Advanced Math 6) Solve the following problem (Hint: Try to use a variation of Diffie-Hellman Exchange) Given: We pick a big prime p and a generator g. - Andy has a secret a E Z/(p – 1)Z. - Boyle has a secret b E Z/(p – 1)Z. - Andy sends g^a to Boyle. Boyle sends g^b to Andy. Solve: (a) Show that a key is indeed exchanged; that is, Andy and Boyle can both compute g - a - b (mod p). (b) Show that this key-exchange is very bad compared to Diffie-Hellman.

Algebra & Trigonometry with Analytic Geometry
13th Edition
ISBN:9781133382119
Author:Swokowski
Publisher:Swokowski
Chapter10: Sequences, Series, And Probability
Section10.5: The Binomial Theorem
Problem 16E
Question
4
Advanced Math
6) Solve the following problem (Hint: Try to use a
variation of Diffie-Hellman Exchange)
Given:
- We pick a big prime p and a generator g.
- Andy has a secret a E Z/(p – 1)Z.
Boyle has a secret b E Z/(p – 1)Z.
- Andy sends g^a to Boyle. Boyle sends g^b to
Andy.
Solve:
(a) Show that a key is indeed exchanged; that is,
Andy and Boyle can both compute g - a – b (mod
p).
(b) Show that this key-exchange is very bad
compared to Diffie-Hellman.
Transcribed Image Text:Advanced Math 6) Solve the following problem (Hint: Try to use a variation of Diffie-Hellman Exchange) Given: - We pick a big prime p and a generator g. - Andy has a secret a E Z/(p – 1)Z. Boyle has a secret b E Z/(p – 1)Z. - Andy sends g^a to Boyle. Boyle sends g^b to Andy. Solve: (a) Show that a key is indeed exchanged; that is, Andy and Boyle can both compute g - a – b (mod p). (b) Show that this key-exchange is very bad compared to Diffie-Hellman.
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