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Let the modified NTRU be $h=f/g$ such that $f$ is not necessarily a short polynomial, is the NTRU problem still hard in this case?

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Finding an answer is not hard, but answers will not be unique. Given $h$, pick your favourite short polynomial $g$ then compute $f=gh$ using multiplication mod $X^n-1$. As $f$ is unconstrained the resulting answer is a legitimate solution.

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  • $\begingroup$ Thanks dear professor $\endgroup$
    – Don Freecs
    Feb 10 at 14:09
  • $\begingroup$ I don't know if I need to open another question or keep discussing here, another question how about distinguishing from uniform? $\endgroup$
    – Don Freecs
    Feb 10 at 18:17
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    $\begingroup$ @DonFreecs I think the answers will be pretty uniform as well; fixing invertible $g$ and letting $h$ run over all possible values will give all values of $f$ and vice-versa. $\endgroup$
    – Daniel S
    Feb 11 at 12:05

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