d-MUL - Optimizing and Implementing a Multidimensional Scalar Multiplication Algorithm over Elliptic Curves.

This paper aims to answer whether d-MUL, the multidimensional scalar point multiplication algorithm, can be implemented efficiently. d-MUL is known to access costly matrix operations and requires memory access frequently. In the first part of the paper, we derive several theoretical results on the structure and the construction of the addition chains in d-MUL. These results are interesting on their own right. In the second part of the paper, we exploit our theoretical results, and propose an optimized variant of d-MUL. Our implementation results show that d-MUL can be very practical for small d, and it remains as an interesting algorithm to further explore for parallel implementation and cryptographic applications.