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Computer Science > Discrete Mathematics

arXiv:2306.15002 (cs)
[Submitted on 26 Jun 2023]

Title:Integer Linear Programming Modeling of Addition Sequences With Additional Constraints for Evaluation of Power Terms

Authors:Muhammad Abbas, Oscar Gustafsson
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Abstract:In this work, an integer linear programming (ILP) based model is proposed for the computation of a minimal cost addition sequence for a given set of integers. Since exponents are additive under multiplication, the minimal length addition sequence will provide an economical solution for the evaluation of a requested set of power terms. This is turn, finds application in, e.g., window-based exponentiation for cryptography and polynomial evaluation. Not only is an optimal model proposed, the model is extended to consider different costs for multipliers and squarers as well as controlling the depth of the resulting addition sequence.
Comments: This manuscript was written in 2012, and, hence, lacks more recent references
Subjects: Discrete Mathematics (cs.DM)
Cite as: arXiv:2306.15002 [cs.DM]
  (or arXiv:2306.15002v1 [cs.DM] for this version)
  https://doi.org/10.48550/arXiv.2306.15002

Submission history

From: Oscar Gustafsson [view email]
[v1] Mon, 26 Jun 2023 18:39:40 UTC (18 KB)
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