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In this work, an integer linear programming (ILP) based model is proposed forthe computation of a minimal cost addition sequence for a given set ofintegers. Since exponents are additive under multiplication, the minimal lengthaddition sequence will provide an economical solution for the evaluation of arequested set of power terms. This is turn, finds application in, e.g.,window-based exponentiation for cryptography and polynomial evaluation. Notonly is an optimal model proposed, the model is extended to consider differentcosts for multipliers and squarers as well as controlling the depth of theresulting addition sequence.

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