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Improve the design of circuit, config, and instances for CycleFold #158

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Depends on #123. Before #123 gets merged, a diff can be found here: winderica:protogalaxy-based-ivc...winderica:refactor-cyclefold.

This PR aims to refactor the existing code related to CycleFold improve the design. Specifically, it:

  • Adds support for multiple random values when accumulating points in CF circuit, while maintaining the efficiency of current implementation for multiple points. (See the comments in Protogalaxy based IVC #123 (comment))
  • Extract the construction of cf_u.x into a separate function. Before this PR, cf_u.x is manually constructed by concatenating randomness and points in all augmented circuits of Nova, HyperNova, and ProtoGalaxy, as observed in Protogalaxy based IVC #123 (comment).
  • ...

These values will be used as hints to the augmented circuit
…simplify the construction of incoming CF instances
@winderica winderica mentioned this pull request Sep 11, 2024
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