Fast Multi-computations with Integer Similarity Strategy

Multi-computations in finite groups, such as multiexponentiations and multi-scalar multiplications, are very important in ElGamallike public key cryptosystems. Algorithms to improve multi-computations can be classified into two main categories: precomputing methods and recoding methods. The first one uses a table to store the precomputed values, and the second one finds a better binary signed-digit (BSD) representation. In this article, we propose a new integer similarity strategy for multi-computations. The proposed strategy can aid with precomputing methods or recoding methods to further improve the performance of multi-computations. Based on the integer similarity strategy, we propose two efficient algorithms to improve the performance for BSD sparse forms. The performance factor can be improved from 1.556 to 1.444 and to 1.407, respectively.