Universite Bordeaux 1
Verifiability is central to building protocols and systems with integrity. Initially, efficient methods employed the fiat-shamir heuristics. Since 2008, the groth-sahai techniques have been the most efficient in constructing non-interactive witness indistinguishable and zero-knowledge proofs for algebraic relations. For the important task of proving membership in linear subspaces, the researchers (Asiacrypt 2013) gave significantly more efficient proofs in the Quasi-Adaptive setting (QA-NIZK). For membership of the row space of a txn matrix, their QA-NIZK proofs save O(2t) group elements compared to groth-sahai.