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Günter Rote:

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Finding a shortest vector in a two-dimensional lattice modulo `m`

*Theoretical Computer Science* **172** (1997), 303–308. doi:10.1016/S0304-3975(96)00185-5
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Abstract

We find the shortest non-zero vector in the lattice of all integer multiples
of the vector (`a`,`b`) modulo `m`, for given integers 0<`a`,`b`<`m`.
We reduce the problem to the computation of a Minkowski-reduced basis for
a planar lattice and thereby show that the problem can be solved in `O`(log
`m` (log log `m`)^{2}) bit operations.
Last update: October 26, 2001.