ApproximateSecret Sharing in Field of Real Numbers

Area of Science:

• Cryptography and Information Security
• Big Data Analytics
• Numerical Analysis

Background:

• Traditional Shamir's Secret Sharing (SSS) is limited in handling floating-point and high-precision real numbers.
• Big data necessitates robust encryption for sensitive financial and medical information.
• Existing methods struggle with the complexities of real-number domains in secret sharing.

Purpose of the Study:

• To propose an optimized Shamir's Secret Sharing (SSS) algorithm for real numbers.
• To address the limitations of traditional SSS in floating-point and high-precision scenarios.
• To enhance the security and precision of secret sharing for diverse real-number types.

Main Methods:

• Developed a type-specific coding algorithm for categorizing real numbers (rational, special irrational, common irrational, general irrational).
• Implemented lossless transmission for rational and some irrational numbers, and low-loss recovery for general irrationals.
• Integrated a type-coding system into polynomial coefficients and employed Bernoulli-distributed random bit injection for enhanced security.

Main Results:

• The proposed algorithm achieves lossless transmission for rational, special irrational, and common irrational numbers.
• Low-loss recovery is demonstrated for general irrationals, maintaining data integrity.
• Experimental validation confirms the algorithm's effectiveness in balancing precision and security across different real-number types.

Conclusions:

• The novel SSS optimization effectively handles real numbers, overcoming limitations of traditional integer-based schemes.
• This approach offers a more versatile and secure solution for big data encryption in critical applications.
• The type-specific coding and random bit injection provide a robust framework for real-number secret sharing.