Side-Channel Attacks in ECC: A General Technique for Varying the Parametrization of the Elliptic Curve

  • Loren D. Olson
Part of the Lecture Notes in Computer Science book series (LNCS, volume 3156)


Side-channel attacks in elliptic curve cryptography occur with the unintentional leakage of information during processing. A critical operation is that of computing nP where n is a positive integer and P is a point on the elliptic curve E. Implementations of the binary algorithm may reveal whether P+Q is computed for \(P\ne Q\) or P=Q as the case may be. Several methods of dealing with this problem have been suggested. Here we describe a general technique for producing a large number of different representations of the points on E in characteristic p≥ 5, all having a uniform implementation of P+Q. The parametrization may be changed for each computation of nP at essentially no cost. It is applicable to all elliptic curves in characteristic p≥ 5, and thus may be used with all curves included in present and future standards for p≥ 5.


Elliptic curves ECC cryptography side-channel attacks weighted projective curves uniform addition formula 


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Copyright information

© Springer-Verlag Berlin Heidelberg 2004

Authors and Affiliations

  • Loren D. Olson
    • 1
  1. 1.Dept. of Mathematics and StatisticsUniversity of TromsøTromsøNorway

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