Polynomial Commitment in a Verkle Tree Based on a Non-Positional Polynomial Notation
Algazy K.T. Sakan K.S. Nyssanbayeva S.E. Khompysh A.
2025Tech Science Press
Computers, Materials and Continua
2025#84Issue 11581 - 1595 pp.
This paper examines the application of the Verkle tree—an efficient data structure that leverages commitments and a novel proof technique in cryptographic solutions. Unlike traditional Merkle trees, the Verkle tree significantly reduces signature size by utilizing polynomial and vector commitments. Compact proofs also accelerate the verification process, reducing computational overhead, which makes Verkle trees particularly useful. The study proposes a new approach based on a non-positional polynomial notation (NPN) employing the Chinese Remainder Theorem (CRT). CRT enables efficient data representation and verification by decomposing data into smaller, independent components, simplifying computations, reducing overhead, and enhancing scalability. This technique facilitates parallel data processing, which is especially advantageous in cryptographic applications such as commitment and proof construction in Verkle trees, as well as in systems with constrained computational resources. Theoretical foundations of the approach, its advantages, and practical implementation aspects are explored, including resistance to potential attacks, application domains, and a comparative analysis with existing methods based on well-known parameters and characteristics. An analysis of potential attacks and vulnerabilities, including greatest common divisor (GCD) attacks, approximate multiple attacks (LLL lattice-based), brute-force search for irreducible polynomials, and the estimation of their total number, indicates that no vulnerabilities have been identified in the proposed method thus far. Furthermore, the study demonstrates that integrating CRT with Verkle trees ensures high scalability, making this approach promising for blockchain systems and other distributed systems requiring compact and efficient proofs. Copyright
Chinese remainder theorem , non-positional polynomial notation (NPN) , Verkle tree , Verkle tree commitment and proof
Text of the article Перейти на текст статьи
Information Security Laboratory, Institute of Information and Computational Technologies, Almaty, 050010, Kazakhstan
Faculty of Information Technology, Al-Farabi Kazakh National University, Almaty, 050040, Kazakhstan
Faculty of Languages and Humanities, Nur-Mubarak University, Almaty, 050040, Kazakhstan
Information Security Laboratory
Faculty of Information Technology
Faculty of Languages and Humanities
10 лет помогаем публиковать статьи Международный издатель
Книга Публикация научной статьи Волощук 2026 Book Publication of a scientific article 2026