diff --git a/.gitignore b/.gitignore new file mode 100644 index 00000000..1745f702 --- /dev/null +++ b/.gitignore @@ -0,0 +1,101 @@ +# Byte-compiled / optimized / DLL files +__pycache__/ +*.py[cod] +*$py.class + +# C extensions +*.so + +# Distribution / packaging +.Python +env/ +build/ +develop-eggs/ +dist/ +downloads/ +eggs/ +.eggs/ +lib/ +lib64/ +parts/ +sdist/ +var/ +wheels/ +*.egg-info/ +.installed.cfg +*.egg + +# PyInstaller +# Usually these files are written by a python script from a template +# before PyInstaller builds the exe, so as to inject date/other infos into it. +*.manifest +*.spec + +# Installer logs +pip-log.txt +pip-delete-this-directory.txt + +# Unit test / coverage reports +htmlcov/ +.tox/ +.coverage +.coverage.* +.cache +nosetests.xml +coverage.xml +*,cover +.hypothesis/ + +# Translations +*.mo +*.pot + +# Django stuff: +*.log +local_settings.py + +# Flask stuff: +instance/ +.webassets-cache + +# Scrapy stuff: +.scrapy + +# Sphinx documentation +docs/_build/ + +# PyBuilder +target/ + +# Jupyter Notebook +.ipynb_checkpoints + +# pyenv +.python-version + +# celery beat schedule file +celerybeat-schedule + +# SageMath parsed files +*.sage.py + +# dotenv +.env + +# virtualenv +.venv +venv/ +ENV/ + +# Spyder project settings +.spyderproject + +# Rope project settings +.ropeproject + +# mkdocs documentation +/site + +# IDE +.idea + diff --git a/LICENSE.txt b/LICENSE.txt new file mode 100644 index 00000000..94a9ed02 --- /dev/null +++ b/LICENSE.txt @@ -0,0 +1,674 @@ + GNU GENERAL PUBLIC LICENSE + Version 3, 29 June 2007 + + Copyright (C) 2007 Free Software Foundation, Inc. + Everyone is permitted to copy and distribute verbatim copies + of this license document, but changing it is not allowed. + + Preamble + + The GNU General Public License is a free, copyleft license for +software and other kinds of works. + + The licenses for most software and other practical works are designed +to take away your freedom to share and change the works. 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If not, see . + +Also add information on how to contact you by electronic and paper mail. + + If the program does terminal interaction, make it output a short +notice like this when it starts in an interactive mode: + + Copyright (C) + This program comes with ABSOLUTELY NO WARRANTY; for details type `show w'. + This is free software, and you are welcome to redistribute it + under certain conditions; type `show c' for details. + +The hypothetical commands `show w' and `show c' should show the appropriate +parts of the General Public License. Of course, your program's commands +might be different; for a GUI interface, you would use an "about box". + + You should also get your employer (if you work as a programmer) or school, +if any, to sign a "copyright disclaimer" for the program, if necessary. +For more information on this, and how to apply and follow the GNU GPL, see +. + + The GNU General Public License does not permit incorporating your program +into proprietary programs. If your program is a subroutine library, you +may consider it more useful to permit linking proprietary applications with +the library. If this is what you want to do, use the GNU Lesser General +Public License instead of this License. But first, please read +. diff --git a/README.md b/README.md new file mode 100644 index 00000000..88655aba --- /dev/null +++ b/README.md @@ -0,0 +1,10 @@ +pypuf +============= + +Python package to simulate and learn Physically Unclonable Functions. + +Introduction +------------ + +Please see `sim_learn.py` for example usage. + diff --git a/pypuf/__init__.py b/pypuf/__init__.py new file mode 100644 index 00000000..e69de29b diff --git a/pypuf/learner.py b/pypuf/learner.py new file mode 100644 index 00000000..21f2cb95 --- /dev/null +++ b/pypuf/learner.py @@ -0,0 +1,114 @@ +from numpy import sign, dot, around, exp, array, seterr, minimum, abs, full, count_nonzero +from pypuf import simulation + + +class LogisticRegression(): + + class ModelUpdate(): + + def __init__(self, model): + self.model = model + + def update(self, gradient): + #print('model weight array:\n%s' % self.model.weight_array) + #print('gradient:\n%s' % gradient) + return -.3 * gradient + + def __init__(self, training_set, n, k, mu=0, sigma=1): + self.set = training_set + self.n = n + self.k = k + self.mu = 0 + self.sigma = 1 + self.iteration_limit = 100 + self.convergence_decimals = 3 + self.sign_combined_model_responses = None + self.derivative = full(self.set.N, None) + self.min_distance = 1 + + assert self.n == len(training_set.challenges[0]) + + def gradient(self, model): + # compute model responses + model_responses = model.ltf_eval(self.set.challenges) + combined_model_responses = model.combiner_xor(model_responses) + self.sign_combined_model_responses = sign(combined_model_responses) + + # cab the absolute value of this to avoid overflow errors + MAX_RESPONSE_ABS_VALUE = 50 + combined_model_responses = sign(combined_model_responses) * \ + minimum( + full(len(combined_model_responses), MAX_RESPONSE_ABS_VALUE), + abs(combined_model_responses) + ) + + # compute the class probability(?) from + # the (-1,+1)-interval-sigmoid of combined model response on the all inputs + # and the training set responses + self.derivative = .5 * (2 / (1 + exp(-combined_model_responses)) - 1 - self.set.responses) + + ret = array([ + dot( + self.derivative + * + # estimated responses of the l-th LTF, derived from the real total value + # and the (k-1) modelled values + combined_model_responses / model_responses[:,l], + self.set.challenges + ) + for l in range(self.k) + ]) + return ret + + def learn(self): + # let numpy raise excpetions + seterr(all='raise') + + # we start with a random model + model = simulation.LTFArray( + weight_array=simulation.LTFArray.normal_weights(self.n, self.k, self.mu, self.sigma), + transform=simulation.LTFArray.transform_id, + combiner=simulation.LTFArray.combiner_xor, + ) + + updater = self.ModelUpdate(model) # TODO use RProp + + i = 0 + converged = False + distance = 1 + while not converged and distance > .01 and i < self.iteration_limit: + i += 1 + + # compute gradient & update model + gradient = self.gradient(model) + self.print_status(model) + model.weight_array += updater.update(gradient) + + # check convergence + converged = ( + [0] * self.n == + around(gradient, decimals=self.convergence_decimals) + ).all() + + # check accuracy + distance = (self.set.N - count_nonzero(self.set.responses == self.sign_combined_model_responses)) / self.set.N + self.min_distance = min(distance, self.min_distance) + + if not converged and distance > .01: + print('WARNING, MODEL DID NOT CONVERGE') + + return model + + def print_status(self, model): + return # debug output disabled + print('\nLR Training Set vs. Model Responses vs. Class Probability\n----------------------------------------------------------') + for (idx,c) in enumerate(self.set.challenges): + print(' '.join(['%+1d' % ci for ci in c]) + + ' => ' + + ('+1' if self.set.responses[idx] == 1 else '-1') + + ' ' + + ' '.join([('%+ 7.2f' % mr) for mr in model.ltf_eval([c])[0]]) + + ' ' + + ('% 10.5f' % self.class_probability[idx]) + ) + diff --git a/pypuf/simulation.py b/pypuf/simulation.py new file mode 100644 index 00000000..047c9b7c --- /dev/null +++ b/pypuf/simulation.py @@ -0,0 +1,66 @@ +from numpy import prod, shape, random, sign, dot, concatenate, array + + +class LTFArray(): + """ + Class that simulates k LTFs with n bits and a constant term each. + """ + + @staticmethod + def combiner_xor(r): + """ + combines output responses with the XOR operation + :param r: a list with a number of vectors of single LTF results + :return: a list of full results, one for each + """ + return prod(r, 1) + + @staticmethod + def transform_id(c, l): + """ + Input transformation that does nothing. + :return: + """ + return c + + @staticmethod + def normal_weights(n, k, mu=0, sigma=1): + """ + Returns weights for an array of k LTFs of size n each. + The weights are drawn from a normal distribution with given + mean and std. deviation, if parameters are omitted, the + standard normal distribution is used. + """ + return random.normal(loc=mu, scale=sigma, size=(k, n)) + + def __init__(self, weight_array, transform, combiner): + (self.k, self.n) = shape(weight_array) + self.weight_array = weight_array + self.transform = transform + self.combiner = combiner + + def eval(self, inputs): + """ + evaluates a given list of challenges + :param x: list of challenges + :return: list of responses + """ + return sign(self.val(inputs)) + + def val(self, inputs): + return self.combiner(self.ltf_eval(inputs)) # TODO input transform + + def ltf_eval(self, inputs): + """ + :return: array + """ + return array([ + [ + dot( + x, + self.weight_array[l] + ) + for l in range(self.k) + ] + for x in inputs + ]) diff --git a/pypuf/tools.py b/pypuf/tools.py new file mode 100644 index 00000000..9286681d --- /dev/null +++ b/pypuf/tools.py @@ -0,0 +1,54 @@ +from numpy import random, count_nonzero +import itertools + + +def random_input(n): + """ + returns a random {-1,1}-vector of length `n`. + """ + return random.choice((-1, +1), n) + + +def all_inputs(n): + """ + returns an iterator for all {-1,1}-vectors of length `n`. + """ + return itertools.product((-1, +1), repeat=n) + + +def random_inputs(n, num): + """ + returns an iterator for a random sample of {-1,1}-vectors of length `n` (with replacement). + """ + for i in range(num): + yield random_input(n) + + +def