Reverse Decomposition in Post-Quantum Cryptography for Side-Channel Resistance
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Solution Overview
Problem
Post-quantum cryptographic algorithms like Dilithium and Kyber require substantial processing and memory resources, and are vulnerable to side-channel attacks, particularly on low-resource devices such as card readers and IoT devices.
Innovation Solution
Implement reverse decomposition techniques to swap the high and low parts of intermediate vectors in polynomial-based computations, using significance δ=(q−1)/α, and combine with masking techniques to protect against side-channel attacks.
Engineering Contradictions & Design Principles
Engineering Contradiction Analysis
1Reliability
If post-quantum cryptographic algorithms (Dilithium, Kyber) are implemented on low-resource devices, then security against quantum attacks is improved, but processing and memory resource consumption increases
Solution Approach 1:
The patent segments intermediate polynomial values into high-order and low-order parts, allowing selective processing. By decomposing polynomials into segments based on significance thresholds, the system processes only necessary portions of data, reducing overall computational burden while maintaining cryptographic security.
Solution Approach 2:
The patent extracts and processes only the significant high-order parts of intermediate values during cryptographic operations, setting less significant low-order parts to zero. This extraction approach reduces processing requirements by eliminating computation on data that does not contribute meaningfully to the cryptographic outcome.
2Reliability
If post-quantum cryptographic algorithms are implemented on low-resource devices, then security against quantum attacks is improved, but memory resource consumption increases
Solution Approach 1:
The patent extracts only the essential high-order components of intermediate values for storage and processing, discarding less significant low-order parts. This reduces memory requirements by storing only the critical portions of cryptographic data that are necessary for security.
Solution Approach 2:
The patent segments cryptographic intermediate values into high-significance and low-significance portions, allowing the system to store and manage smaller subsets of data. By segmenting the polynomial representations and processing them in manageable parts, memory consumption is reduced while maintaining algorithmic integrity.
3Manufacturing precision
If standard decomposition methods are used in cryptographic computations, then computational correctness is maintained, but processing time and resource consumption increase
Solution Approach 1:
The patent inverts the traditional decomposition approach by setting high-order parts to zero and retaining low-order parts, rather than the conventional method of keeping high-order and discarding low-order parts. This inversion, combined with the significance-based processing, accelerates computation by focusing on the most impactful data portions while maintaining cryptographic correctness through proper modular arithmetic operations.
Solution Approach 2:
The patent changes the processing parameters by applying significance thresholds (δ=(q-1)/α) to determine which parts of intermediate values require full processing versus which can be simplified or zeroed. This parameter-based approach optimizes the balance between computational correctness and processing efficiency by adapting the level of processing to the actual significance of each data portion.
Data Source
AI summary
Disclosed aspects and implementations are directed to systems and techniques for efficient execution of post-quantum cryptographic applications and protection of cryptographic computations against side-channel attacks. In one example, techniques for performing a cryptographic operation include generating a first value and computing, by the processing device, a second value. A low part of the second value is mapped to a high part of a product of a public value and the first value and a high part of the second value is mapped to a low part of the product of the public value and the first value. The techniques further include computing, using the second value, an output of the cryptographic operation that includes a digital signature for an input into the cryptographic operation or a ciphertext encrypting the input into the cryptographic operation.