TESTING THE «ARITHMETIZATION» SOFTWARE MODEL OF THE  ZK-STARK PROTOCOL

Oleg Averkov

doi:10.36074/grail-of-science.15.05.2026.115

TESTING THE «ARITHMETIZATION» SOFTWARE MODEL OF THE ZK-STARK PROTOCOL

Authors

Oleg Averkov V. N. Karazin Kharkiv National University, Ukraine https://orcid.org/0000-0002-1169-9393

DOI:

https://doi.org/10.36074/grail-of-science.15.05.2026.115

Keywords:

ZK-STARK, Arithmetization, software model, testing, interpolation, efficiency

Summary

This article presents testing results of a software model of the first stage of the ZK-STARK zero-knowledge cryptographic protocol, namely the “Arithmetization” stage. Using a specific computational problem, the study investigates how the execution time of the “Arithmetization” software model depends on the number of input Fibonacci numbers and the selected interpolation method. Three interpolation methods are compared: the inverse matrix method, Gaussian elimination, and the inverse Fast Fourier Transform. The testing results show that the efficiency of the “Arithmetization” stage is determined by the time complexity of the interpolation method used. Recommendations are formulated regarding the most efficient software model and its optimization through the improvement of the software implementation and the use of specialized computer algebra tools.

Downloads

PDF

Downloads

Download data is not yet available.

License

References

StarkWare. (2019, March 14). Arithmetization II: “We need to go deeper”. Medium. https://medium.com/starkware/arithmetization-ii-403c3b3f4355

StarkWare. (2019, February 20). Arithmetization I. Medium. https://medium.com/starkware/arithmetization-i-15c046390862

Massachusetts Institute of Technology. (n.d.). Big O notation. MIT 16.070 Introduction to Computers and Programming. https://web.mit.edu/16.070/www/lecture/big_o.pdf

StarkWare. (2019, February 5). STARK math: The journey begins. Medium. https://medium.com/starkware/stark-math-the-journey-begins-51bd2b063c71

Кравченко, П., Скрябін, Б. & Дубініна, О. (2019). Блокчейн і децентралізовані системи: Навчальний посібник для студентів закладів вищої освіти: У 3 частинах. Ч. 1. ПРОМАРТ.

Lantz, L., & Cawrey, D. (2021). Mastering blockchain: Unlocking the power of cryptocurrencies and smart contracts. O’Reilly Media.

Singhal, B., Dhameja, G., & Panda, P. S. (2018). Beginning blockchain: A beginner’s guide to building blockchain solutions. Apress. DOI: https://doi.org/10.1007/978-1-4842-3444-0

StarkWare. (n.d.). STARK math – A very short primer. STARKWARE. https://starkware.co/stark-math-a-very-short-primer/

KuCoin. (2025, October 14). Top Ethereum ZK Rollup Projects for 2025. KuCoin Learn. https://www.kucoin.com/ru/learn/crypto/top-ethereum-zk-rollup-projects

Bosma, W., Cannon, J., & Playoust, C. (1997). The Magma algebra system I: The user language. Journal of Symbolic Computation, 24(3–4), 235–265. https://doi.org/10.1006/jsco.1996.0125 DOI: https://doi.org/10.1006/jsco.1996.0125

Magma Computational Algebra Group. (2025, November 28). Finite fields. Magma handbook. https://magma.maths.usyd.edu.au/magma/handbook/text/209#1779.