Question

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^a (mod p) to Bob, and Bob sends B ? g^b (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.

Uploaded: 2022-08-12T06:54:36-08:00
Duration: 5 min 57 s
Channel: Adi S

          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^a (mod p) to Bob, and Bob sends B ? g^b (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^a (mod p) to Bob, and Bob sends B ? g^b (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.

Added by Whitney K.

Calculus: Early Transcendentals

James Stewart 8th Edition

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08/12/2022

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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^a (mod p) to Bob, and Bob sends B ≡ g^b (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.