DiffieHellman key exchange using addition Consider the Diffi

Diffie-Hellman key exchange using addition Consider the Diffie-Hellman key exchange (DHKE) protocol using the additive finite group (Z_p, +) of prime order p (yes, every element except the identity element are generators, isn\'t that nice?!). The group operation f(a, b) = a b is modular addition computed, i.e. a b = a + b mod p. (a) What is the identity element? How can h = g^i be computed, where i Z_p? (b) Show that both parties output the same key when performing the DHKE using (Z_p, +). (c) Analyze the security of the scheme when using (Z_p, +). Show a concrete attack and argue conceptually why it is insecure.

Solution

I can\'t offer a closed form for the sum, but it\'s clear that the average cost peaks at powers of two with successive such peak values asymptoti