Lecture 15 - Zero Knowledge Proofs

An important point is that, although this is not usually stressed, the standardNP -completeness reductions also reduce the solution or witness from one problem to the other. That is, along with the function reduce(·) we also have a function red′ that maps a number w such that w2 = x to a 3-coloring c : V → {R,G,B} of the graph G = reduce(x, n). This can be used for the prover to convert their private input into an input appropriate for the 3COL protocol.