ApproximateSecret Sharing in Field of Real Numbers

TL;DR

This paper introduces a new method to securely share secrets using real numbers, improving precision and security for different types of numerical data.

Contribution

The novel approach optimizes Shamir’s Secret Sharing for real numbers by introducing type-specific coding and random bit injection.

Findings

The proposed algorithm achieves lossless transmission for rational and special/common irrationals.

Low-loss recovery is enabled for general irrationals using Bernoulli-distributed random bits.

Experiments confirm the method's effectiveness in balancing precision and security for various real-number types.

Abstract

In the era of big data, the security of information encryption systems has garnered extensive attention, particularly in critical domains such as financial transactions and medical data management. While traditional Shamir’s Secret Sharing (SSS) ensures secure integer sharing through threshold cryptography, it exhibits inherent limitations when applied to floating-point domains and high-precision numerical scenarios. To address these issues, this paper proposes an innovative algorithm to optimize SSS via type-specific coding for real numbers. By categorizing real numbers into four types—rational numbers, special irrationals, common irrationals, and general irrationals—our approach achieves lossless transmission for rational numbers, special irrationals, and common irrationals, while enabling low-loss recovery for general irrationals. The scheme leverages a type-coding system to embed data category identifiers in polynomial coefficients, combined with Bernoulli-distributed random bit injection to enhance security. The experimental results validate its effectiveness in balancing precision and security across various real-number types.

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