Lattice-Based Post-Quantum iO from Circular Security with Random Opening Assumption

Explore advanced cryptographic research in this conference talk that presents a novel approach to constructing lattice-based post-quantum indistinguishability obfuscation (iO) using a new security assumption called Circular Security with Random Opening (CRO). Learn about the fundamental challenges in building post-quantum iO under simple and well-founded assumptions, and understand how previous constructions combining fully homomorphic encryption with decryption hints have been vulnerable to cryptanalytic attacks due to structural weaknesses in their underlying LWE-with-hint assumptions. Discover how the CRO assumption addresses these vulnerabilities through two critical properties: marginal uniformity of the hint distribution and prevention of noise leakage during natural hint usage, effectively ruling out important classes of attack strategies that have compromised earlier assumptions. Gain insights into the evolution of iO construction techniques, starting with the Brakerski et al. framework from Eurocrypt 2020, and examine the specific leakages that have been exploited in attacks against previous schemes. Understand the core design principles behind this new construction that eliminate known vulnerable structures, providing a qualitatively different target for cryptanalysis compared to existing lattice-based assumptions for indistinguishability obfuscation.