Cryptography Research, Inc.

Ilya Stupakov

Anton Kochepasov

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.

Efficient computation of bivariate statistical moments for side channel vulnerability evaluation

Systems and methods for efficient computation of univariate statistical moments. An example method comprises: receiving a plurality of input traces, wherein each trace of the plurality of input traces includes a plurality of sample points; appending, to a trace matrix comprising combinations of pre-determined degrees of the sample points, a plurality of rows representing the plurality of input traces; appending, to a classifier matrix, a plurality of columns representing metadata associated with the plurality of input traces; applying a defined transformation to the classifier matrix to produce a transformed classifier matrix; incrementing an accumulator matrix by a product of the transformed classifier matrix and the trace matrix; computing, using a first subset of elements of the accumulator matrix, a first statistical moment for a first portion of the input traces identified by a first subset of elements of the classifier matrix, wherein the first subset of elements of the classifier matrix is identified by a first classifier value; and computing, by subtracting each element of the first subset of elements of the accumulator matrix from a corresponding sum of elements of the input traces stored by the accumulator matrix, a second statistical moment for a second portion of the input traces identified by a second subset of elements of the classifier matrix, wherein the second subset of elements of the classifier matrix is identified by a second classifier value.

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Novosibirsk, Russia

Ilya Stupakov