Efficient Scalar Multiplication of ECC Using Lookup Table and Fast Repeating Point Doubling

• DOI: 10.3390/math13060924
• Publication Date: 2025-03-11T14:53:07Z
• Authors: Fu-Jung Kan; Yan-Haw Chen; Jeng-Jung Wang; Chong-Dao Lee
• Keywords: Lookup table; Scalar multiplication; Table (database)

Reducing the computation time of scalar multiplication for elliptic curve cryptography is a significant challenge. This study proposes an efficient method curves over finite fields GF(2m). The proposed first converts into binary number. Then, using Horner’s rule, number divided fixed-length bit-words. Each bit-word undergoes repeating point doubling, which can be precomputed. However, doubling typically involves numerous inverse operations. To address this, effort has been made to develop formulas that minimize With formula, regardless how many times operation repeated, only single required. Over GF(2m), outperforms sliding window method, currently regarded as fastest available. introduced require more multiplications, squares, and additions. reduce these operations, we further optimize square operations; however, this introduces trade-off between memory size. These challenges are key areas future improvement.