The secure judgment of graphic similarity against malicious adversaries and its applications

Input: Alice owns a graphic \(O\) and Bob owns a graphic \(P\)

Output: \(P(O,P) = \left\{ {\begin{array}{*{20}l} 0, & {O\;and\;P\;are\;\, isomorphism}\\ 1, & {O\;and\;P\;are\;not\;isomorphism}\end{array} } \right.\)

Preparation: Alice generates public key \(n\) and private key \(\lambda\). Alice constructs a vector according to the above method to obtain \(Z_{1} = {(}a_{1} ,a_{2} ,…,a_{{m_{a} }} {)}\). At the same time, Bob constructs vectors to obtain \(Z_{2} = (b_{1} ,b_{2} ,…,b_{{m_{b} }} )\) and \(Z^{\prime}_{2} = (b^{\prime}_{1} ,b^{\prime}_{2} ,…,b^{\prime}_{{m_{b} }}…