29011-4_43
Hu, Y., Jia, H.: A new Gaussian sampling for trapdoor lattices with arbitrary modulus. Des. Codes Crypt. 87(11), 2553–2570 (2019). https://doi.org/10.1007/s10623-019-00635-8
Alkim, E., et al.: The lattice-based digital signature scheme qTESLA. IACR Cryptology ePrint Archive 2019/85 (2019)
Chuengsatiansup, C., Prest, T., Stehlé, D., Wallet, A., Xagawa, K.: Modfalcon: compact signatures based on module NTRU lattices. IACR Cryptology ePrint Archive 2019/1456 (2019)
Peikert, C.: An efficient and parallel gaussian sampler for lattices. In: Rabin, T. (ed.) CRYPTO 2010. LNCS, vol. 6223, pp. 80–97. Springer, Heidelberg (2010). https://doi.org/10.1007/978-3-642-14623-7_5
Clear, M., McGoldrick, C.: Multi-identity and multi-key leveled FHE from learning with errors. In: Gennaro, R., Robshaw, M. (eds.) CRYPTO 2015. LNCS, vol. 9216, pp. 630–656. Springer, Heidelberg (2015). https://doi.org/10.1007/978-3-662-48000-7_31
Gentry, C., Sahai, A., Waters, B.: Homomorphic encryption from learning with errors: conceptually-simpler, asymptotically-faster, attribute-based. In: Canetti, R., Garay, J.A. (eds.) CRYPTO 2013. LNCS, vol. 8042, pp. 75–92. Springer, Heidelberg (2013). https://doi.org/10.1007/978-3-642-40041-4_5
Ducas, L., Lyubashevsky, V., Prest, T.: Efficient identity-based encryption over NTRU lattices. In: Sarkar, P., Iwata, T. (eds.) ASIACRYPT 2014. LNCS, vol. 8874, pp. 22–41. Springer, Heidelberg (2014). https://doi.org/10.1007/978-3-662-45608-8_2
Peikert, C.: A decade of lattice cryptography. Found. Trends Theor. Comput. Sci. 10(4), 283–424 (2016)
Kirchner, P., et al.: Falcon: fast-fourier lattice-based compact signatures over NTRU. Post-Quantum Cryptography Standardization Round2 Submissions (2019)
Acknowledgement
The authors thank the anonymous reviewers for helpful comments and suggestions. This study was supported by the National Key Research and Development Program of China (Grant No. 2021YFB3100200), the National Key Research and Development Program of China through Project 2021YFA1000600, and Natural Science Foundation of China through Projects 12171114.
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Liu, C., Tang, C., Jia, H. (2022). New Trapdoor and Preimage Sampling on NTRU Lattice. In: Ahene, E., Li, F. (eds) Frontiers in Cyber Security. FCS 2022. Communications in Computer and Information Science, vol 1726. Springer, Singapore. https://doi.org/10.1007/978-981-19-8445-7_18
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