Problem 1 : Fun with Digital Signatures

Scheme 2: Σ(M) = (σ(1 ◦m1), σ(2 ◦m2), . . . , σ(n ◦mn)), where each index i is represented using dlog2(n+ 1)e bits. 3. Choose the smallest n such that d2 log2(n+ 1) + |M | n e ≤ k. (Assume that |M | is small enough and k is large enough to make this is possible.) Then break M up into M = m1 ◦ . . . ◦mn, where each mi is such that |mi| = k − d2log2(n+ 1)e, and mn is padded with 0s as necessary. Scheme 3: Σ(M) = (σ(n ◦ 1 ◦ m1), σ(n ◦ 2 ◦ m2), . . . , σ(n ◦ n ◦ mn)), where each index is represented using dlog2(n+ 1)e bits.