Logistic Regression Attack

The Logistic Regression Attack (LR Attack) was introduced by Rührmair et al. [RSSD10] to model XOR Arbiter PUFs. In pypuf, an modernized and optimized version of the LR attack is implemented using tensorflow. The original implementation is also available from the authors. A study of the data complexity of the LR attack using a different unpublished implementation of the LR attack was done by Tobisch and Becker [TB15].

Example Usage

To run the attack, CRP data of the PUF token under attack is required. Such data can be obtained through experiments on real hardware, or using a simulation. In this example, we use the pypuf XOR Arbiter PUF simulator:

>>> import pypuf.simulation, pypuf.io
>>> puf = pypuf.simulation.XORArbiterPUF(n=64, k=4, seed=1)
>>> crps = pypuf.io.ChallengeResponseSet.from_simulation(puf, N=50000, seed=2)

To run the attack, we configure the attack object with the challenge response data and attack parameters. The parameters need careful adjustment for each choice of security parameters in the PUF. Then the attack is run using the pypuf.attack.LRAttack2021.fit() method.

>>> import pypuf.attack
>>> attack = pypuf.attack.LRAttack2021(crps, seed=3, k=4, bs=1000, lr=.001, epochs=100)
>>> attack.fit()  # doctest:+ELLIPSIS +NORMALIZE_WHITESPACE
    Epoch 1/100
    ...
    50/50 [==============================] - ... - loss: 0.4... - accuracy: 0.9... - val_loss: 0.4643 - val_accuracy: 0.9620
    <pypuf.simulation.base.LTFArray object at 0x...>
>>> model = attack.model

The model accuracy can be measured using the pypuf accuracy metric pypuf.metrics.accuracy().

>>> import pypuf.metrics
>>> pypuf.metrics.similarity(puf, model, seed=4)
array([0.966])

Applicability

The Logistic Regression can be extended to other variants of the XOR Arbiter PUF [WBMS19]. This functionality is currently not yet included in pypuf, so that the user needs to perform the appropriate conversions before using pypuf.attack.LRAttack2021.

This implementation is also suitable to conduct the splitting attack on the Interpose PUF [WMPN19].

API

Performance

The pypuf implementation is tested using tensorflow 2.4 on Intel Xeon E5-2630 v4 attacking \(n\)-bit \(k\)-XOR Arbiter PUFs. The results below are compared with those of Tobisch and Becker [TB15], which have been obtained in 2015 using up to 16 cores.

n	k	CRPs	success rate	duration	cores	[TB15] / 16 cores
64	4	30k	10/10	<1 min	4	<1 min
64	5	260k	10/10	4 min	4	<1 min
64	6	2M	20/20	<1 min	4	1 min
64	7	20M	10/10	3 min	4	55 min
64	8	150M	10/10	28 min	4	391 min
64	9	350M				2266 min
64	9	500M	7/10	14 min	40
64	10	1B	6/10	41 min	40