Alice wants to use the El Gamal Signature Scheme. She chooses an initial value (randomly) k_0. She then uses the value k_i to sign the ith message, where k_i = k_0 + 2i mod (p-1). (Therefore, k_i = k_{i-1} + 2 mod (p – 1) forall i >= 1).

a) Spoz Bob sees 2 consecutive signed messages: (x_i, sig(x_i, k_i)) and (x_{i+1}, sig(x_{i+1}, k_{i+1})). Show how Bob can compute Alice’s secret key, a, without solving the Discrete Log problem. (Note that i doesn’t have to be known for this attack to succeed).

b) Spoz the parameters of this scheme are p = 28703, alpha = 5 and beta = 11339, and the 2 messages Bob sees are: x_i = 12000 : sig(x_i, k_i) = (26530, 19862) and x_{i+1} = 24567 : sig(x_{i+1}, k_{i+1}) = (3081, 7604). Fidn the value of a using the attack described in part a.