Construction from QR assumption Clause Samples

Construction from QR assumption. Consider the Cocks crypto-system, we are going to tweak it so it will construct an IBE crypto-system. The public parameters are going to be: pp = N and msk = (p, q). Note that using the master-secret-key, we can evaluate the square root of an element (We check if it is a square modulo p and modulo q, if it is then it is also square modulo N). We would like to have a random oracle: O : {0, 1}∗ → QR . But we don’t really know how (even heuristic) to O { } → O satisfy the operation of . Meaning that we don’t know how to generate element QRN without knowing the square root. But one thing we can do is to have : 0, 1 ∗ JN . But this is not good enough for the Cocks encryption scheme. So how can we solve it? — We know that in the case of ▇▇▇▇ Integer, that every number with ▇▇▇▇▇▇ Symbol 1 is of the form ( 1)b x2. We are going to use this fact. So, how is this crypto-system going to work? • Setup