Suppose you have a signature scheme S (which is correct and existentially unforgeable), and S can be used to sign any t-bit message. And you have a hash function H which outputs t bits and is...

Suppose you have a signature scheme S (which is correct and existentially unforgeable), and S can be used to sign any t-bit message. And you have a hash function H which outputs t bits and is collision-resistant. Consider a modified signature scheme S’ which can sign messages of unlimited length, where: S’.Sign(sk, m) = S.sign(sk, H(m))

Prove that this scheme is existentially unforgeable as long as S is existentially unforgeable and H is collision-resistant.