Code-based Distributed Polynomial Commitment Scheme with Linear Prover Time and Polylogarithmic Communication

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We present the first fully distributed, code-based polynomial commitment scheme (PCS) that achieves linear prover time and polylogarithmic communication for multilinear polynomials. Our construction builds on Brakedown with proof composition. We design a distributed proof of correct linear encoding. Codeword validity is reduced to a sumcheck relation over the sparse parity-check matrix, whereas systematic consistency is verified through multilinear evaluation checks. These techniques preserve li