In both cases, the theme is parallelism. So for verification, we use all the cores and we do the multi exponentiation in parallel. But because it's small, so proving use, verification uses about 32,000 basis. We can do pre compute n times each base and we can save a lot of work that way when it comes to actual verification and get say an 8x speed up. And because it'ssmall, 32,00 basis, we have enough memory on the system to actually hold this pre computation.

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