scalib.metrics.RLDAInformationEstimator

class scalib.metrics.RLDAInformationEstimator(model, max_popped_classes)

Amount of information that can be extracted from leakage with a RLDA model.

This class can be used to compute Perceived Information (PI) or Training Information (TI) [1] bounds of a RLDA model [2] for a variable.

It estimates the information using

\[\hat{\mathrm{I}}(X,\mathbf{L}) = \mathrm{H}(X) + \frac{1}{|\mathcal{L}'|} \sum_{x \in \mathcal{X}} \sum_{\mathbf{l}\in \mathcal{L}'_x} \log_2 \hat{\mathsf{p}}[x|\mathbf{l}]\]

PI or TI is obtained depending on the validation set used for the estimation.

In order to obtain the PI : use a validation set independent of the training set of the model.

In order to obtain the TI : use as validation set the full training set of the model.

This object assumes that target variable is uniform and uses a clustered version of an RLDA model for faster computation, leading to bounds instead of exact values. If the bounds are not tight enough, change the parameters of the clustered model.

The validation set is provided to this object by calling fit_u(), and the estimated information is recovered with get_information(). The estimator is further subject some variance due to the sampling of the validation set. The estimated standard deviation can be obtained with get_deviation().

Examples

>>> from scalib.modeling import RLDAClassifier
>>> from scalib.metrics import RLDAInformationEstimator
>>> import numpy as np
>>> traces_model = np.random.randint(0,256,(5000,10),dtype=np.int16)
>>> labels_model = np.random.randint(0,256,(5000,1),dtype=np.uint64)
>>> rlda = RLDAClassifier(8, 3)
>>> rlda.fit_u(traces_model, labels_model)
>>> rlda.solve()
>>> cl = rlda.get_clustered_model(0,0.5,100, False)
>>> it = RLDAInformationEstimator(cl, 0)
>>> traces_test = np.random.randint(0,256,(5000,10),dtype=np.int16)
>>> labels_test = np.random.randint(0,256,(5000,),dtype=np.uint64)
>>> it.fit_u(traces_test, labels_test)
>>> pi_l,pi_u = it.get_information()

See also

scalib.modeling.RLDAClassifier.get_clustered_model

Clustered model to use with RLDAInformationEstimator.

References

[1]

Loïc Masure, Gaëtan Cassiers, Julien M. Hendrickx, and François-Xavier Standaert. Information bounds and convergence rates for side-channel security evaluators. IACR Cryptol. ePrint Arch., pages 490, 2022.

[2] (1,2)

Gaëtan Cassiers, Henri Devillez, François-Xavier Standaert, and Balazs Udvarhelyi. Efficient regression-based linear discriminant analysis for side-channel security evaluations: towards analytical attacks against 32-bit implementations. IACR Transactions on Cryptographic Hardware and Embedded Systems, 2023.

Parameters:

• model (ClusteredModel) – The clustered model, it is obtained by calling get_clustered_model() on an RLDA object.

• max_popped_classes (int) – Number of classes that are calculated without using the associated cluster. Corresponds to parameter \(\zeta\) in [2].

Methods

fit_u(traces, x)	Updates the estimatore with the given traces and the corresponding labels.
get_deviation()	Compute the approximate deviation of the information estimator for the lower and upper bound.
get_information()	Returns the lower and upper bound information estimation.

fit_u(traces, x)

Updates the estimatore with the given traces and the corresponding labels.

This can be called multiple times with parts of the dataset: the state is accumulated.

Parameters:

• traces (array_like, int16) – Array that contains the traces. Shape: (n,ns).

• x (array_like, uint64) – Label for each trace. Shape (n,).

get_information()

Returns the lower and upper bound information estimation.

Return type:

Tuple[float, float]

get_deviation()

Compute the approximate deviation of the information estimator for the lower and upper bound. Returns the deviation of the lower bound, the upper bound, and the number of traces used for the estimation.

Return type:

Tuple[float, float, int]