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Is generating semirandom blake256 hashes until packed points is on the curve, a safe algorithm to avoid the discrete log between the generated points?

I know there are more robust methods, but I wanted to know about this specific one For any distinct said randomly generated point : $P_i,P_j\in \{P_1,...,P_k\}$ it should be hard to find $s$ such that ...
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Will an integer program to deterministically factor integers help derandomize $\mathbb F_q[x]$ factoring?

There are many analogies between the objects $\mathbb F_q[x]$ and $\mathbb Z$. Supposing there is a fixed (say $10^9$) dimension linear integer program (describable without any objective function) in ...