Patent Number:
6,252,959
Title:
Method and system for point multiplication in elliptic curve cryptosystem
Abstract:
A point doubling method for elliptic curve cryptosystems is disclosed in which 2.sup.k P=(X.sub.k, y.sub.k) is directly calculated from P=(x,y) without computing intermediate points such as 2P, 4P, etc. The advantage in this direct calculation technique is that the number of inverses in the underlying field GF(2.sup.k) is reduced. Although this does not come without a price. In most implementations, the number of multiplications is increased. The present invention is based upon the recognition that for most practical applications, the inversion is by far the most expensive operation to perform of the inversion, multiplication, addition, and squaring in the point doubling operations. As a result, the net time to perform the additional multiplications is less than the time required to perform the inversion,the multiplications effectively replace, thereby yielding in the efficiency of the present invention.
Inventors:
Paar; Christof (Northampton, MA), Guajardo; Jorge (Worcester, MA)
Assignee:
Worcester Polytechnic Institute
International Classification:
G06F 7/72 (20060101); G06F 7/60 (20060101); H04L 009/28 (); H04L 009/30 ()
Expiration Date:
06/26/2018