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

Nigel Smart, Fre Vercauteren, Joseph H.. Silverman, An algebraic approach to NTRU (q = 2^n) via Witt vectors and overdetermined systems of nonlinear equations. . *Security in Communication Networks (SCN 2004)*. ISBN 3-540-24301-1, pp. 278–298. January 2005. No electronic version available. External information
## 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.

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