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Annual International Conference on the Theory and Applications of Cryptographic Techniques

EUROCRYPT 2021: Advances in Cryptology – EUROCRYPT 2021 pp 498–527Cite as

New Lattice Two-Stage Sampling Technique and Its Applications to Functional Encryption – Stronger Security and Smaller Ciphertexts

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Part of the book series: Lecture Notes in Computer Science ((LNSC,volume 12696))

Abstract

This work proposes a new lattice two-stage sampling technique, generalizing the prior two-stage sampling method of Gentry, Peikert, and Vaikuntanathan (STOC ’08). By using our new technique as a key building block, we can significantly improve security and efficiency of the current state of the arts of simulation-based functional encryption. Particularly, our functional encryption achieves \((Q,\mathsf {poly})\) simulation-based semi-adaptive security that allows arbitrary pre- and post-challenge key queries, and has succinct ciphertexts with only an additive O(Q) overhead.

Additionally, our two-stage sampling technique can derive new feasibilities of indistinguishability-based adaptively-secure \(\mathsf {IB} \)-\(\mathsf {FE} \) for inner products and semi-adaptively-secure \(\mathsf {AB} \)-\(\mathsf {FE} \) for inner products, breaking several technical limitations of the recent work by Abdalla, Catalano, Gay, and Ursu (Asiacrypt ’20).

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Notes

  1. 1.

    We note that both the names “index” and “attribute” have been used interchangeably in the literature.

  2. 2.

    For example in \(\mathsf {IBE}\) and \(\mathsf {ABE}\), 0-keys are useful for decrypting other ciphertexts with satisfying indices. They just cannot decrypt the specific (challenge) index.

  3. 3.

    We notice that \((\mathsf {poly},\mathsf {poly})\) \(\mathsf {SIM}\)-based security is not possible by the lower bound of [4]. Thus, \((Q,\mathsf {poly})\) \(\mathsf {SIM}\)-based security is the best we can hope for in this model.

  4. 4.

    A very-selective scheme requires the adversary to commit to both the challenge index and function in the very beginning of the security experiment.

  5. 5.

    The reason why [2] cannot apply the light-weight method is because its basic construction only achieves very selective security, whereas the technique of [17, 30] can be applied to the selective security only over index.

  6. 6.

    Notice that the reusable garbled circuits following from our \(\mathsf {SIM}\)-secure \(\mathsf {FE}\)  can achieve \(\mathsf {SA}\)-\(\mathsf {SIM}\) security, and support general circuits and any arbitrary pre- and post-challenge key query, for one query.

  7. 7.

    To sample \(\mathcal {D}_{\Lambda _q^{\boldsymbol{u}}(\mathbf {A}),s} \), the current sampling algorithm requires that \(s> \Vert \widetilde{\mathbf {T}}_{\mathbf {A}}\Vert \omega (\sqrt{\log m})\). According to the best known (to our knowledge) trapdoor generation, the smallest s we can sample would be \(\omega (\sqrt{n\log q} \cdot \sqrt{\log m})\), which is much larger than the required bound for Lemma 4.1.

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Acknowledgements

We would like to thank the anonymous reviewers of Eurocrypt 2021 for their insightful advices. Qiqi Lai is supported by the National Key R&D Program of China (2017YFB0802000), the National Natural Science Foundation of China (61802241, U2001205, 61772326, 61802242), the Natural Science Basic Research Plan in Shaanxi Province of China (2019JQ-360), the National Cryptography Development Foundation during the 13th Five-year Plan Period (MMJJ20180217), and the Fundamental Research Funds for the Central Universities (GK202103093). Feng-Hao Liu and Zhedong Wang are supported by an NSF Award CNS-1657040 and an NSF Career Award CNS-1942400. Any opinions, findings, and conclusions or recommendations expressed in this material are those of the author(s) and do not necessarily reflect the views of the sponsors.

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Authors and Affiliations

  1. School of Computer Science, Shaanxi Normal University, Xi’an, China

    Qiqi Lai

  2. State Key Laboratory of Integrated Service Networks, Xidian University, Xi’an, China

    Qiqi Lai

  3. Florida Atlantic University, Boca Raton, FL, USA

    Feng-Hao Liu & Zhedong Wang

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  1. Inria, Paris, France

    Anne Canteaut

  2. UCLouvain, Louvain-la-Neuve, Belgium

    François-Xavier Standaert

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Lai, Q., Liu, FH., Wang, Z. (2021). New Lattice Two-Stage Sampling Technique and Its Applications to Functional Encryption – Stronger Security and Smaller Ciphertexts. In: Canteaut, A., Standaert, FX. (eds) Advances in Cryptology – EUROCRYPT 2021. EUROCRYPT 2021. Lecture Notes in Computer Science(), vol 12696. Springer, Cham. https://doi.org/10.1007/978-3-030-77870-5_18

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