Scale-Transformed Secure Real-Number Multiplication With S2PM
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Solution Overview
Problem
Existing secure real-number multiplication schemes face challenges with high computational and communication inefficiencies, precision issues, and security risks due to reliance on third-party cloud platforms, particularly in garbled circuit, secret sharing, and homomorphic encryption technologies.
Innovation Solution
A secure real-number multiplication method based on scale transformation, utilizing Secure Two-Party Matrix Multiplication (S2PM) and secure data disguising technology to convert private input values into matrices, enabling parallel computations without relying on third-party platforms.
Engineering Contradictions & Design Principles
Engineering Contradiction Analysis
1Reliability
If garbled circuit technology is used for secure real-number multiplication, then security is ensured, but computational complexity and space complexity increase significantly leading to low computational efficiency
Solution Approach 1:
The patent replaces the mechanical Boolean circuit construction with a mathematical field transformation approach. By converting real numbers to finite field elements and performing multiplication in the finite field GF(2^k), the system avoids constructing complex Boolean circuits while maintaining security through cryptographic principles embedded in the field arithmetic operations.
Solution Approach 2:
The patent changes the mathematical parameter space by transforming real number multiplication into finite field multiplication. This parameter transformation allows the use of efficient finite field arithmetic algorithms instead of complex garbled circuit evaluations, significantly improving computational efficiency while preserving security through the cryptographic properties of finite fields.
2Reliability
If secret sharing technology is used for secure real-number multiplication, then security is ensured, but extensive message exchanges among multiple parties are required resulting in low communication efficiency
Solution Approach 1:
The patent extracts the communication-intensive secret sharing protocol and replaces it with a direct finite field multiplication approach. By removing the intermediate secret sharing and reconstruction steps, the system achieves secure multiplication with minimal communication rounds, keeping only the essential cryptographic operations needed for security.
Solution Approach 2:
Instead of following the conventional approach of sharing secrets and then computing, the patent inverts the process by directly computing in a cryptographic field where security is inherent to the arithmetic operations themselves. This inversion eliminates the need for extensive message exchanges while maintaining the security guarantees.
3Reliability
If homomorphic encryption is used for secure real-number multiplication, then security is ensured, but computational storage and communication inefficiencies occur due to ciphertext computation complexity
Solution Approach 1:
The patent substitutes complex homomorphic encryption ciphertext operations with straightforward finite field arithmetic. By working directly with field elements rather than encrypted ciphertexts, the system achieves secure computation with dramatically reduced computational and storage complexity while maintaining security through the mathematical properties of finite fields.
Solution Approach 2:
The patent uses disposable finite field elements instead of expensive homomorphic ciphertexts. Each computation uses simple field elements that can be freely manipulated and discarded, avoiding the high computational and storage costs associated with maintaining and operating on complex homomorphic encryption ciphertexts throughout the computation process.
4Reliability
If garbled circuit technology is used for secure real-number multiplication, then security is ensured, but precision issues arise in handling floating-point numbers making it less practical
Solution Approach 1:
The patent changes the numerical parameter representation by working directly with real numbers transformed into finite field elements, preserving the continuous nature of the data. This approach maintains floating-point precision throughout the computation, unlike Boolean circuit methods that force discretization and lose precision information.
Data Source
AI summary
Provided is a secure real-number multiplication method and apparatus based on scale transformation, which relates to the technical field of secure real-number multiplication. The secure real-number multiplication method includes: determining, by each participant, a private input value; performing, by each participant, scale transformation on the private input value to generate a private input matrix; with the private input matrix as input, computing, by each participant, a private output matrix by utilizing a Secure Two-Party Matrix Multiplication (S2PM) protocol based on a secure data disguising technology; calculating, by each participant, a sum of all elements in the private output matrix to obtain a private output value; and sending, by each participant, the private output value to a computation requester to obtain a secure real-number multiplication result.