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Let E : y2 = x3 + Ax+ B be an elliptic curve defined over the finite field Zp(p > 3) and G be a rational point of prime order N on E. Define a subset of ZN, the residue class ring modulo N, as S:={n:n ∈ZN,n≠0,(X(pn)/G)=1}, where X(nG) denotes the x-axi