1. Consider a variant of one-time pad where we avoid choosing the all-zeroes key. The mod- ified KeyGen algorithm can be written as: KeyGen: do kr {0,1}^ until k + 01 return k - Hence k is uniformly distributed over the set of all nonzero strings of length 1. The Enc and Dec algorithms are the same as normal one-time pad. Formally show that this new encryption scheme does not satisfy one-time secrecy. Explic- itly state the libraries that are relevant for this problem; write a calling program; derive the relevant output probabilities