BIKE Key Encapsulation Using AFFT Polynomial Transforms
Find Innovative SolutionsGenerate Solutions
Solution Overview
Problem
The Bit Flipping Key Encapsulation (BIKE) scheme, a post-quantum cryptographic method, is computationally burdensome and requires significant memory footprint, particularly in lightweight devices like smart cards and servers, due to polynomial multiplication operations.
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 operations with bit-reversal permutation operations. This substitution transforms the computational mechanism from algebraic multiplication to permutation-based operations, significantly reducing computational complexity while preserving the cryptographic security properties of the BIKE scheme.
Solution Approach 2:
The patent modifies the representation and processing parameters of the cryptographic operations. By changing from standard polynomial coefficient representation to bit-reversal permutation representation, the computational parameters are optimized to reduce the number of operations required while maintaining the same security level.
2Ease of operation
If polynomial multiplication operations are performed in key generation, encapsulation, and decapsulation, then cryptographic functionality is achieved, but computation time increases
Solution Approach 1:
The patent systematically replaces polynomial multiplication operations with bit-reversal permutation operations across all three main phases (key generation, encapsulation, decapsulation). This substitution consistently reduces computation time while preserving the essential cryptographic functionality of key exchange and message encryption/decryption.
Solution Approach 2:
The patent performs bit-reversal permutations as preliminary operations before the main computational steps. By pre-processing the data in bit-reversal order, subsequent operations become more efficient, reducing the overall computation time required for cryptographic operations.
Data Source
AI summary
Optimized BIKE method comprising: setting system parameters and Hash functions; generating a public key () and a private key (); encapsulating 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 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 ({umlaut over (h)}0) of the private key () or the single public element ({umlaut over (h)}) of the public key () is a vector in the AFFT domain.