# #StackBounty: #lattice-crypto Finding the basis of the transpose of a q-ary lattice

### Bounty: 50

Given $$q$$ and a matrix $$A in mathbb{Z}_q^{n times m}$$, the $$q$$-ary lattice is defined as
$$Lambda(A)={x in mathbb{Z}^m:Ax=0 bmod q}$$
An instance of a q-ary lattice and its short basis is computed in Generating short basis for hard random lattices. Once the short basis $$T_A$$ for $$Lambda(A)$$ is given, computing the short vector $$s$$ in $$Lambda (A)$$ is given in SamplePre algorithm.

Is it possible to find a short basis for $$Lambda(A^T)$$, if we are given a short basis of $$Lambda(A)$$?

Basically I want to find the short vector $$s^prime$$ such that $$A^Ts^prime=0 bmod q$$.

Get this bounty!!!

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