IEEE Solid-States Circuits Magazine - Summer 2019 - 60

transmission of CRPs because replay
attacks are inherently prevented by
the very low probability of reusing a
CRP. This enables the adoption of the
popular and particularly simple security protocols based on CRP exchange,
where the response is compared to
the golden response in the server.
As a major difference with respect to
weak PUFs, such protocols for strong
PUFs can forgive the instability of a
limited number of bits in the response
(e.g., by associating the correctness of
a response to the adequate closeness
to the golden value rather than to bitaccurate matching). In other words,
bit stability in strong PUFs is relaxed
compared to that in weak PUFs.

PUF Quality and
Fundamental Metrics
PUFs are essentially made up of circuits that magnify within-die variations while rejecting the effect of all
other variation contributions, such as
■ die to die-to maintain uniform
statistical properties of the response across dice
■ voltage and temperature-so that
the responses are nearly independent of their inevitable fluctuations
■ aging-to maintain consistent response throughout the life of the
device.
The quality of a PUF is assessed
through a number of well-established
metrics that quantify the PUF response
stability, degree of randomness, sen-

sitivity to variations, area and energy
efficiency, and so on [7]. As the first
metric for PUF stability, the unstable
bit count is the cumulative count of occasionally flipping bits over the whole
population of PUF bit cells for a given
number of repeated iterations under the
same challenge. The unstable bit count
provides information on the worst-case
incorrect bit count under the pessimistic assumption that all bits can be simultaneously flipped (e.g., they exhibit
correlation, whereas their actual flipping might also be affected by random
phenomena such as thermal noise) and
no stability-enhancement method is introduced. As a more relevant stability
metric, the bit error rate (BER) counts
the average of the simultaneous instability for the PUF word output, which,
in turn, sets the key error rate (KER)
(i.e., the probability of having at least
one flipped bit in a response). Because
an incorrect key leads to a failing transaction (e.g., in the communication between two devices), the KER needs to
be kept low enough so that the medium
time before fault (MTBF) is comparable
to, or at least a significant fraction of,
the life of the device.
By definition, the MTBF is the ratio of the average PUF interaccess
time t inter-access (i.e., the time between
two successive PUF accesses) and the
probability of the KER having a PUF
failure due to instability. In a typical case of a duty-cycled sensor node
where a measurement is taken every

1E + 12

MTBF (s)

1E + 10
10 Years
One Year
One Month

1E + 08
1E + 06
1E + 04
1E + 02

1E + 00
1E - 07 1E - 06 1E - 05 1E - 04 1E - 03 1E - 02 1E - 01
PUF KER
PUF Interaccess Time = 1 s
PUF Interaccess Time = 1 h

PUF Interaccess Time = 1 min
PUF Interaccess Time = 1 Day

FIGURE 5: The PUF MTBF versus KER for various PUF interaccess times.

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IEEE SOLID-STATE CIRCUITS MAGAZINE

time the node is woken up, t inter-access
is simply the wake-up period [2] (i.e.,
the period following which the node
moves to the active mode after entering sleep mode). As per the plot in Figure 5, a reasonable MTBF on the order
of years requires the KER to be on the
order of a typical target of 10 -6 in a
PUF with t inter-access = 1 min. Such KER
targets can be relaxed by two orders
of magnitude or more when t inter-access
increases to hours or longer.
The repeatability of the responses
is quantified by the average intra-PUF
Hamming distance (HD) between the
response and the golden key (i.e., the
number of bits by which they differ)
[50]. Better repeatability makes the intra-PUF HD closer to the ideal value of
0. The PUF uniqueness is quantified by
the inter-PUF HD as defined by the average HD between the responses to the
same challenge coming from different
dice [50]. If perfectly random, the response of two dice to the same challenge would differ by 50% of their bits
on average. In actual PUF implementations, the inter-PUF HD is statistically
distributed, and the deviation of its
average from the ideal value measures
how unique (i.e., chip specific) the PUF
responses are. The identifiability is related to both the intra- and inter-PUF
HD, as a PUF in a die is easier to identify from other dice if the inter-PUF HD
is large (i.e., close to 50%) and the intra-PUF HD is small (i.e., close to 0). Accordingly, the identifiability is defined
as the ratio of the average intra- and
inter-PUF HD [50].
The randomness of the responses
is measured by various metrics. The
most immediate is the 0/1 bias (i.e.,
the probability of having a 0 or a 1), the
difference of which compared to the
ideal 50% value is a proxy for the level
of randomness degradation. Being interdependent (see the "Entropy Generation" section), the Shannon entropy
of the responses is routinely used as a
metric. The more stringent suite of National Institute of Standards and Technology (NIST) statistical pass/fail tests
[72] is routinely used to assess whether an adequate level of randomness is
achieved. The 0/1 bias requirement
IEEE Solid-States Circuits Magazine - Summer 2019

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