Supporting　proofs　of　evaluations,　polynomial　commitment　schemes　(PCS)　are　crucial　in　secure　distributed　systems.　Schemes　based　on　fast　Reed-Solomon　interactive　oracle　proofs　(RS-IOP)　of　proximity　have　recently　emerged,　offering　transparent　setup,　plausible　post-quantum　security,　efficient　operations,　and,　notably,　sublinear　proof　size　and　verification.　Manifesting　a　new　paradigm,　PCS　with　one-to-many　proof　can　enhance　the　performance　of　(asynchronous)　verifiable　secret　sharing　((A)VSS),　a　cornerstone　in　distributed　computing,　for　proving　multiple　evaluations　to　multiple　verifiers.　Current　RS-IOP-based　multivariate　PCS,　including　HyperPlonk　(Eurocrypt＇23)　and　Virgo　(S&P＇20),　however,　only　offer　quasi-linear　prover　complexity　in　the　polynomial　size.　We　propose　PolyFRIM,　a　fast　RS-IOP-based　multivariate　PCS　with　optimal　linear　prover　complexity,　5-25×　faster　than　prior　arts　while　ensuring　competent　proof　size　and　verification.　Heeding　the　challenging　absence　of　FFT　circuits　for　multivariate　evaluation,　PolyFRIM　surpasses　Zhang　et　al.＇s　(Usenix　Sec.＇22)　one-to-many　univariate　PCS,　accelerating　proving　by　4-7×　and　verification　by　2-4×　with　25%　shorter　proof.　Leveraging　PolyFRIM,　we　propose　an　AVSS　scheme　FRISS　with　a　better　efficiency　tradeoff　than　prior　arts　from　multivariate　PCS,　including　Bingo　(Crypto＇23)　and　Haven　(FC＇21).　©　USENIX　Security　Symposium　2024.All　rights　reserved.