Method for generating and verifying electronic signatures and privacy communication using elliptic curves
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United States of America Patent
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Aug 15, 1995
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app pub date -
Sep 27, 1993
filing date -
Sep 28, 1992
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Abstract
The present invention discloses a method of generating and verifying electronic signatures for signed communication via a public digital network system by using an elliptic curve. The method is characterized by the step of supplying on the network system public data to each of users from a system provider, wherein an element P whose x-coordinate has 0 is chosen, a single parameter is chosen for the elliptic curve E over a finite field and its base point, and a prime number p is chosen such that one of p=2.sup.t +.alpha. and p=2.sup.t -.alpha. where t is a positive integer and .alpha. is a positive integer. Accordingly, fewer parameters can represent the elliptic curve E, base point P, field of definition GF(p), and order of the base point P, and either the x-coordinate or y-coordinate of the base point P have a small value. As a result, the elliptic curve addition kP can be calculated faster for any k.
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