HQC Polynomial Multiplication Using AFFT for Lower Cryptographic Load
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Solution Overview
Problem
The Hamming Quasi-Cyclic (HQC) post-quantum cryptographic scheme is computationally burdensome and requires significant memory footprint, particularly in lightweight devices like smart cards and servers, due to high polynomial multiplication operations.
Innovation Solution
The HQC scheme is optimized by using Additive Fast Fourier Transforms (AFFTs) to transform operands into an AFFT domain, reducing polynomial multiplication operations by performing pointwise multiplications instead, thus minimizing computational load and memory requirements.
Engineering Contradictions & Design Principles
Engineering Contradiction Analysis
1Reliability
If polynomial multiplication operations are performed in the HQC scheme, then cryptographic security is achieved, but computational load and memory footprint increase significantly
Solution Approach 1:
The patent introduces an intermediary transformation (Fast Fourier Transform or similar) that converts polynomial multiplication into pointwise multiplication in a transformed domain. This intermediary step allows the system to maintain cryptographic security while reducing computational complexity from O(n²) to O(n log n), thereby resolving the contradiction between security and computational load.
Solution Approach 2:
The patent changes the parameter representation of polynomials by transforming them into the frequency domain using FFT. This parameter transformation enables the same cryptographic operations to be performed with reduced computational effort, as pointwise multiplication in the transformed domain is significantly faster than direct polynomial multiplication.
2Reliability
If polynomial multiplication operations are performed in the HQC scheme, then cryptographic functionality is maintained, but memory footprint increases
Solution Approach 1:
The FFT transformation serves as an intermediary that reorganizes polynomial data in a way that reduces memory requirements. By converting polynomials to their frequency domain representations, the system can perform cryptographic operations with smaller working memory footprints, as the transformed representation requires less space for intermediate calculations.
3Reliability
If traditional polynomial multiplication is used in encryption and decryption, then cryptographic correctness is ensured, but processing speed decreases
Solution Approach 1:
The patent applies parameter transformation through FFT to change the domain in which polynomial multiplication is performed. This transformation maintains cryptographic correctness because the mathematical equivalence is preserved, while dramatically improving processing speed by reducing the complexity from O(n²) to O(n log n) operations.
Data Source
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AI summary
Optimized HQC post-quantum cryptographic method (200) comprising: setting (210) global parameters; generating (220) a public key ( pk˜) and a private key ( sk˜); encrypting (230) a message (m) with the public key to obtain a ciphertext (c); and decrypting (240) the ciphertext with the private key to retrieve the message. The method computes a product between first and second operands of the size n binary polynomial type by way of a pointwise product between first and second transformed operand resulting in an AFFT like function applied to the first and second operand respectively, so that at least one element among the second private element (ÿ) of the private key ( sk˜), the first public element (h) of the public key ( pk˜) and the second public element (ÿ) of the public key ( pk˜) is a vector in the AFFT domain.