Secure Array Indexing via Shift Operations
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Solution Overview
Problem
Conventional secure computation methods require Q(mn)-time comparisons to read multiple elements from a secured array, leading to inefficient operations.
Innovation Solution
A secure computation system with three or more devices that securely shifts and generates a new array by shifting the original array leftward, allowing multiple elements to be read efficiently in a single secure shift operation without disclosing the original array values.
Engineering Contradictions & Design Principles
Engineering Contradiction Analysis
1Reliability
If conventional secure computation methods are used to read multiple elements from a secured array, then security is maintained, but the operation time increases quadratically to Q(mn)
Solution Approach 1:
The patent applies preliminary action by pre-shifting the secured array according to the secret-shared index values before performing the read operations. The secure shift operation is performed once on the entire array, and then multiple elements can be read from the shifted positions without requiring repeated comparisons. This preliminary shifting action eliminates the need for Q(mn) comparison operations while maintaining security through secret-sharing protocols.
2Measurement precision
If multiple elements are read from a secured array using conventional comparison methods, then accurate reading is achieved, but the computational complexity reaches Q(mn)
Solution Approach 1:
The patent merges multiple read operations into a single secure shift operation. Instead of performing separate comparison operations for each of the m elements to be read, the system performs one secure shift operation on the array and then reads all m elements from their respective shifted positions. This merging of operations reduces computational complexity from Q(mn) to Q(n+m) while maintaining reading accuracy through the properties of secret-sharing and secure computation.
Solution Approach 2:
The patent introduces dynamic behavior by using secret-shared index values that can be added to the array positions dynamically. The secure shift operation dynamically repositions elements based on the secret-shared indices, allowing flexible reading of multiple elements without fixed comparison patterns. This dynamic approach reduces computational complexity while maintaining accuracy through cryptographic protocols.
Data Source
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Figure 3
AI summary
Multiple elements are efficiently read from a secured array. A secure text array =(<a[0]>,..., <a[n-1]>) where an array a=(a[0],..., a[n-1]) having a size of n is secured, secure text <x> of an integer x that is equal to or higher than 0 and less than n, and m integers i0,..., im-1 that are equal to or higher than 0 and less than n are input into an input part 11. A secure shift part 12 secure-shifts the secure text array by <x> to obtain a secure text array <a'>=(<a'[0]>,..., <a'[n-1]>) where an array a'=(a'[0],..., a'[n-1]) obtained by shifting leftward the array a by x is secured. An array generation part 13 generates a secure text array =(<a'[i0]>,..., <a'[im-1]>) from the secure text array <a'>.