Lossy Cryptography from Code-Based Assumptions

Over the past few decades, we have seen a proliferation of advanced cryptographic primitives with lossy or homomorphic properties built from various assumptions such as Quadratic Residuosity, Decisional Diffie-Hellman, and Learning with Errors. These primitives imply hard problems in the complexity class $SZK$ (statistical zero-knowledge); as a consequence, they can only be based on assumptions that are broken in $BPP^{SZK}$. This poses a barrier for building advanced primitives from code-based assumptions, as the only known such assumption is Learning Parity …

advanced can class code complexity cryptographic cryptography cs.cc cs.cr cs.it diffie errors hard hellman imply knowledge lossy math.it problems proliferation