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Blending FHE-NTRU Keys – The Excalibur Property

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Progress in Cryptology – INDOCRYPT 2016 (INDOCRYPT 2016)

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Abstract

Can Bob give Alice his decryption secret and be convinced that she will not give it to someone else? This is achieved by a proxy re-encryption scheme where Alice does not have Bob’s secret but instead she can transform ciphertexts in order to decrypt them with her own key. In this article, we answer this question in a different perspective, relying on a property that can be found in the well-known modified NTRU encryption scheme. We show how parties can collaborate to one-way-glue their secret-keys together, giving Alice’s secret-key the additional ability to decrypt Bob’s ciphertexts. The main advantage is that the protocols we propose can be plugged directly to the modified NTRU scheme with no post-key-generation space or time costs, nor any modification of ciphertexts. In addition, this property translates to the NTRU-based multikey homomorphic scheme, allowing to equip a hierarchic chain of users with automatic re-encryption of messages and supporting homomorphic operations of ciphertexts. To achieve this, we propose two-party computation protocols in cyclotomic polynomial rings. We base the security in presence of various types of adversaries on the RLWE and DSPR assumptions, and on two new problems in the modified NTRU ring.

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Acknowledgments

We would like to thank Pablo Schinke Gross for suggesting the term Excalibur and the INDOCRYPT 2016 anonymous reviewers for their helpful comments. This work has been supported in part by the FUI CRYPTOCOMP project.

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Authors and Affiliations

  1. Laboratoire de Mathématiques de Versailles, UVSQ, CNRS, Université Paris-Saclay, 78035, Versailles, France

    Louis Goubin & Francisco José Vial Prado

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  1. Louis Goubin
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  2. Francisco José Vial Prado
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Correspondence to Francisco José Vial Prado .

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Editors and Affiliations

  1. University of Haifa , Haifa, Israel

    Orr Dunkelman

  2. Indraprashtha Institute of Information Technology (IIIT-D), New Delhi, India

    Somitra Kumar Sanadhya

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Goubin, L., Vial Prado, F.J. (2016). Blending FHE-NTRU Keys – The Excalibur Property. In: Dunkelman, O., Sanadhya, S. (eds) Progress in Cryptology – INDOCRYPT 2016. INDOCRYPT 2016. Lecture Notes in Computer Science(), vol 10095. Springer, Cham. https://doi.org/10.1007/978-3-319-49890-4_1

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  • DOI: https://doi.org/10.1007/978-3-319-49890-4_1

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