Modular Inversion Protection via Additive Share Segmentation
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Solution Overview
Problem
Existing cryptographic data processing systems are vulnerable to external monitoring attacks, particularly side-channel attacks that exploit power consumption and other physical parameters during modular inversion operations, which can lead to unauthorized access to encryption keys.
Innovation Solution
The method generates two masked shares from the public exponent to compute the private exponent, using random integers and the Euler totient function to protect modular inversion operations, ensuring that the private key is derived as a sum of additive shares, thereby resisting external monitoring attacks.
Engineering Contradictions & Design Principles
Engineering Contradiction Analysis
1Reliability
If modular inversion operations are performed using traditional methods, then computational efficiency is maintained, but the system becomes vulnerable to external monitoring attacks and side-channel attacks
Solution Approach 1:
The patent segments the private exponent computation into multiple additive shares (e.g., d = d1 + d2 mod φ(n)). Each share is computed independently using masked inputs, and the final private exponent is reconstructed by summing the shares. This segmentation prevents external monitoring attacks because each individual share computation leaks less information than the full operation.
Solution Approach 2:
The patent applies preliminary masking to the public exponent and other inputs before performing modular inversion operations. Random masks are generated and combined with the actual values in advance, so that even if side-channel attacks monitor the computation, the masks conceal the true secret values throughout the calculation process.
2Reliability
If random masking is applied to protect against side-channel attacks, then security against external monitoring is improved, but computational overhead and processing time increase
Solution Approach 1:
By dividing the computation into segmented shares that can be processed in parallel, the patent reduces the overall processing time despite the added masking operations. Each share computation is independent and can be executed simultaneously, offsetting the overhead of generating and managing masks.
Solution Approach 2:
The patent changes the computational parameters by working in the residue number system (RNS) representation, which allows modular arithmetic operations to be performed more efficiently. This parameter transformation enables faster computation of masked shares while maintaining security properties.
3Reliability
If multiple masked shares are computed and combined, then protection against external monitoring attacks is strengthened, but the quantity of computational operations increases
Solution Approach 1:
The computation is segmented into a fixed small number of shares (e.g., 2-4 shares), which provides sufficient security against external monitoring while limiting the increase in computational operations. This segmented approach balances security requirements with computational efficiency.
Solution Approach 2:
The patent merges multiple share computations into a unified reconstruction step where the masked shares are summed to recover the private exponent. This combining operation efficiently consolidates the results of multiple protected computations into the final secret key without requiring additional complex operations.
Data Source
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AI summary
Systems and methods for performing modular inversion operations in a manner protected from external monitoring attacks. An example method comprises: determining, by a processor, a first masked value based on a public cryptographic key and a first random integer value; determining a second masked value based on the public cryptographic key and a second random integer value; and determining, based on the first masked value and the second masked value, a private cryptographic key represented by a modular inversion of the public cryptographic key.