Diffie–Hellman key exchange

Diffie–Hellman (DH) key exchange[nb 1] is a mathematical method of securely generating a symmetric cryptographic key over a public channel and was one of the first protocols as conceived by Ralph Merkle and named after Whitfield Diffie and Martin Hellman.[1] DH is one of the earliest practical examples of public key exchange implemented within the field of cryptography. Published in 1976 by Diffie and Hellman, this is the earliest publicly known work that proposed the idea of a private key and a corresponding public key.

Traditionally, secure encrypted communication between two parties required that they first exchange keys by some secure physical means, such as paper key lists transported by a trusted courier. The Diffie–Hellman key exchange method allows two parties that have no prior knowledge of each other to jointly establish a shared secret key over an insecure channel. This key can then be used to encrypt subsequent communications using a symmetric-key cipher.

Diffie–Hellman is used to secure a variety of Internet services. However, research published in October 2015 suggests that the parameters in use for many DH Internet applications at that time are not strong enough to prevent compromise by very well-funded attackers, such as the security services of some countries.[2]

The scheme was published by Whitfield Diffie and Martin Hellman in 1976,[3] but in 1997 it was revealed that James H. Ellis,[4] Clifford Cocks, and Malcolm J. Williamson of GCHQ, the British signals intelligence agency, had previously shown in 1969[5] how public-key cryptography could be achieved.[6]

Although Diffie–Hellman key exchange itself is a non-authenticated key-agreement protocol, it provides the basis for a variety of authenticated protocols, and is used to provide forward secrecy in Transport Layer Security's ephemeral modes (referred to as EDH or DHE depending on the cipher suite).

The method was followed shortly afterwards by RSA, an implementation of public-key cryptography using asymmetric algorithms.

Expired US patent 4200770[7] from 1977 describes the now public-domain algorithm. It credits Hellman, Diffie, and Merkle as inventors.


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  1. ^ Merkle, Ralph C. (April 1978). "Secure Communications Over Insecure Channels". Communications of the ACM. 21 (4): 294–299. CiteSeerX 10.1.1.364.5157. doi:10.1145/359460.359473. S2CID 6967714. Received August, 1975; revised September 1977
  2. ^ Cite error: The named reference imperfectfs was invoked but never defined (see the help page).
  3. ^ Diffie, Whitfield; Hellman, Martin E. (November 1976). "New Directions in Cryptography" (PDF). IEEE Transactions on Information Theory. 22 (6): 644–654. CiteSeerX 10.1.1.37.9720. doi:10.1109/TIT.1976.1055638. Archived (PDF) from the original on 2014-11-29.
  4. ^ Ellis, J. H. (January 1970). "The possibility of Non-Secret digital encryption" (PDF). CESG Research Report. Archived from the original (PDF) on 2014-10-30. Retrieved 2015-08-28.
  5. ^ "The Possibility of Secure Secret Digital Encryption" (PDF). Archived (PDF) from the original on 2017-02-16. Retrieved 2017-07-08.
  6. ^ "GCHQ trio recognised for key to secure shopping online". BBC News. 5 October 2010. Archived from the original on 10 August 2014. Retrieved 5 August 2014.
  7. ^ US patent 4200770 
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