Bivariate Statistical Moment Computation for Side-Channel Evaluation
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Solution Overview
Problem
Existing methods for evaluating side channel attack vulnerability in cryptographic data processing devices are computationally inefficient, especially when dealing with large data sets, which hinders effective protection against malicious attacks.
Innovation Solution
The implementation of efficient one-pass methods for computing higher-order bivariate statistical moments, utilizing matrix operations to iteratively update intermediate results, significantly reducing computational complexity and enabling faster evaluation of side channel attack vulnerability.
Engineering Contradictions & Design Principles
Engineering Contradiction Analysis
1Measurement precision
If traditional methods are used to compute bivariate statistical moments for side channel analysis, then measurement precision is maintained, but computational time increases significantly
Solution Approach 1:
The patent pre-computes and stores power models that represent the relationship between cryptographic operations and power consumption characteristics. These pre-computed models are then reused during side channel analysis, avoiding the need to re-compute statistical moments from scratch for each analysis, thus reducing computational time while maintaining accuracy
Solution Approach 2:
The patent creates simplified representations (copies) of the complex power consumption data through statistical moment computations. These computed moments serve as compact summaries that capture essential characteristics of the power traces, enabling faster analysis without losing critical information needed for vulnerability detection
2Productivity
If efficient one-pass methods are used to compute higher-order bivariate statistical moments, then productivity is improved, but device complexity increases
Solution Approach 1:
The patent divides the computation of higher-order statistical moments into separate, independent passes for each moment order (e.g., computing second-order moments separately from third-order moments). Each pass processes the data independently using optimized algorithms, achieving O(n) complexity per pass while avoiding the combinatorial explosion that would result from computing all moments simultaneously
Solution Approach 2:
The patent transforms the computational problem by introducing an iterative dimension where statistical moments are computed sequentially across multiple passes. Instead of computing all moments in a single complex operation, the solution iterates through different moment orders, with each iteration building upon previous results, thereby reducing the complexity of individual computational steps
Data Source
AI summary
Systems and methods for efficient computation of bivariate statistical moments. An example method comprises: determining exponents characterizing a bivariate mean value referenced by a definition of a statistical moment to be computed; receiving an input data set representing a plurality of observed values of one or more variables, the input data including a plurality of traces, each trace of the plurality of traces including a plurality of sample points; generating an initial matrix comprising combinations of pre-determined degrees of the sample points; producing an intermediate result matrix represented by a product of multiplying a transpose of the initial matrix by the initial matrix; retrieving an element of the intermediate result matrix, wherein indices of the element are defined based on the exponents; and using the retrieved element of the intermediate result matrix to compute the statistical moment.