Matrix Multiplication Shuffling for Side-Channel Attack Resistance
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Solution Overview
Problem
Current post-quantum cryptography algorithms using matrix multiplication are vulnerable to side-channel attacks such as simple power analysis (SPA) and differential power analysis (DPA) attacks, which threaten the security of public-key infrastructure.
Innovation Solution
Shuffling the order of execution of multiplication operations between elements of matrices during matrix multiplication operations to increase the randomness and reduce the likelihood of intermediate values being predictable, thereby enhancing security against side-channel attacks.
Engineering Contradictions & Design Principles
Engineering Contradiction Analysis
1Reliability
If matrix multiplication operation is performed using conventional order, then computation efficiency is maintained, but security against side-channel attacks deteriorates
Solution Approach 1:
The patent applies dynamics by making the execution order of multiplication operations variable and adaptive. Instead of using a fixed conventional order, the system dynamically shuffles the execution sequence based on operational requirements, making the computation pattern changeable and unpredictable to attackers while maintaining computational correctness
Solution Approach 2:
The patent implements periodic action by repeatedly shuffling the execution order of multiplication operations in a systematic manner. The shuffling process creates periodic variations in the computation pattern, ensuring that the same operation sequence does not repeat predictably, thereby countering side-channel attacks that rely on pattern recognition
2Reliability
If shuffling order of multiplication operations is implemented, then security against side-channel attacks is improved, but device complexity increases
Solution Approach 1:
The patent applies parameter changes by modifying the execution order parameter of the matrix multiplication operation. Instead of changing the fundamental algorithm or data structures, the system varies the temporal arrangement parameter (execution sequence) to achieve security enhancement with minimal impact on overall system complexity
Solution Approach 2:
The patent introduces an intermediary shuffling mechanism that sits between the standard matrix multiplication algorithm and its execution. This intermediary component manages the reordering of operations without fundamentally altering the core multiplication logic, thereby isolating the complexity to a manageable layer
3Reliability
If shuffling order of multiplication operations is implemented, then intermediate values become less predictable, but computation time increases
Solution Approach 1:
The patent applies preliminary action by pre-computing and storing multiple valid execution order permutations before the actual matrix multiplication is performed. This preparation work is done in advance, so that during the actual computation, the system can quickly select and apply a pre-approved shuffled order without significant overhead
Data Source
AI summary
A method for performing a matrix multiplication operation being secure against side-channel attacks according to one embodiment, which is performed by a computing device comprising one or more processors and a memory storing one or more programs to be executed by the one or more processors, includes shuffling an order of execution of multiplication operations between elements of a first matrix and elements of a second matrix for a matrix multiplication operation between the first matrix and the second matrix; and performing the matrix multiplication operation based on the shuffled order of execution.