Add CTLs across segment proofs

[sai-deng]

@4l0n50 mentioned an great idea this morning to have all Keccak operations at the last segment, along with some assembly logic changes.

I think it may also be possible to implement this as cross-lookup among segment proofs. Instead of performing Keccak CTL check within the root (segment) circuit, we could modify the segment aggregation circuit to include CTL across segment proofs. This way, we can move all Keccak operations into a single segment and use it as the global lookup table for all other segments.

This method should also help reduce the size of other tables, including the kernel size in the memory table, among others. As a result, we can achieve improved recursion and proving speeds.

[Nashtare]

Related issue (benefiting from cross segment CTLs): #244

[sai-deng]

Some thoughts on implementation details:

We first need to generate all segment traces, which could be a drawback as it requires more memory. Next, we need to observe the trace caps of tables in all segments before generating the random oracles and starting the proving process. We will make the challenger state and all challenges public inputs for segment proofs. In the last segment, we need to ensure that the challenger’s outputs match the public challenge values.