sample_inputs(n, num): + """ + returns an iterator for either random samples of {-1,1}-vectors of length `n` if `num` < 2^n, + and an iterator for all {-1,1}-vectors of length `n` otherwise. + Note that we return only 2^n vectors even with `num` > 2^n. + In other words, the output of this function is deterministic if and only if num >= 2^n. + """ + return random_inputs(n, num) if num < 2**n else all_inputs(n) + + +def approx_dist(a, b, num): + """ + approximate the distance of two functions a, b by evaluating a random set of inputs. + a, b needs to have eval() method and input_length member. + :return: probability (randomly uniform x) for a.eval(x) != b.eval(x) + """ + assert a.n == b.n + d = 0 + inputs = list(random_inputs(a.n, num)) + return (num - count_nonzero(a.eval(inputs) == b.eval(inputs))) / num + + +class TrainingSet(): + + def __init__(self, instance, N): + self.challenges = list(sample_inputs(instance.n, N)) + self.responses = instance.eval(self.challenges) + self.N = N diff --git a/sim_learn.py b/sim_learn.py new file mode 100644 index 00000000..e682a9d9 --- /dev/null +++ b/sim_learn.py @@ -0,0 +1,33 @@ +from numpy import random +from pypuf import simulation, learner, tools +import time + + +n = 64 +k = 2 +N = 6000 +restarts = 3 + +print('Learning %s-bit %s XOR Arbiter PUF with %s CRPs and %s restarts.\n' % (n, k, N, restarts)) + +random.seed(0xbeef) # reproduce 'random' numbers, remove to obtain different results + +instance = simulation.LTFArray( + weight_array=simulation.LTFArray.normal_weights(n, k), + transform=simulation.LTFArray.transform_id, + combiner=simulation.LTFArray.combiner_xor, +) + +lr_learner = learner.LogisticRegression( + tools.TrainingSet(instance=instance, N=N), + n, + k, +) + +for i in range(restarts): + print('%i/%i ---------------------------------' % (i+1, restarts)) + start = time.time() + model = lr_learner.learn() + print('training time: % 5.3fs' % (time.time() - start)) + print('min training distance: % 5.3f' % lr_learner.min_distance) + print('test distance (1000 samples): % 5.3f\n' % tools.approx_dist(instance, model, min(1000, 2**n))) diff --git a/test/__init__.py b/test/__init__.py new file mode 100644 index 00000000..e69de29b diff --git a/test/test_simulation.py b/test/test_simulation.py new file mode 100644 index 00000000..0c2a6944 --- /dev/null +++ b/test/test_simulation.py @@ -0,0 +1,108 @@ +import unittest +from pypuf import simulation +from numpy.testing import assert_array_equal +from numpy import shape, dot, random, prod + + +class TestCombiner(unittest.TestCase): + + def test_combine_xor(self): + assert_array_equal( + simulation.LTFArray.combiner_xor( + [ + [ 1, 1, -3, 1], + [-1, -1, -1, 1], + [-2, -2, 2, 1] + ] + ), + [ + -3, + -1, + 8 + ] + ) + + +class TestInputTransformation(unittest.TestCase): + + def test_id(self): + test_array = [ + [ + [-1, 1, 1, -1, -1], + [-1, -1, -1, -1, -1], + [ 1, 1, -1, -1, -1], + ], + [ + [ 1, 1, 1, -1, -1], + [-1, -1, -1, -1, -1], + [-1, 1, -1, -1, -1], + ], + [ + [-1, 1, 1, -1, -1], + [-1, -1, -1, -1, -1], + [-1, 1, -1, -1, -1], + ] + ] + for l in range(5): + assert_array_equal( + simulation.LTFArray.transform_id(test_array, l), + test_array + ) + + +class TestLTFArray(unittest.TestCase): + + test_set = [ + # n, k, mu, sigma + (64, 4, 0, 1), + (4, 16, 0, 1), + (16, 4, 10, .5), + ] + + def test_random_weights(self): + for test_parameters in self.test_set: + n = test_parameters[0] + k = test_parameters[1] + mu = test_parameters[2] + sigma = test_parameters[3] + self.assertTupleEqual(shape(simulation.LTFArray.normal_weights(n, k, mu, sigma)), (k, n)) + + def test_ltf_eval(self): + """ + Test ltf_eval for correct evaluation of LTFs. + This is a probabilistic test, relying on random input. + """ + + N = 100 # number of random inputs per test set + + def ltf_eval_slow(x, w): + """ + evaluate a single input x with a single ltf specified by weights w + """ + assert len(x) == len(w) + return dot(x, w) + + for test_parameters in self.test_set: + n = test_parameters[0] + k = test_parameters[1] + mu = test_parameters[2] + sigma = test_parameters[3] + + inputs = random.choice([-1,+1], (N, n)) + + ltf_array = simulation.LTFArray( + weight_array=simulation.LTFArray.normal_weights(n, k, mu, sigma), + transform=simulation.LTFArray.transform_id, + combiner=simulation.LTFArray.combiner_xor, + ) + + fast_evaluation_result = ltf_array.ltf_eval(inputs) + slow_evaluation_result = [] + for x in inputs: + slow_evaluation_result.append( + [ ltf_eval_slow(x, ltf_array.weight_array[l]) for l in range(k) ] + ) + + self.assertTupleEqual(shape(slow_evaluation_result), (N, k)) + self.assertTupleEqual(shape(fast_evaluation_result), (N, k)) + assert_array_equal(slow_evaluation_result, fast_evaluation_result)