Literature Review Open Access

A Review on Heuristics for Addition Chain Problem: Towards Efficient Public Key Cryptosystems

Adamu Muhammad Noma1, Abdullah Muhammed1, Mohamad Afendee Mohamed2 and Zuriati Ahmad Zulkarnain1
  • 1 Universiti Putra Malaysia, Malaysia
  • 2 Universiti Sultan ZainalAbidin, Malaysia


Field exponentiation and scalar multiplication are the pillars of and the most computationally expensive operations in the public key cryptosystems. Optimizing the operation is the key to the efficiency of the systems. Analogous to the optimization is solving addition chain problem. In this study, we survey from the onset of the addition chain problem to the state-of-the-art heuristics for optimizing it, with the view to identifying fundamental issues that when addressed renders the heuristics most optimal mean of minimizing the two operations in various public key cryptosystems. Thus, our emphasis is specifically on the heuristics: Their various constraints and implementations efficiencies. We present possible ways forwards toward the optimal solution for the addition chain problem that can be efficiently applied for optimal implementation of the public key cryptosystems.

Journal of Computer Science
Volume 13 No. 8, 2017, 275-289


Submitted On: 3 December 2016 Published On: 1 June 2017

How to Cite: Noma, A. M., Muhammed, A., Mohamed, M. A. & Zulkarnain, Z. A. (2017). A Review on Heuristics for Addition Chain Problem: Towards Efficient Public Key Cryptosystems. Journal of Computer Science, 13(8), 275-289.

  • 2 Citations



  • Heuristics
  • Addition Chain Problem
  • Modular Exponentiation
  • Scalar Multiplication
  • Public Key Cryptosystem