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Blending FHE-NTRU Keys – The Excalibur Property

  • Louis Goubin
  • Francisco José Vial Prado
Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 10095)

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.

Keywords

Encryption Scheme Quadratic System Validation Protocol Random Polynomial Malicious Adversary 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

Notes

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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Copyright information

© Springer International Publishing AG 2016

Authors and Affiliations

  1. 1.Laboratoire de Mathématiques de Versailles, UVSQ, CNRSUniversité Paris-SaclayVersaillesFrance

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