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[tvla] minor clean-up changes #154

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Sep 12, 2023
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[tvla] minor clean-up changes #154

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1c3a4bf
[tvla] Move ttest fuctions into a separate file
vrozic Sep 8, 2023
abcd16f
[tvla] Set HAMMING_WEIGHT as the default leakage model
vrozic Sep 8, 2023
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138 changes: 7 additions & 131 deletions cw/tvla.py
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Open in desktop
Original file line number Diff line number Diff line change
Expand Up @@ -7,6 +7,7 @@
import logging as log
import multiprocessing
import os
import sys
from pathlib import Path
from types import SimpleNamespace

Expand All @@ -17,10 +18,13 @@
import yaml
from chipwhisperer.analyzer import aes_funcs
from joblib import Parallel, delayed
from scipy.stats import ttest_ind_from_stats

from util import plot

ABS_PATH = os.path.dirname(os.path.abspath(__file__))
sys.path.append(ABS_PATH + '/../util')
from ttest import ttest_hist_xy # noqa : E402

app = typer.Typer(add_completion=False)


Expand Down Expand Up @@ -82,133 +86,6 @@ def plot_fvsr_stats(traces, leakage):
"tmp/diff_var_trace.html")


# A set of functions for working with histograms.
# The distributions are stored in two matrices x and y with dimensions (M, N) where:
# - M equals the number of time samples times the number of orders, and
# - N equals the number of values (i.e. the resolution).
# The matrices hold the following data:
# - x holds the values (all rows are the same for 1st order), and
# - y holds the probabilities (one probability distribution per row/time sample).


def mean_hist_xy(x, y):
"""
Computes mean values for a set of distributions.

Both x and y are (M, N) matrices, the return value is a (M, ) vector.
"""
return np.divide(np.sum(x * y, axis=1), np.sum(y, axis=1))


def var_hist_xy(x, y, mu):
"""
Computes variances for a set of distributions.

This amounts to E[(X - E[X])**2].

Both x and y are (M, N) matrices, mu is a (M, ) vector, the return value is a (M, ) vector.
"""

# Replicate mu.
num_values = x.shape[1]
mu = np.transpose(np.tile(mu, (num_values, 1)))

# Compute the variances.
x_mu_2 = np.power(x - mu, 2)
return mean_hist_xy(x_mu_2, y)


def ttest1_hist_xy(x_a, y_a, x_b, y_b):
"""
Basic first-order t-test.

Everything needs to be a matrix.
"""
mu1 = mean_hist_xy(x_a, y_a)
mu2 = mean_hist_xy(x_b, y_b)
std1 = np.sqrt(var_hist_xy(x_a, y_a, mu1))
std2 = np.sqrt(var_hist_xy(x_b, y_b, mu2))
N1 = np.sum(y_a, axis=1)
N2 = np.sum(y_b, axis=1)
return ttest_ind_from_stats(mu1,
std1,
N1,
mu2,
std2,
N2,
equal_var=False,
alternative='two-sided')[0]


def ttest_hist_xy(x_a, y_a, x_b, y_b, num_orders):
"""
Welch's t-test for orders 1,..., num_orders.

For more details see: Reparaz et. al. "Fast Leakage Assessment", CHES 2017.
available at: https://eprint.iacr.org/2017/624.pdf

x_a and x_b are (M/num_orders, N) matrices holding the values, one value vector per row.
y_a and y_b are (M/num_orders, N) matrices holding the distributions, one distribution per row.

