[HGI-News] HGI-Seminar, Donnerstag 8.6.06: Delaying and Merging Operations in Scalar Multiplication

[Newsletter des Horst Görtz Instituts]

                  Prof. Dr. Roberto Avanzi, CITS, RUB

              Donnerstag 8. Juni 2006, 13:15 Uhr IC 4 / 39-41

        Delaying and Merging Operations in Scalar Multiplication:
                 Applications to Curve-Based Cryptosystems

In this presentation we introduce scalar multiplication algorithms for
several classes of elliptic and hyperelliptic curves using different types
of operations beside the group addition: doubling, halving and Frobenius
operation. The methods are variations on Yao's scalar multiplication
algorithm that allow an intrinsic parallelism of operations to become
apparent.  We can thus merge several group operations and reduce the
number of field operations by means of  Montgomery's trick. The results
are that scalar multiplication on elliptic curves in even characteristic
based on point halving can be improved by about 10% and the performance
of Koblitz curves can be improved by at least 20%.

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