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The term "truncated polynomials" shouldn't really be used in relation to NTRU. A truncated polynomial is, strictly speaking, a polynomial with terms of order N or more discarded. NTRU instead uses polynomials mod $X^N-1$. So, for example, if $N=3$, then $x^2+1 * x^2+1$ = $x^4+2x^2+1$. Truncated this is simply $2x^2+1$. Reduced mod $X^3-1$, it's $2x^2 + x + ...

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