Secure Floating-Point Noise Addition by Replacing Mantissa Zeros
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Solution Overview
Problem
Current floating-point arithmetic solutions in differential privacy leak sensitive information due to precision loss in floating-point representations, allowing unauthorized users to exploit these traces and break the differential privacy guarantee.
Innovation Solution
Replace trailing zeros in the mantissa of floating-point numbers with random digits to prevent information leakage, ensuring that the output floating-point numbers are free from traces of sensitive non-integer input values, thus maintaining differential privacy.
Engineering Contradictions & Design Principles
Engineering Contradiction Analysis
1Productivity
If floating-point arithmetic operations are performed to add noise for differential privacy, then data analysis capability is improved, but precision loss occurs that leaks sensitive information
Solution Approach 1:
The patent extracts and removes the problematic trailing zeros from the floating-point representation that contain sensitive information traces. By identifying and eliminating these specific digits that leak information while preserving the overall noise addition mechanism, the system maintains differential privacy functionality without the information leakage vulnerability.
Solution Approach 2:
The patent applies local quality by treating different parts of the floating-point number differently. Specifically, it modifies only the trailing zero digits in the mantissa while leaving other parts unchanged. This localized modification prevents information leakage at critical positions without disrupting the overall noise addition process that enables differential privacy.
2Reliability
If noise is added to floating-point numbers using standard arithmetic, then differential privacy guarantee is improved, but traces of sensitive input values remain exploitable
Solution Approach 1:
The patent applies preliminary anti-action by proactively modifying the floating-point representation before an attacker can exploit the traces. By preemptively replacing trailing zeros with random digits, the system neutralizes the vulnerability to precision-based attacks before they can be executed, thereby strengthening the differential privacy guarantee.
Solution Approach 2:
The patent converts the harmful effect of trailing zeros (which contain exploitable information) into a beneficial feature by replacing them with random digits. This transformation turns what was previously a security vulnerability into a protective mechanism that actively prevents information leakage while maintaining the noise addition's privacy-guaranteeing properties.
3Loss of information
If trailing zeros are replaced with random digits, then information leakage is prevented, but additional processing steps are required
Solution Approach 1:
The patent performs preliminary action by identifying and marking the trailing zero positions in the floating-point mantissa before the actual replacement occurs. This pre-processing step organizes the complexity management by establishing a clear procedure: locate trailing zeros, generate random digits, and replace. This structured approach minimizes the overall processing complexity compared to more comprehensive redesigns.
Data Source
AI summary
Secure noise addition in floating-point numbers is provided. It is determined whether digits of a mantissa of a summed floating-point number include a set of trailing zeros at an end of the mantissa of the summed floating-point number. In response to determining that the digits of the mantissa of the summed floating-point number include the set of trailing zeros at the end of the mantissa of the summed floating-point number, the set of trailing zeros at the end of the mantissa of the summed floating-point number is replaced with a set of digits selected from a group of random digits to form an output floating-point number that is free from traces of a sensitive non-integer input value satisfying differential privacy guarantee of data security immune from floating-point attack.