Paper 2026/1636 Original: eprint.iacr.org/2026/1636 ↗

How to use Polynomially-Hard iO: Turing Machine Obfuscation and More

Abstract

We revisit the notion of PViO [Jain-Jin, FOCS’22] – an indistinguishability obfuscation (iO) scheme for Turing machines with unbounded input length that guarantees security for pairs of machines whose equivalence can be proven in Cook’s Theory PV. Known constructions of PViO require subexponentially-hard iO for circuits. We give the first construction based on polynomially-hard iO and other standard assumptions. We further show how to replace iO with EFiO – an efficiently falsifiable variant, thus obtaining a construction based on efficiently falsifiable assumptions. Central to our result is a new twist to the celebrated punctured programming technique [Sahai-Waters, STOC’14], where one can program an obfuscated probabilistic function on its entire input domain in one shot instead of an input-by-input manner. Our key ingredient is the notion of function secret sharing [Boyle-Gilboa-Ishai, EUROCRYPT’15]. We further show the versatility of our technique by removing the use of complexity-leveraging in two applications of iO: unleveled fully homomorphic encryption, and adaptively-sound succinct non-interactive arguments for “trapdoor” languages.