Secure Inverse Square Root Computation via Bit Decomposition
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Solution Overview
Problem
Existing methods for secure computation, such as those described in NPL 1, are computationally expensive and inefficient for calculating the inverse of a square root.
Innovation Solution
A secure inverse square root computation system and method that utilizes a network of secure computation apparatuses to efficiently calculate the inverse of a square root by decomposing input values into bit sequences, generating normalization multipliers, and performing inverse normalization operations.
Engineering Contradictions & Design Principles
Engineering Contradiction Analysis
1Reliability
If existing secure computation methods are used to calculate the inverse of a square root, then the calculation can be performed securely, but the computational cost is high and processing speed is slow
Solution Approach 1:
The patent segments the calculation process into distinct modules: bit decomposition unit that breaks down the input share value into bit sequences, normalization multiplier generation unit that creates optimization multipliers, inverse square root calculation unit that performs the core computation, and inverse normalization unit that restores the result. This segmentation allows each unit to be optimized independently, improving overall processing speed while maintaining secure computation through share value manipulation throughout the pipeline.
Solution Approach 2:
The patent applies preliminary action by generating normalization multipliers before the inverse square root calculation. The bit decomposition unit processes the input share value in advance to create optimized bit sequences, and the normalization multiplier generation unit prepares optimization multipliers based on these sequences. This preliminary processing reduces the computational burden during the actual inverse square root calculation, significantly improving processing speed.
2Reliability
If existing secure computation methods are used to calculate the inverse of a square root, then the calculation can be performed securely, but the computational complexity is high
Solution Approach 1:
The patent changes parameters by representing all computations in terms of share values and bit sequences rather than direct numerical operations. The system transforms the input share value [a] into bit sequences {a₀}, {a₁}, ..., {aλ-1} and processes throughout the calculation pipeline using these representations. This parameter change simplifies the computational complexity by enabling efficient bitwise operations and share value manipulations instead of complex mathematical operations on encrypted data.
Solution Approach 2:
The patent introduces intermediary elements including bit sequences as intermediaries between the input share value and the final result. The bit decomposition unit creates these intermediary bit sequences that facilitate the calculation. Additionally, normalization multipliers serve as intermediaries that simplify the inverse square root computation. These intermediaries reduce computational complexity by breaking down complex operations into simpler steps that can be performed efficiently on share values.
Data Source
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AI summary
In secure computation, the inverse of a square root is calculated at high speed. A secure inverse square root computation system (100) receives [a] as an input and calculates [1/√a]. The bit decomposition unit (11) generates a bit representation {a0}, ..., {aλ - 1} of a. A first bit sequence generation unit (12) calculates {a'i} = {ai} ∨ {ai + 1} to generate {a'0},..., {a'λ' - 1}. A flag sequence generation unit (13) generates {x0}, ..., {xλ' - 1} indicating a most significant bit of {a'0},..., {a'λ' - 1}. A normalization multiplier generation unit (14) generates [c'] by bit-connecting {xλ'-1}, ..., {x0}. A second bit sequence generation unit (15) sets {a"i} = {a2i} to generate {a"0}, ..., {a"λ' - 1}. A flag calculation unit (16) sums {xj}{a"j} to calculate a share value {r}. A normalization unit (18) calculates [b]: = [c'][c'][2a] when r = 1 and [b]: = [c'][c'][a] when r = 0. An inverse square root calculation unit (19) calculates [w]: = [1/√b] ∗ √2 when r = 1, and [w]: = [1/√b] when r = 0. An inverse normalization unit (20) multiplies [1/√a]: = [w][c'].