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In shortest vector problem, given a lattice in $\Bbb Z^n$, we seek the shortest non-zero vector in the lattice. This problem is computationally difficult.

Answer in Evidence for integer factorization is in $P$ seems to suggest some connections between polynomial analog of this problem that is easy? What is the precise polynomial analog of this problem and is there any connection to discrete logarithms?

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    $\begingroup$ Factorization in a UFD generally means factorization into irreducibles, so factorization in $\mathbb Z[x]$ is harder than factorization in $\mathbb Z$. Possibly you mean that factorization in $\mathbb Q[x]$ is relatively easy, as is factorization in $\mathbb F_q[x]$. $\endgroup$ Commented Sep 15, 2015 at 2:49
  • $\begingroup$ @JoeSilverman 'primitive' polynomial $\endgroup$ Commented Sep 15, 2015 at 9:54
  • $\begingroup$ Factoring polynomials with content $1$ is easy. $\endgroup$ Commented Sep 16, 2015 at 3:56
  • $\begingroup$ Fine, you've changed the wording of your question to say that the polynomials in $\mathbb Z[x]$ are primitive, i.e., the gcd of the coefficients if $1$, thereby making my earlier comment irrelevant. $\endgroup$ Commented Sep 16, 2015 at 11:21
  • $\begingroup$ @JoeSilverman Actually I knew this beforehand. I just made a mistake which is now corrected thanks to your observance $\endgroup$ Commented Sep 16, 2015 at 19:48

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Not sure about the first, but for the second, yes:

Claus-Peter Schnorr. Factoring Integers and Computing Discrete Logarithms via Diophantine Approximations. In Eurocrypt 1991, volume 547 of LNCS, pages 281–293. Springer, 1991

Alexander May. Using LLL-Reduction for Solving RSA and Factorization Problems. In Nguyen and Vallee [NV10], pages 315–348.

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