1. (10 points) Consider the SHA-3 options with a block size of 1024 bits and assume that each of the lanes in the first message block (P0) has at least one nonzero bit. To start, all of the lanes in the internal state matrix that correspond to the capacity portion of the initial state are all zeros. Show how long it will take before all of these lanes have at least one nonzero bit. Note: Ignore the permutation. That is, keep track of the original zero lanes even after they have changed position in the matrix. (a) State variable as 55 matrix A of 64 bit words Table 11.6 Step Functions in SHA-3 (a) step function (b) Rotation values by word position in matrix