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1. In the Diffie-Hellman key exchange protocol, Alice and Bob choose a large prime p and a primitive root g for p. As usual, Alice sends A = g" (mod p) to Bob, and Bob sends B = g* (mod p) to Alice. Suppose Oscar bribes Bob to tell him the values of p, b and B. Bob soon regrets it and doesn't tell him the value of g. Show how Oscar can determine g from his knowledge of p, b and B, provided that gcd(b, p – 1) = 1. Hint: Obviously, Oscar attended all Cryptography classes, and therefore knows a little about Fermat.

1. In the Diffie-Hellman key exchange protocol, Alice and Bob choose a large prime p and a primitive root g for p. As usual, Alice sends A = g" (mod p) to Bob, and Bob sends B = g* (mod p) to Alice. Suppose Oscar bribes Bob to tell him the values of p, b and B. Bob soon regrets it and doesn't tell him the value of g. Show how Oscar can determine g from his knowledge of p, b and B, provided that gcd(b, p – 1) = 1. Hint: Obviously, Oscar attended all Cryptography classes, and therefore knows a little about Fermat.

Advanced Engineering Mathematics
Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
Problem 1RQ
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1. In the Diffie-Hellman key exchange protocol, Alice and Bob choose a large prime p and a primitive root g for p. As usual, Alice sends A = g* (mod p) to Bob, and Bob sends B = g* (mod p) to Alice. Suppose Oscar bribes Bob to tell him the values of p, b and B. Bob soon regrets it and doesn't tell him the value of g. Show how Oscar can determine g from his knowledge of p, b and B, provided that ged(b, p – 1) = 1. Hint: Obviously, Oscar attended all Cryptography classes, and therefore knows a little about Fermat.
Transcribed Image Text:1. In the Diffie-Hellman key exchange protocol, Alice and Bob choose a large prime p and a primitive root g for p. As usual, Alice sends A = g* (mod p) to Bob, and Bob sends B = g* (mod p) to Alice. Suppose Oscar bribes Bob to tell him the values of p, b and B. Bob soon regrets it and doesn't tell him the value of g. Show how Oscar can determine g from his knowledge of p, b and B, provided that ged(b, p – 1) = 1. Hint: Obviously, Oscar attended all Cryptography classes, and therefore knows a little about Fermat.
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