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A much better way to choose r is while 1: s = random.getrandbits(KEYSIZE+privacyparameter) r = 1+(s%(n-1)) if gcd(r,n) == 1: break; . privacyparameter is chosen by the blinder. If $\:$ gcd(m,n) = 1 $\:$ then the statistical distance between the distribution of blinded_token and the uniform distribution on units mod n is less $\:$ ...