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
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.