We show polynomial-time quantum algorithms for the following problems:
(*) Short integer solution (SIS) problem under the infinity norm, where the public matrix is very wide, the modulus is a polynomially large prime, and the bound of infinity norm is set to be half of the modulus minus a ... more >>>

It is well known that any Linear Threshold Function, $f$,
on $\{ 0, 1\}^n$ has a representation with
integer coefficients with $O(n \log n)$ bits.
We study the problem of finding a small representation
in polynomial time. Given a representation of $f$
with arbitrary size coefficients, we give a polynomial
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