Bias

The response bias is one of the fundamental metrics for the response behavior of PUFs. Large response bias enable trivial modeling attacks on the PUF as the attacker can just guess the more likely of the two responses.

PUF bias is in the literature also known as balance or uniformity.

Note that per bit encoding in pypuf, a bias of zero means a perfectly unbiased behavior, whereas bias of -1 and 1 means that the PUF under test always returns -1 and 1, respectively. To convert the pypuf bias value \(b\) into the more traditional 0-1-scale, use \(1/2 - b/2\).

pypuf.metrics.bias(instance: Simulation, seed: int, N: int = 1000) → ndarray

Approximates the bias of a given simulation by generating N random challenges using seed seed and computing the bias for each of the \(m \geq 1\) response bits given by the instance,

\[b_l = E_x \left[ f(x)_l \right],\]

where \(f\) is the function computed by instance and \(f(x)_l, 1 \leq l \leq m\) is the \(l\)-th response bit.

Arbiter PUF simulations in pypuf per additive delay model almost unbiased:

>>> from pypuf.simulation import ArbiterPUF
>>> from pypuf.metrics import bias
>>> bias(ArbiterPUF(n=128, seed=42), seed=1)
-0.004

On the other hand, 2-XOR Arbiter PUFs can have relatively large bias [WP20].

>>> from pypuf.simulation import XORArbiterPUF
>>> bias(XORArbiterPUF(n=64, k=2, seed=2), seed=2)
-0.086

pypuf.metrics.bias_data(responses: ndarray) → ndarray

Given an arrays of responses of shape \((N, m)\), returns the \(m\) bias values of the response bits,

\[b_l = E_x \left[ f(x)_l \right],\]

where \(f\) is the function given by responses and \(f(x)_l, 1 \leq l \leq m\) is the \(l\)-th response bit.

If response length \(m\) is greater than 1, the bias is given for each bit seperately. To obtain the general bias, average the response.

Returns an array of shape \((m,)\).