On the Security of the ElGamal-Type Signature Scheme with Small Parameters

Hidenori KUWAKADO  Hatsukazu TANAKA  

IEICE TRANSACTIONS on Fundamentals of Electronics, Communications and Computer Sciences   Vol.E82-A   No.1   pp.93-97
Publication Date: 1999/01/25
Online ISSN: 
Print ISSN: 0916-8508
Type of Manuscript: Special Section PAPER (Special Section on Cryptography and Information Security)
digital signature,  continued fraction,  ElGamal signature,  DSA,  

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The security of the ElGamal-type signature scheme is based on the difficulty of solving a discrete logarithm problem. If a random value that is introduced in the signing procedure is small, then the time for generating signature can be reduced. This strategy is particularly advantageous when a signer uses a smart card. In this paper, we show that the secret key can be computed efficiently if the random value is less than O(q) where q is the order of the generator.