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refac: improve pcs interface #225

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Commits on Jan 9, 2024

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Commits on Jan 10, 2024

  1. refac: enable TranscriptRead|Writer to choose transcript writing

    This is needed by improving PCS interface.
    chokobole committed Jan 10, 2024
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  2. refac: refactor transcript and organize commitment schemes

    This commit solves 2 problems.
    
    1. `Transcript` was only able to handle field or curve point.
       Since proof and hash algorithm can take arbitrary types, this limitation is
       overcame.
    
    2. The interfaces of `VectorCommitmentScheme` and
       `UnivariatePolynomialCommitmentScheme` are organized.
    
       When committing, the cases are divided into 3 cases.
    
       - non interactive: e.g, SHPlonk, MerkleTree
       - non interactive with random: e.g, Pedersen
       - interactive: e.g, FRI
    
      When opening, the cases are divided into 2 cases.
    
      - non interactive: e.g, MerkleTree
      - interactive: e.g, SHPlonk and FRI
    
      When verifying, the cases are divided into 2 cases.
    
      - both committing and opening is non interactive: e.g, MerkleTree
      - either committing or opening is interative: e.g, SHPlonk and FRI
    chokobole committed Jan 10, 2024
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