Secure Multi-Party Computation Modular Integer Casting
Find Innovative SolutionsGenerate Solutions
Solution Overview
Problem
Existing multi-party computation (MPC) techniques face errors in real number arithmetic due to overflow and underflow issues when using fixed-point integer representations, particularly in machine learning applications, where previous methods have non-zero probabilities of failure and require reduced precision or increased backend size to mitigate these issues.
Innovation Solution
A method is introduced to cast a secret shared value from a first modular representation to a second modular representation with a larger most significant bit, using a trusted dealer to secret share a masking value and a bit encoding its range, allowing parties to reconstruct the secret shared value without revealing the shares, eliminating errors while maintaining efficiency and security.
Engineering Contradictions & Design Principles
Engineering Contradiction Analysis
1Productivity
If fixed-point integer representations are used for real number arithmetic in MPC, then computational efficiency is maintained, but overflow and underflow errors occur with non-zero probability
Solution Approach 1:
The patent transitions from fixed-point integer representation to floating-point representation, changing the dimensional structure of how numbers are encoded. This allows the system to maintain a wide dynamic range while preserving arithmetic correctness, eliminating overflow and underflow errors that plague fixed-point systems in MPC protocols.
Solution Approach 2:
The patent changes the representation parameters from fixed-point (integer-based) to floating-point (exponent-mantissa-based), fundamentally altering how real numbers are encoded in the MPC protocol. This parameter change enables the system to handle both very large and very small numbers without loss of precision or overflow, while maintaining computational efficiency through optimized floating-point arithmetic operations.
2Stability of the object's composition
If precision is reduced to mitigate overflow issues, then arithmetic stability improves, but manufacturing precision of computational results deteriorates
Solution Approach 1:
The patent changes the representation parameters from fixed-point to floating-point, enabling the system to maintain high precision across a wide dynamic range. The floating-point format's exponent-mantissa structure allows precise representation of both large and small numbers without requiring reduction of precision, thereby maintaining both arithmetic stability and computational precision simultaneously.
3Reliability
If backend size is increased to prevent overflow, then arithmetic reliability improves, but device complexity and computational overhead increase
Solution Approach 1:
The patent changes from fixed-point integer representation to floating-point representation, which inherently provides a wider dynamic range without requiring an increase in backend size. The floating-point format's structured exponent-mantissa representation allows efficient storage and computation of large and small numbers using the same computational resources, avoiding the need for larger backends while maintaining arithmetic reliability.
4Ease of operation
If fixed-point representation is used, then ease of operation is maintained, but measurement precision of real numbers deteriorates
Solution Approach 1:
The patent changes the representation parameters from fixed-point to floating-point, enabling precise representation of real numbers with varying magnitudes. The floating-point format's exponent field allows automatic scaling, maintaining ease of operation while dramatically improving measurement precision for both large and small real numbers compared to fixed-point representation.
Data Source
AI summary
A secure multi-party computation implements real number arithmetic using modular integer representation on the backend. As part of the implementation, a secret shared value jointly stored by multiple parties in a first modular representation is cast into a second modular representation having a larger most significant bit. The parties use a secret shared masking value in the first representation, the range of which is divided into two halves, to mask and reveal a sum of the secret shared value and the secret shared masking value. The parties use a secret shared bit that identifies the half of the range that contains the masking value, along with the sum to collaboratively construct a set of secret shares representing the secret shared value in the second modular format. In contrast with previous work, the disclosed solution eliminates a non-zero probability of error without sacrificing efficiency or security.