Implementing Candidate Graded Encoding Schemes from Ideal Lattices

Martin Albrecht, Catalin Cocis, Fabien Laguillaumie, Adeline Langlois

Research output: Chapter in Book/Report/Conference proceedingConference contribution


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
Number of pages24
ISBN (Electronic)978-3-662-48799-0
ISBN (Print)978-3-662-48799-0
Publication statusPublished - 30 Dec 2015

Publication series

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

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