Journal of Cryptographic Engineering

, Volume 9, Issue 1, pp 1–19 | Cite as

Constructing multidimensional differential addition chains and their applications

  • Aaron Hutchinson
  • Koray KarabinaEmail author
Regular Paper


We propose new algorithms for constructing multidimensional differential addition chains and for performing multidimensional scalar point multiplication based on these chains. Our algorithms work in any dimension and offer some key efficiency and security features. In particular, our scalar point multiplication algorithm is uniform, it can be parallelized, and differential addition formulas can be deployed. It also allows trading speed for precomputation cost and storage requirements. These key features and our theoretical estimates indicate that this new algorithm may offer some performance advantages over the existing point multiplication algorithms in practice. We also report some experimental results and verify some of our theoretical findings, and a simplistic Magma implementation is provided.


Differential addition chains Side-channel resistance Elliptic curves Scalar multiplication Cryptographic algorithms 

Mathematics Subject Classification

94A60 14G50 



The authors would like to thank reviewers for their comments and corrections. Research reported in this paper was supported by the Army Research Office under award number W911NF-17-1-0311. The content is solely the responsibility of the authors and does not necessarily represent the official views of the Army Research Office.


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Copyright information

© Springer-Verlag GmbH Germany 2017

Authors and Affiliations

  1. 1.Florida Atlantic UniversityBoca RatonUSA

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