15 - Diffie Hellman Introduction Cryptography and Protocols...

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Introduction Diffie – Hellman Cryptography and Protocols Andrei Bulatov
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Cryptography and Protocols – Diffie – Hellman 15-2 Key Exchange Using public key cryptography is expensive. A better way is to use in it limited amount to generate a key for a private key cryptosystem If p is prime then there is a primitive root modulo p, that is a number g such that Diffie – Hellman protocol: - Alice chooses a prime q and finds a primitive root g - Alice chooses a random X from {1, …, q – 2} and sends p, q and to Bob - Bob chooses random Y from {1, …, q – 2} and sends to Alice - Alice and Bob compute (by computing and respectively. They use k as a private key } , , , , { } 1 , , 2 , 1 { 1 3 2 - = - p g g g g p K K ) (mod ˆ q g X X ) (mod ˆ q g Y Y ) (mod q g k XY X Y ˆ Y X ˆ
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Cryptography and Protocols – Diffie – Hellman 15-3 Diffie – Hellman Protocol Alice Bob * p X Z * p Y Z X g Y g X Y g k ) ( = Y X g k ) ( =
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15 - Diffie Hellman Introduction Cryptography and Protocols...

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