Implementing Candidate Graded Encoding Schemes from Ideal Lattices. / Albrecht, Martin; Cocis, Catalin; Laguillaumie, Fabien; Langlois, Adeline.

Advances in Cryptology – ASIACRYPT 2015. ed. / Tetsu Iwata; Jung Hee Cheon. Springer, 2015. p. 752-775 ( Lecture Notes in Computer Science; Vol. 9453).

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Abstract

Multilinear maps have become popular tools for designing cryptographic schemes since a first approximate realisation candidate was proposed by Garg, Gentry and Halevi (GGH). This construction was later improved by Langlois, Stehlé and Steinfeld who proposed GGHLite which offers smaller parameter sizes. In this work, we provide the first implementation of such approximate multilinear maps based on ideal lattices. Implementing GGH-like schemes naively would not allow instantiating it for non-trivial parameter sizes. We hence propose a strategy which reduces parameter sizes further and several technical improvements to allow for an efficient implementation. In particular, since finding a prime ideal when generating instances is an expensive operation, we show how we can drop this requirement. We also propose algorithms and implementations for sampling from discrete Gaussians, for inverting in some Cyclotomic number fields and for computing norms of ideals in some Cyclotomic number rings. Due to our improvements we were able to compute a multilinear jigsaw puzzle for κ=52κ=52 (resp. κ=38κ=38) and λ=52λ=52 (resp. λ=80λ=80).
Original languageEnglish
Title of host publicationAdvances in Cryptology – ASIACRYPT 2015
EditorsTetsu Iwata, Jung Hee Cheon
PublisherSpringer
Pages752-775
Number of pages24
ISBN (Electronic)978-3-662-48799-0
ISBN (Print)978-3-662-48799-0
DOIs
Publication statusPublished - 30 Dec 2015

Publication series

Name Lecture Notes in Computer Science
PublisherSpringer
Volume9453
ISSN (Print)0302-9743

Projects

This open access research output is licenced under a Creative Commons Attribution-NonCommercial-NoDerivs 3.0 Unported License.

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