Secure Right Shift Computation System Using Additive Secret Sharing
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Solution Overview
Problem
Existing secure computation methods, such as those using secret sharing, face challenges with overflow issues when performing high-speed right shift computation and division, especially when dealing with repeated operations that increase numerical accuracy.
Innovation Solution
A secure computation system comprising multiple secure computation apparatuses that perform right shift and division operations using distributed values obtained through secret sharing, allowing for high-speed processing while avoiding overflow issues.
Engineering Contradictions & Design Principles
Engineering Contradiction Analysis
1Reliability
If secret sharing methods are used for secure computation, then data security is improved, but computational speed deteriorates
Solution Approach 1:
The patent segments the computation process into multiple phases: converting secret-shared values to additive secret-sharing format, performing the right shift operation on the converted format, and converting back to secret-sharing format. This segmentation allows each phase to be optimized independently, improving overall computational speed while maintaining security.
Solution Approach 2:
The patent changes the representation parameter of the secret-shared value from standard secret-sharing format to additive secret-sharing format temporarily during computation. This parameter change enables more efficient right shift operations, as the additive format allows direct arithmetic manipulation without requiring complex cryptographic operations.
2Measurement precision
If right shift computation is performed repeatedly to increase numerical accuracy, then computation precision is improved, but overflow occurs
Solution Approach 1:
The patent performs preliminary conversion of the secret-shared value to additive secret-sharing format before the right shift operation. This preliminary action prepares the data in a format that allows for controlled arithmetic operations, preventing overflow during repeated right shift computations while maintaining numerical accuracy.
Solution Approach 2:
The additive secret-sharing format serves as an intermediary representation between the input secret-sharing format and the final result. This intermediary format enables safe arithmetic operations including repeated right shifts, as it allows direct manipulation of the underlying values without immediately exposing them, thus preventing overflow while maintaining precision.
3Productivity
If conventional right shift methods are used on integer rings with powers of two, then computational speed is improved, but adaptability deteriorates
Solution Approach 1:
The patent creates a universal right shift computation method that works across different mathematical fields including integer rings, finite fields, and polynomial rings. By using additive secret-sharing as an intermediate representation, the method maintains high computational speed while becoming adaptable to various cryptographic applications and data types, not just integer rings with powers of two.
Data Source
AI summary
The present invention implements high-speed right shift computation and division in secure computation. According to the present invention, a public value multiplication part calculates [a′]=[2ua] from a distributed value [a] of a value “a.” A first conversion part converts [a′] into additive secret sharing. A right shift computation part calculates <s>i=<a′>i>>b+u. A second conversion part converts <s> into linear secret sharing. A first bit conversion part converts lower u bits of <a′>i into {a′i mod 2u}. A quotient transfer part 16 obtains lower u bits of −Σi<m{a′i mod 2u} as {q}. A second bit conversion part converts lower b+u bits of <a′>i into {a′iR}={a′i mod 2b+u}. An addition part calculates {z}=Σi<m{a′iR}+{q}, and obtains a bit sequence {zQ} of a (b+u)-th bit and after of {z}. A third conversion part converts {q} and {zQ} into linear secret sharing. An output computation part outputs [s]−[2l−(b+u)q]+[zQ] as [a>>b].