Knowledge Of Exponent (KOE)¶
Given points \(P\) and \(Q\) with \(P . k = Q\) (\(k\) is an unknown variable), and another point \(C\), it is impossible to determine \(C.k\) unless \(C\) is “derived” from \(P\) in a previously known or acknowledged relationship.
Consider a scenario where a pair of points \((P,Q)\) is provided, and \(P.k=Q\), where the value of \(k\) is unknown. Now, suppose we have another pair \((R,S)\) with \(R.k=S\). The knowledge of exponent assumption implies that the only way to generate the pair \((R,S)\) is by taking \(P\) and \(Q\), and multiplying both by some factor \(r\).