BIKE Key Encapsulation Using AFFT Polynomial Multiplication
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Solution Overview
Problem
The Bit Flipping Key Encapsulation (BIKE) scheme, a post-quantum cryptographic method based on Error-Correcting Codes, is computationally burdensome and requires significant memory footprint, particularly in lightweight devices like smart cards and servers, due to high-degree polynomial multiplications.
Innovation Solution
The optimized BIKE scheme employs Additive Fast Fourier Transforms (AFFTs) to transform binary polynomials into an AFFT domain, reducing computational load by performing pointwise multiplications instead of traditional polynomial products, thus optimizing key generation, encapsulation, and decapsulation processes.
Engineering Contradictions & Design Principles
Engineering Contradiction Analysis
1Reliability
If traditional polynomial multiplication is used in BIKE scheme, then cryptographic security is maintained, but computational load and memory footprint increase significantly
Solution Approach 1:
The patent replaces traditional polynomial multiplication with a transformed domain computation system. By applying Fast Fourier Transform (FFT) to convert polynomials into frequency domain representations, the multiplication operation is substituted with pointwise multiplication of transformed coefficients, which is computationally more efficient while maintaining cryptographic security properties
Solution Approach 2:
The patent changes the representation parameters of polynomial data from time domain coefficients to frequency domain coefficients via FFT transformation. This parameter transformation enables the same cryptographic function to be performed with reduced computational complexity, as pointwise multiplication in frequency domain requires fewer operations than polynomial multiplication in time domain
2Reliability
If traditional polynomial multiplication is used in BIKE scheme, then cryptographic functionality is preserved, but memory footprint increases
Solution Approach 1:
The patent substitutes the memory-intensive polynomial multiplication process with a transformed domain computation approach. The FFT transformation reorganizes data in a way that enables efficient pointwise multiplication, significantly reducing the memory resources required to store intermediate computation results while preserving cryptographic functionality
3Productivity
If AFFT transformation is applied to optimize polynomial multiplication, then computational load is reduced by 20% in key generation, but additional transformation steps are required
Solution Approach 1:
The patent applies FFT transformation as a preliminary step before performing polynomial multiplication. By pre-transforming the polynomial coefficients into the frequency domain, the subsequent multiplication operation becomes computationally simpler (pointwise multiplication), and the overall process efficiency is improved despite the added transformation step
Solution Approach 2:
The patent introduces the frequency domain as an intermediary representation between the input polynomials and the final product. The FFT transformation creates this intermediate domain where computations are more efficient, and then an inverse FFT transforms the result back to the time domain, serving as a computational mediator that reduces overall complexity
4Productivity
If AFFT transformation is used for encapsulation and decapsulation, then computational load is reduced by 12% and 18% respectively, but implementation complexity increases
Solution Approach 1:
The patent applies FFT transformation as a preliminary step in both encapsulation and decapsulation processes. By transforming the relevant polynomials into the frequency domain before performing multiplication operations, the computational load is reduced by 12% in encapsulation and 18% in decapsulation, making the operations more efficient despite the additional transformation steps required
Solution Approach 2:
The patent changes the computational parameters from direct polynomial multiplication to transformed domain pointwise multiplication. This parameter change in the representation domain enables the significant computational savings observed in encapsulation and decapsulation operations, trading implementation complexity for improved productivity
Data Source
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AI summary
Optimized BIKE method (200) comprising: setting (210) system parameters and Hash functions; generating (220) a public key ( pk˜) and a private key ( sk˜); encapsulating (230) a message (m) into a ciphertext (c) using the public key, and computing a pseudo-message (K) using the message and the ciphertext; and, decapsulation (240) the ciphertext using the private key to retrieve the pseudo-message. The method computes a product between first and second operands of a size n binary polynomial type by way of a pointwise product between first and second transformed operands resulting in an AFFT like function applied to the first and second operands respectively, so that at least one element among the first private element (ḧ0) of the private key ( sk˜) or the single public element (ḧ) of the public key ( pk˜) is a vector in the AFFT domain.