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.

翻译：本文提出一种基于整数线性规划（ILP）的模型，用于计算给定整数集合的最小成本加法序列。由于指数在乘法下具有可加性，最小长度加法序列可为需求幂项集合的求值提供经济高效的解决方案。该方案可应用于密码学中基于窗口的指数运算及多项式求值等领域。本文不仅提出了最优模型，还将模型扩展至考虑乘法器与平方器的不同成本，并控制生成加法序列的深度。