Jonathan Ku, Guanglei Zhou, Jiawen Wu, Junyao Zhang, Haoxuan Shan, Changchun Zhou, JV Rajendran, Yiran Chen, Hai Li · 2026 · arXiv (Cornell University)
DOI: 10.48550/arxiv.2610.27452 · cited by 0 works (OpenAlex) · open-access PDF
Este sistema de multiplicación multi-bucket (MSM) es una operación criptográfica fundamental utilizada en criptografía de curva elíptica (ECC) a través de una amplia gama de aplicaciones. Su cálculo involucra intensivas adiciones de puntos de curva elíptica (PADD). MSM desempeña un papel crítico en los primitivos criptográficos actuales como los compromisos de ejecución polinómicos a gran escala y las pruebas de bucket cero (ZKPs), donde a menudo se convierte en el botón de ejecución de tres pasos principales: fusión de puntos, agregación de buckets y agregación de ventanas. En consecuencia, la optimización de MSM es una área activa de investigación centrada en reducir la complejidad computacional y acelerar el rendimiento. El actual algoritmo de botón de
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's bucket method, which consists of three main steps: point merging, bucket aggregation, and window aggregation. Among these, the point merging step is the primary performance bottleneck. Our work targets this major computational bottleneck. To reduce operations for practical applications, we propose a novel Scalar Redundancy Elimination (SRE) algorithm with three approaches: a vanilla array-based approach, a list-based greedy approach, and a list-based exhaustive approach, all incorporating an early stopping technique. Depending on the use case, these strategies can be integrated into our modified MSM algorithm, which is based on Pippenger's bucket method. As a result, our proposed MSM algorithm, enhanced with the SRE technique, incurs less than $3\%$ additional search time, while reducing the number of operations by $25\%$, leading to a $30\%$ speedup in runtime compared to the standard Pippenger's bucket method. This translates to a $10 \sim 20\%$ runtime reduction in various ZKP systems that rely heavily on MSM.
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Topics: Scalar multiplication, Redundancy (engineering), Computer science, Mathematical proof, Cryptography, Speedup
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