Paper 2004/306

The Static Diffie-Hellman Problem

Daniel R. L. Brown and Robert P. Gallant


The static Diffie-Hellman problem (SDHP) is the special case of the classic Diffie-Hellman problem where one of the public keys is fixed. We establish that the SDHP is almost as hard as the associated discrete logarithm problem. We do this by giving a reduction that shows that if the SDHP can be solved then the associated private key can be found. The reduction also establishes that certain systems have less security than anticipated. The systems affected are based on static Diffie-Hellman key agreement and do not use a key derivation function. This includes some cryptographic protocols: basic ElGamal encryption; Chaum and van Antwerpen's undeniable signature scheme; and Ford and Kaliski's key retrieval scheme, which is currently being standardized in IEEE P1363.2.

Note: revisions in the interest of clarity

Available format(s)
Public-key cryptography
Publication info
Published elsewhere. Submitted to Eurocrypt 2005 (preliminary version)
Static Diffie-HellmanElGamal EncryptionFord-Kaliski Key RetrievalProvable Security
Contact author(s)
dbrown @ certicom com
2005-06-24: revised
2004-11-16: received
See all versions
Short URL
Creative Commons Attribution


      author = {Daniel R.  L.  Brown and Robert P.  Gallant},
      title = {The Static Diffie-Hellman Problem},
      howpublished = {Cryptology ePrint Archive, Paper 2004/306},
      year = {2004},
      note = {\url{}},
      url = {}
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