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

TL;DR

This paper introduces an ILP model to find minimal cost addition sequences for computing power terms, optimizing cryptographic and polynomial evaluations by considering various operation costs and sequence depth.

Contribution

It presents a novel ILP-based approach for minimal addition sequence computation with extended constraints for operation costs and depth control.

Findings

Optimal ILP model for addition sequences

Extended model includes cost and depth constraints

Applicable to cryptography and polynomial evaluation

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.