Game on: a performance comparison of interpolation techniques applied to Shamir's secret sharing

Public-key encryption is typically managed through a public key infrastructure. However, it relies on a central control point, the certification authority, which acts as a single point of failure. Recent technological advancements have led to the need for decentralized cryptographic protocols. This paper presents a comprehensive study on enhancing public-key encryption via threshold cryptography and multiparty computation to ensure robust security in decentralized systems. The focus lies in exploring various polynomial
interpolation techniques within Shamir’s secret sharing scheme, particularly addressing the efficiency and practicality of Newton interpolation, fast Fourier transformation (FFT), and advanced versions of Lagrange’s method. Utilizing SageMath for a dedicated testing environment, the research investigates the swiftest interpolation methods for secret recovery, introducing new shares into the system, and evaluating the impact of optimizations on performance. The findings highlight FFT as the most effective interpolation method
in speed and efficiency, albeit with limitations on the number of shares that can be processed. This paper critically evaluates these interpolation techniques against practical constraints and aims to answer pivotal research questions regarding the optimal approach for large-scale scenarios, challenging existing notions on the efficiency of Newton’s method and providing experimental evidence to support the superiority of FFT in specific contexts.