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The Static Diffie-Hellman Problem
Authors: Daniel R. L. Brown, Robert P. GallantAbstract:
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.
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