Method for exponentiation in a public-key cryptosystem
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United States of America Patent
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Dec 7, 1999
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Jan 7, 1998
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Jan 7, 1995
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Abstract
The present invention relates to an improved method for performing modular exponentiation to a fixed base element. The method includes exponentiating a first digital input signal g by a second digital input signal R, where g is a fixed signal unique to a cryptographic system and R is a randomly generated digital signal, to compute a third digital signal g.sup.R. The exponentiating includes pre-computing and storing a plurality of values depending only upon the fixed signal g in a plurality of memory locations within a computing device and then speeding up the computation of g.sup.R using the stored values. The invented exponentiation method can substantially reduce the amount of computation required to compute the value for g.sup.R. Exponentiation methods according to embodiments of the present invention may be used in a variety of cryptographic systems, e.g., Schnorr identification scheme, Digital Signature Standard (DSS), and Diffie-Hellman key agreement scheme, etc.
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