The return value is (num_orders, M/num_orders)
"""

num_values = x_a.shape[1]
num_samples = y_a.shape[0]

#############
# y_a / y_b #
#############

# y_a and y_b are the same for all orders and can simply be replicated along the first axis.
y_a_ord = np.tile(y_a, (num_orders, 1))
y_b_ord = np.tile(y_b, (num_orders, 1))

#############
# x_a / x_b #
#############

# x_a and x_b are different on a per-order basis. Start with an empty array.
x_a_ord = np.zeros((num_samples * num_orders, num_values))
x_b_ord = np.zeros((num_samples * num_orders, num_values))

# Compute shareable intermediate results.
if num_orders > 1:
mu_a = mean_hist_xy(x_a, y_a)
mu_b = mean_hist_xy(x_b, y_b)
if num_orders > 2:
var_a = var_hist_xy(x_a, y_a, mu_a)
var_b = var_hist_xy(x_b, y_b, mu_b)
sigma_a = np.transpose(np.tile(np.sqrt(var_a), (num_values, 1)))
sigma_b = np.transpose(np.tile(np.sqrt(var_b), (num_values, 1)))

# Fill in the values.
for i_order in range(num_orders):
if i_order == 0:
# First order takes the values as is.
x_a_ord[0:num_samples, :] = x_a
x_b_ord[0:num_samples, :] = x_b
else:
# Second order takes the variance.
tmp_a = x_a - np.transpose(np.tile(mu_a, (num_values, 1)))
tmp_b = x_b - np.transpose(np.tile(mu_b, (num_values, 1)))
if i_order > 1:
# Higher orders take the higher order moments, and also divide by sigma.
tmp_a = np.divide(tmp_a, sigma_a)
tmp_b = np.divide(tmp_b, sigma_b)

# Take the power and fill in the values.
tmp_a = np.power(tmp_a, i_order + 1)
tmp_b = np.power(tmp_b, i_order + 1)
x_a_ord[i_order * num_samples:(i_order + 1) * num_samples, :] = tmp_a
x_b_ord[i_order * num_samples:(i_order + 1) * num_samples, :] = tmp_b

# Compute Welch's t-test for all requested orders.
ttest = ttest1_hist_xy(x_a_ord, y_a_ord, x_b_ord, y_b_ord)

return np.reshape(ttest, (num_orders, num_samples))


def compute_statistics(num_orders, rnd_list, byte_list, histograms, x_axis):
""" Computing t-test statistics for a set of time samples.
"""
Expand Down Expand Up @@ -292,7 +169,7 @@ def compute_histograms_aes(trace_resolution, rnd_list, byte_list, traces, leakag
return histograms


def compute_leakage_aes(keys, plaintexts, leakage_model):
def compute_leakage_aes(keys, plaintexts, leakage_model = 'HAMMING_WEIGHT'):
"""
Sensitive variable is always byte-sized.

Expand Down Expand Up @@ -690,8 +567,7 @@ def run_tvla(ctx: typer.Context):
log.info("Computing Leakage")
leakage = Parallel(n_jobs=num_jobs)(
delayed(compute_leakage_aes)(keys[i:i + trace_step_leakage],
plaintexts[i:i + trace_step_leakage],
'HAMMING_WEIGHT')
plaintexts[i:i + trace_step_leakage])
for i in range(0, num_traces, trace_step_leakage))
leakage = np.concatenate((leakage[:]), axis=2)
if save_to_disk_leakage:
Expand Down
133 changes: 133 additions & 0 deletions util/ttest.py
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Open in desktop
Original file line number Diff line number Diff line change
@@ -0,0 +1,133 @@
#!/usr/bin/env python3
# Copyright lowRISC contributors.
# Licensed under the Apache License, Version 2.0, see LICENSE for details.
# SPDX-License-Identifier: Apache-2.0

import numpy as np
from scipy.stats import ttest_ind_from_stats

# A set of functions for working with histograms.
# The distributions are stored in two matrices x and y with dimensions (M, N) where:
# - M equals the number of time samples times the number of orders, and
# - N equals the number of values (i.e. the resolution).
# The matrices hold the following data:
# - x holds the values (all rows are the same for 1st order), and
# - y holds the probabilities (one probability distribution per row/time sample).


def mean_hist_xy(x, y):
"""
Computes mean values for a set of distributions.

Both x and y are (M, N) matrices, the return value is a (M, ) vector.
"""
return np.divide(np.sum(x * y, axis=1), np.sum(y, axis=1))


def var_hist_xy(x, y, mu):
"""
Computes variances for a set of distributions.

