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Augmented Learning with Errors: The Untapped Potential of the Error Term

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Financial Cryptography and Data Security (FC 2015)

Part of the book series: Lecture Notes in Computer Science ((LNSC,volume 8975))

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Abstract

The Learning with Errors (LWE) problem has gained a lot of attention in recent years leading to a series of new cryptographic applications. Interestingly, cryptographic primitives based on LWE often do not exploit the full potential of the error term beside of its importance for security. To this end, we introduce a novel LWE-close assumption, namely Augmented Learning with Errors (A-LWE), which allows one to hide auxiliary data injected into the error term by a technique that we call message embedding. In particular, it enables existing cryptosystems to strongly increase the message throughput per ciphertext. We show that A-LWE is for certain instantiations at least as hard as the LWE problem. This inherently leads to new cryptographic constructions providing high data load encryption and customized security properties as required, for instance, in economic environments such as stock markets resp. for financial transactions. The security of those constructions basically stems from the hardness to solve the A-LWE problem.As an application we introduce (among others) the first lattice-based replayable chosen-ciphertext secure encryption scheme from A-LWE.

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Notes

  1. 1.

    We show that if matrix \(\mathbf {A}\) is fixed and each secret \(\mathbf {s}\) is uniformly sampled from \(\mathbb {Z}_q^n\), the entropy of \(\mathbf {s}\) suffices to sample the entire error term from \(\mathcal {D}_{\varLambda ^{\perp }_{\mathbf {v}}(\mathbf {G}),\alpha q}\).

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Acknowledgments

The work presented in this paper was performed within the context of the Software Cluster project Sinnodium and Software Campus project IT-GiKo by Rachid El Bansarkhani. It was funded by the German Federal Ministry of Education and Research (BMBF). Özgür Dagdelen and Johannes Buchmann are supported by BMBF within EC-SPRIDE. The authors thank Steven Galbraith for useful comments.

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  1. Technische Universität Darmstadt, Fachbereich Informatik, Kryptographie und Computeralgebra, Hochschulstraße 10, 64289, Darmstadt, Germany

    Rachid El Bansarkhani, Özgür Dagdelen & Johannes Buchmann

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  1. Rachid El Bansarkhani
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Correspondence to Rachid El Bansarkhani .

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  1. University of Innsbruck, Innsbruck, Austria

    Rainer Böhme

  2. NTT Laboratories, Tokyo, Japan

    Tatsuaki Okamoto

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El Bansarkhani, R., Dagdelen, Ö., Buchmann, J. (2015). Augmented Learning with Errors: The Untapped Potential of the Error Term. In: Böhme, R., Okamoto, T. (eds) Financial Cryptography and Data Security. FC 2015. Lecture Notes in Computer Science(), vol 8975. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-662-47854-7_20

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