M-ary Precomputation-Based Accelerated Scalar Multiplication Algorithms for Enhanced Elliptic Curve Cryptography
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arXiv
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| Main Authors: | , , , , , |
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| Format: | Preprint |
| Published: |
2025
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| _version_ | 1866918008399593472 |
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| author | Wu, Tongxi Liu, Xufeng Yang, Jin Zhu, Yijie Zeng, Shunyang Zhan, Mingming |
| author_facet | Wu, Tongxi Liu, Xufeng Yang, Jin Zhu, Yijie Zeng, Shunyang Zhan, Mingming |
| contents | Efficient scalar multiplication is critical for enhancing the performance of elliptic curve cryptography (ECC), especially in applications requiring large-scale or real-time cryptographic operations. This paper proposes an M-ary precomputation-based scalar multiplication algorithm, aiming to optimize both computational efficiency and memory usage. The method reduces the time complexity from $Θ(Q \log p)$ to $Θ\left(\frac{Q \log p}{\log Q}\right)$ and achieves a memory complexity of $Θ\left(\frac{Q \log p}{\log^2 Q}\right)$. Experiments on ElGamal encryption and NS3-based communication simulations validate its effectiveness. On secp256k1, the proposed method achieves up to a 59\% reduction in encryption time and 30\% memory savings. In network simulations, the binary-optimized variant reduces communication time by 22.1\% on secp384r1 and simulation time by 25.4\% on secp521r1. The results demonstrate the scalability, efficiency, and practical applicability of the proposed algorithm. The source code will be publicly released upon acceptance. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2505_01845 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | M-ary Precomputation-Based Accelerated Scalar Multiplication Algorithms for Enhanced Elliptic Curve Cryptography Wu, Tongxi Liu, Xufeng Yang, Jin Zhu, Yijie Zeng, Shunyang Zhan, Mingming Cryptography and Security Efficient scalar multiplication is critical for enhancing the performance of elliptic curve cryptography (ECC), especially in applications requiring large-scale or real-time cryptographic operations. This paper proposes an M-ary precomputation-based scalar multiplication algorithm, aiming to optimize both computational efficiency and memory usage. The method reduces the time complexity from $Θ(Q \log p)$ to $Θ\left(\frac{Q \log p}{\log Q}\right)$ and achieves a memory complexity of $Θ\left(\frac{Q \log p}{\log^2 Q}\right)$. Experiments on ElGamal encryption and NS3-based communication simulations validate its effectiveness. On secp256k1, the proposed method achieves up to a 59\% reduction in encryption time and 30\% memory savings. In network simulations, the binary-optimized variant reduces communication time by 22.1\% on secp384r1 and simulation time by 25.4\% on secp521r1. The results demonstrate the scalability, efficiency, and practical applicability of the proposed algorithm. The source code will be publicly released upon acceptance. |
| title | M-ary Precomputation-Based Accelerated Scalar Multiplication Algorithms for Enhanced Elliptic Curve Cryptography |
| topic | Cryptography and Security |
| url | https://arxiv.org/abs/2505.01845 |