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An algebraic approach to NTRU (q = 2^n) via Witt vectors and overdetermined systems of nonlinear equations.

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

Original languageEnglish
Title of host publicationSecurity and Cryptography for Networks - SCN 2006
Publisher or commissioning bodySpringer Berlin Heidelberg
Pages278 - 298
Number of pages20
Volume3352
ISBN (Print)3540243011
DatePublished - Jan 2005

Abstract

We use the theory of Witt vectors to develop an algebraic approach for studying the NTRU primitive with $q$~parameter equal to a power of two. This results in a system of nonlinear algebraic equations over~$\FF_2$ having many symmetries, which is reminiscent of the approach of Courtois, Murphy, Pieprzyk, Robshaw and others for studying the structure of block ciphers such as the~AES. We study whether this approach to NTRU provides any immediate security threat and conclude that under the most favourable assumptions, the method is of asymptotic interest but is completely impractical at current or likely future parameter sizes.

Additional information

Conference Proceedings/Title of Journal: Security in Communication Networks (SCN 2004)

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