|Ψ0|2 is the proability of seeing state |0> and Ψ12 is the probability of seeing state |1> respectively. Finding period is sufficient to break Discrete logs => Breaks ECDSA => Given public key one can find the private key. For any signing algorithm like RSA and BLS (but not ECDSA) where signature = H(m)Sk, one can commit to a particular Sk and then find split it across signers.