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Diffie–Hellman Day

The 6th November 1976 seminal paper of Whitfield Diffie and Martin Hellman which was p “New Directions in Cryptography”, is a landmark in the history of cryptography. They introduced the fundamental concepts of a trapdoor one-way function, a public-key cryptosystem, and a digital signature scheme. Also, they presented a protocol, the so-called Diffie–Hellman protocol, allowing two parties who share no secret information initially, to generate a mutual secret key.

Diffie-Hellman is mostly used to protect the exchange of keys used to create a connection using symmetric encryption.

The Diffie–Hellman key exchange method allows two parties that have no prior knowledge of each other to jointly set up a shared secret key over an insecure channel. This key can be used to encrypt subsequent communications using a symmetric key cipher.

According to Diffie–Hellman attempts to solve the chicken-or-egg problem in cryptography: for Alice and Bob to communicate securely over a public channel such as the Internet they need to share a common encryption key. But for them to agree on such a key they need to be able to communicate securely over a public channel.

In the first step, Alice and Bob both choose a (large) random number, which they both keep secret. Let’s call Alice’s number a and Bob’s number b. Now using a ‘mechanism’ (more on which later) that is part of the protocol, Alice uses a to compute a second number, which is denoted ga. Bob uses the same mechanism to compute a number gb. Alice and Bob then share ga and gb with each other, over a public channel. So we are now in the following situation:

Alice knows a, ga and gb;                           Bob knows b, ga and gb;

Anyone being able to read their communication only knows ga and gb.

Now using the same mechanism as before, Alice uses her secret number a and the number gb, which Bob sent her, to create a new number (gb)a. Bob, likewise, uses b and ga to create a number (ga)b. Because maths can be kind like that, (gb)a and (ga)b are in fact the same number. This is the shared key they will use.

The reason this works is that, while it is easy for Alice to use a to compute ga, it is impossible for someone who only knows ga to compute a — and the same of course also holds for b and gb. It is also impossible to compute the shared secret key using only ga and gb.

This is useful because you can use this technique to create an encryption key with someone, and then start encrypting your traffic with that key. And even if the traffic is recorded and later analyzed, there’s absolutely no way to figure out what the key was, even the exchanges that created it may have been visible. This is where perfect forward secrecy comes from. Nobody analyzing the traffic at a later date can break in because the key was never saved, never transmitted, and never made visible anywhere. 

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