Jonathan Ku, Guanglei Zhou, Jiawen Wu, Junyao Zhang, Haoxuan Shan, Changchun Zhou, JV Rajendran, Yiran Chen · 2026 · arXiv
DOI: 10.48550/arXiv.2610.27452 · open-access PDF
Multi-Scalar Multiplication (MSM) は、広範囲のアプリケーションでエリプト曲線暗号化(ECC)で使用される基本的な暗号化操作です。その計算には、強力なエリプト曲線ポイント追加(PADD)が含まれます。 MSM は、ポリノミアルゴリズムの約束やゼロ知識の証明(ZKPs)などの暗号化原理に重要な役割を果たし、しばしばランタイムのボトルネックになります。したがって、最適化 MSM は、計算の複雑さを減らし、パフォーマンスを加速させることに焦点を当てた研究のアクティブな領域です。大規模な MSM の現在の最先端アルゴリズムは Pippenger です。
Machine translation (Meta M2M100); the English original follows.
Multi-Scalar Multiplication (MSM) is a fundamental cryptographic operation used in Elliptic Curve Cryptography (ECC) across a wide range of applications. Its computation involves intensive elliptic curve point additions (PADD). MSM plays a critical role in cryptographic primitives such as polynomial commitments and zero-knowledge proofs (ZKPs), where it often becomes the runtime bottleneck. Consequently, optimizing MSM is an active area of research focused on reducing computational complexity and accelerating performance. The current state-of-the-art algorithm for large-scale MSM is Pippenger'
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