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feat: implement SuperNova #283

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feat: implement SuperNova #283

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Commits on Jun 8, 2024

  1. feat: implement SuperNova 

    This implements [Supernova](https://eprint.iacr.org/2022/1758), allowing:
- a 'pay-as-you-go' cost structure for folding operations, through the SuperNova folding scheme,
- a final SNARK that efficiently compresses an instance of this folded proof, through batching techniques.

References:
- the [blog post](https://blog.lurk-lang.org/posts/arecibo-supernova/#technical-release-note-supernova-protocol-integration-into-nova) goes into our construction,
  and links to two more specialized notes on [the `CompressedSNARK` for Supernova](https://hackmd.io/@adr1anh/BJw1g0aBT) along with our variant of the [public input padding issue](https://hackmd.io/@adr1anh/Sy08YaVBa).
- the Readme at `src/supernova/Readme.md`

This backports the following Arecibo PRs:
- argumentcomputer/arecibo#2
- argumentcomputer/arecibo#3
- argumentcomputer/arecibo#10
- argumentcomputer/arecibo#16
- argumentcomputer/arecibo#23
- argumentcomputer/arecibo#30
- argumentcomputer/arecibo#28
- argumentcomputer/arecibo#41
- argumentcomputer/arecibo#45
- argumentcomputer/arecibo#50
- argumentcomputer/arecibo#56
- argumentcomputer/arecibo#51
- argumentcomputer/arecibo#72
- argumentcomputer/arecibo#92
- argumentcomputer/arecibo#95
- argumentcomputer/arecibo#97
- argumentcomputer/arecibo#101
- argumentcomputer/arecibo#110
- argumentcomputer/arecibo#106
- argumentcomputer/arecibo#112
- argumentcomputer/arecibo#114
- argumentcomputer/arecibo#119
- argumentcomputer/arecibo#120
- argumentcomputer/arecibo#127
- argumentcomputer/arecibo#123
- argumentcomputer/arecibo#131
- argumentcomputer/arecibo#174
- argumentcomputer/arecibo#175
- argumentcomputer/arecibo#182

Co-authored-by: WYATT <[email protected]>
Co-authored-by: Hanting Zhang <[email protected]>
Co-authored-by: Ming <[email protected]>
Co-authored-by: porcuquine <[email protected]>
Co-authored-by: Samuel Burnham <[email protected]>
Co-authored-by: Matej Penciak <[email protected]>
Co-authored-by: Adrian Hamelink <[email protected]>
    @huitseeker @wyattbenno777
    @winston-h-zhang @hero78119 @porcuquine @samuelburnham @mpenciak @adr1anh
    8 people committed Jun 8, 2024
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  2. fix: rename CircuitShape -> R1CSWithArity

    @huitseeker
    huitseeker committed Jun 8, 2024
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  3. fix: move traits::circuit_supernova inside supernova::circuit

    @huitseeker
    huitseeker committed Jun 8, 2024
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  4. chore: removing all uneeded public modifiers 

    - removing public modifier in  src/spartan/ppsnark.rs

- removing public modifier in  src/spartan/sumcheck/mod.rs

- removing public modifier in src/spartan/mod.rs

- removing public modifier in src/spartan/polys/masked_eq.rs

- removing public modifier in src/supernova/mod.rs
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  5. fix: Augmentation -> Augmented circuit & other typos

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    huitseeker committed Jun 8, 2024
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  6. Fix docs (microsoft#249) 

    * Refactor 'CircuitShape' references to 'R1CSWithArity'

- Implemented terminology update: all occurrences of `CircuitShape` have been replaced with `R1CSWithArity`
- Corrected method return descriptions to reflect changes in terminology
- Amended related notes and comments to maintain consistency and clarity in the codebase.

Leftover from argumentcomputer/arecibo#235

* Fix Supernova module documentation and code comments

- Update comments for struct `PublicParams` in `mod.rs` to reflect the correct association with `R1CSWithArity`.
- Alter codeblock tag in `Readme.md` from `ignore` to `text`.
- Revise mathematical formula in `Readme.md` for the current iteration of $F$ by including brackets around `0` in the base case inputs.
    @huitseeker
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