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Why will the polynomial f almost always have an inverse for NTRU?

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In many NTRU material it is said that with our choice of the polynomial $f$, it will almost always have an inverse. Maybe it's a stupid question, but why will it almost always have an inverse element? And why is it recommended to take the polynomial $1 + pF$ in order to have the inverse? And one more question: why is it necessary in this scheme that $g$($x$) does not have an inverse element? What is this restriction used for?

Maarten Bodewes avatar
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