Multi-party distributed multiplication using pre-computed tables
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Solution Overview
Problem
Existing multi-party distributed multiplication methods are inefficient for performing arithmetic operations on large rings, as they require significant calculation amounts and cannot execute arbitrary arithmetic operations in a variant manner.
Innovation Solution
A multi-party distributed multiplication system that uses two devices to communicate and authenticate each other's public keys, generating commitments, encrypted texts, and product shares to calculate the product of two values on a ring, ensuring legitimacy and efficiency through noise removal and authentication processes.
Engineering Contradictions & Design Principles
Engineering Contradiction Analysis
1Productivity
If existing multi-party distributed multiplication methods are used for arithmetic operations on large rings, then the calculation amount becomes tremendous and arbitrary arithmetic operations cannot be executed in a variant manner, but the patent enables efficient calculation in a variant manner with reduced calculation complexity
Solution Approach 1:
The patent segments the arithmetic operation into two distinct phases: a setup phase that pre-computes and stores multiplication tables, and an execution phase that performs the actual multiplication by table lookup. This segmentation transforms the computationally intensive arbitrary arithmetic operation into an efficient process that leverages pre-computed data, resolving the contradiction between productivity and device complexity.
2Loss of time
If existing methods are used to perform arbitrary arithmetic operations on large rings, then significant calculation amounts are required, but the patent reduces calculation complexity through pre-computed multiplication tables
Solution Approach 1:
The patent applies preliminary action by pre-computing and storing multiplication tables during a setup phase before the actual arithmetic operations are performed. The multiplication tables contain pre-calculated products of all possible value pairs in the ring, which are stored for later retrieval. This preliminary computation eliminates the need for complex real-time calculations during the execution phase, significantly reducing calculation time despite the initial setup effort.
Data Source
AI summary
A multi-party variance multiplication device includes: an initial setting device which generates a first public key by using an inputted system parameter; a commitment generation device which generates a commitment of a first input value based on the system parameter and a random number; an encryption device which generates an encrypted text of the first input value based on the system parameter, the random number, and the first public key; an authentication device which generates a certificate that authenticates a range of the first input value based on the system parameter, the random number, the first public key, and the second public key already public; a decryption device which generates a decrypted text by decrypting a noisy encrypted text based on the system parameter, the first public key, and a private key; and a noise removal device which generates a product variance by removing a noise from the decrypted text.