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Note on Extractability of PST Polynomial Commitment Scheme
eprint.iacr.orgpaper

Note on Extractability of PST Polynomial Commitment Scheme

This IACR ePrint note revisits a 2025 Crypto paper by Belohorec et al. that proved the PST multivariate polynomial commitment scheme is black-box extractable under two new assumptions, ARSDH(n) and GARSDH(n). The authors show both are in fact equivalent to the original ARSDH assumption from Lipmaa et al. (Eurocrypt 2024), and separately identify a gap in the proof that canonical PST is extractable under GARSDH(n). This matters for implementers and auditors relying on PST/KZG-style polynomial commitments, as it clarifies the actual cryptographic strength underpinning extractability claims used in zk-SNARK and other succinct-proof constructions.

TL;DR A cryptography note shows two new falsifiable assumptions used to prove PST polynomial-commitment extractability collapse to the original ARSDH assumption, and flags a gap in the GARSDH(n) extractability proof.
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Organisations named here

  • ARSDH
  • GARSDH
  • Janno Siim
  • Pritam Pal

Technologies named here

  • PST polynomial commitment scheme
  • KZG polynomial commitment
  • KZG
  • PST

Techniques named here

  • Assumption equivalence proofs
  • Proof gap identification

Also named here

  • Belohorec et al.
  • Lipmaa et al.

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