This amounts to E[(X - E[X])**2].

Both x and y are (M, N) matrices, mu is a (M, ) vector, the return value is a (M, ) vector.
"""

# Replicate mu.
num_values = x.shape[1]
mu = np.transpose(np.tile(mu, (num_values, 1)))

# Compute the variances.
x_mu_2 = np.power(x - mu, 2)
return mean_hist_xy(x_mu_2, y)


def ttest1_hist_xy(x_a, y_a, x_b, y_b):
"""
Basic first-order t-test.

Everything needs to be a matrix.
"""
mu1 = mean_hist_xy(x_a, y_a)
mu2 = mean_hist_xy(x_b, y_b)
std1 = np.sqrt(var_hist_xy(x_a, y_a, mu1))
std2 = np.sqrt(var_hist_xy(x_b, y_b, mu2))
N1 = np.sum(y_a, axis=1)
N2 = np.sum(y_b, axis=1)
return ttest_ind_from_stats(mu1,
std1,
N1,
mu2,
std2,
N2,
equal_var=False,
alternative='two-sided')[0]


def ttest_hist_xy(x_a, y_a, x_b, y_b, num_orders):
"""
Welch's t-test for orders 1,..., num_orders.

For more details see: Reparaz et. al. "Fast Leakage Assessment", CHES 2017.
available at: https://eprint.iacr.org/2017/624.pdf

x_a and x_b are (M/num_orders, N) matrices holding the values, one value vector per row.
y_a and y_b are (M/num_orders, N) matrices holding the distributions, one distribution per row.

The return value is (num_orders, M/num_orders)
"""

num_values = x_a.shape[1]
num_samples = y_a.shape[0]

#############
# y_a / y_b #
#############

# y_a and y_b are the same for all orders and can simply be replicated along the first axis.
y_a_ord = np.tile(y_a, (num_orders, 1))
y_b_ord = np.tile(y_b, (num_orders, 1))

#############
# x_a / x_b #
#############

# x_a and x_b are different on a per-order basis. Start with an empty array.
x_a_ord = np.zeros((num_samples * num_orders, num_values))
x_b_ord = np.zeros((num_samples * num_orders, num_values))

# Compute shareable intermediate results.
if num_orders > 1:
mu_a = mean_hist_xy(x_a, y_a)
mu_b = mean_hist_xy(x_b, y_b)
if num_orders > 2:
var_a = var_hist_xy(x_a, y_a, mu_a)
var_b = var_hist_xy(x_b, y_b, mu_b)
sigma_a = np.transpose(np.tile(np.sqrt(var_a), (num_values, 1)))
sigma_b = np.transpose(np.tile(np.sqrt(var_b), (num_values, 1)))

# Fill in the values.
for i_order in range(num_orders):
if i_order == 0:
# First order takes the values as is.
x_a_ord[0:num_samples, :] = x_a
x_b_ord[0:num_samples, :] = x_b
else:
# Second order takes the variance.
tmp_a = x_a - np.transpose(np.tile(mu_a, (num_values, 1)))
tmp_b = x_b - np.transpose(np.tile(mu_b, (num_values, 1)))
if i_order > 1:
# Higher orders take the higher order moments, and also divide by sigma.
tmp_a = np.divide(tmp_a, sigma_a)
tmp_b = np.divide(tmp_b, sigma_b)

# Take the power and fill in the values.
tmp_a = np.power(tmp_a, i_order + 1)
tmp_b = np.power(tmp_b, i_order + 1)
x_a_ord[i_order * num_samples:(i_order + 1) * num_samples, :] = tmp_a
x_b_ord[i_order * num_samples:(i_order + 1) * num_samples, :] = tmp_b

# Compute Welch's t-test for all requested orders.
ttest = ttest1_hist_xy(x_a_ord, y_a_ord, x_b_ord, y_b_ord)

return np.reshape(ttest, (num_orders, num_samples))