Knowledge Soundness of Polynomial Commitments in the Algebraic Group Model Does Not Guarantee Extractability↗ (원문, 새 창)

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The Algebraic Group Model (AGM) has become a standard framework for analyzing the knowledge soundness of group-based polynomial commitment schemes. In this work, we formally establish inherent limitations of this methodology. For many PCSs analyzed in the AGM, the algebraic explanation directly determines a polynomial and any required randomness that together reproduce the commitment. We call this structural property AGM-clarity. The extraction proof then only needs to show that the accepted eva