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Towards a Simpler Lattice Gadget Toolkit

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Public-Key Cryptography – PKC 2022 (PKC 2022)

Part of the book series: Lecture Notes in Computer Science ((LNSC,volume 13177))

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Abstract

As a building block, gadgets and associated algorithms are widely used in advanced lattice cryptosystems. The gadget algorithms for power-of-base moduli are very efficient and simple, however the current algorithms for arbitrary moduli are still complicated and practically more costly despite several efforts. Considering the necessity of arbitrary moduli, developing simpler and more practical gadget algorithms for arbitrary moduli is crucial to improving the practical performance of lattice based applications.

In this work, we propose two new gadget sampling algorithms for arbitrary moduli. Our first algorithm is for gadget Gaussian sampling. It is simple and efficient. One distinguishing feature of our Gaussian sampler is that it does not need floating-point arithmetic, which makes it better compatible with constrained environments. Our second algorithm is for gadget subgaussian sampling. Compared with the existing algorithm, it is simpler, faster, and requires asymptotically less randomness. In addition, our subgaussian sampler achieves an almost equal quality for different practical parameters. Overall these two algorithms provide simpler options for gadget algorithms and enhance the practicality of the gadget toolkit.

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Notes

  1. 1.

    Ideally, gadget sampling can be performed on a lightweight device while other costly computations are done on a powerful machine and in an offline phase.

  2. 2.

    https://palisade-crypto.org/.

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Acknowledgements

We thank Léo Ducas for his helpful comments. This work is supported by the National Natural Science Foundation of China (No. 62102216), the National Key Research and Development Program of China (Grant No. 2018YFA0704701), the Major Program of Guangdong Basic and Applied Research (Grant No. 2019B030302008) and Major Scientific and Techological Innovation Project of Shandong Province, China (Grant No. 2019JZZY010133).

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Authors and Affiliations

  1. Institute for Advanced Study, Tsinghua University, Beijing, China

    Shiduo Zhang

  2. BNRist, Tsinghua University, Beijing, China

    Yang Yu

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  1. Shiduo Zhang
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Correspondence to Yang Yu .

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Editors and Affiliations

  1. National Institute of Advanced Industrial Science and Technology (AIST), Tokyo, Japan

    Goichiro Hanaoka

  2. Yokohama National University, Yokohama, Japan

    Junji Shikata

  3. The University of Electro-Communications, Tokyo, Japan

    Yohei Watanabe

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Zhang, S., Yu, Y. (2022). Towards a Simpler Lattice Gadget Toolkit. In: Hanaoka, G., Shikata, J., Watanabe, Y. (eds) Public-Key Cryptography – PKC 2022. PKC 2022. Lecture Notes in Computer Science(), vol 13177. Springer, Cham. https://doi.org/10.1007/978-3-030-97121-2_18

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  • DOI: https://doi.org/10.1007/978-3-030-97121-2_18

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