IEEE Solid-States Circuits Magazine - Summer 2019 - 59

Acceptable 0/1 Bias

Acceptable
0/1 Bias

1

≥ 0.998

1
0.8

0.2
0
0

0.58

0.4

0.503

0.6
0.497

The on-chip availability of fixed keys
is essential in security, as exemplified by the retention of chip ID to unambiguously identify a device, the
protection of software intellectual
property (IP) running on a chip, the
remote attestation of hardware and
software integrity, and the creation
of a chip-specific root of trust that
depends on the underlying chip.
Traditionally, static entropy is simply generated off chip before deployment (e.g., at testing time) and stored
in a nonvolatile manner (e.g., fuses
and flash memory). However, such
storage methods are well known to
be vulnerable to a wide range of welldocumented attacks at the software
level as well as physical attacks ranging from noninvasive to invasive
(e.g., see [3], [22], [39], [64], [76], [77],
and [79]). To overcome the limitations of traditional key storage, it is
necessary to ensure that the following properties are met:
■ Physical inspection of the die (e.g.,
imaging and reverse engineering)
should not expose the secret, as
opposed to nonvolatile memories
and fuses.
■ The secret keys should be physically
available only when the chip is powered on, so that the adversary cannot retrieve the key when powered
off because, in this case, the device
would be vulnerable to physical attacks due to the related protection
techniques being disabled.
To overcome these challenges,
PUFs (i.e., physically unclonable functions) have been extensively explored
and more recently introduced in commercial chips and as a commercially
available design IP. From a behavioral
viewpoint (see Figure  4), PUFs are
ideally digital blocks that respond to
inputs (challenges) with perfectly repeatable outputs (responses), where
the input-output mapping is unpredictable and unknown to an external
observer. In PUFs, the responses are
not stored but recreated on the fly,

is necessarily coupled with a cryptoalgorithm). Accordingly, all generated
response bits of weak PUFs must be
perfectly stable when the same challenge is repeatedly applied because
even a single  bit cha nge would
completely disrupt the output of
the coupled crypto-algorithm. Weak
PUFs have been used for several security purposes, such as chip ID and
authentication [10], [27], [71], [80],
lightweight encryption [56], [93],
secure exchange of private keys with
no involvement of public-key cryptography [2], hardware-entangled
cryptography [103], identification of
malicious hardware [50], and strong
PUF creation via synergy with cryptoengines [18].
On the other hand, strong PUFs
exhibit a number of CRPs that increase exponentially with the silicon
area. The abundant availability of
CRPs in strong PUFs allows in-plain

0.42

Static Entropy Generation and PUFs

as defined by chip-specific random
(within-die) variations, thus requiring
the chip to be powered on to deliver
the responses and satisfy both previously described properties. The challenge-response pairs (CRPs) represent
the root of trust as stored in the form
of golden responses or golden keys
on a secure server at a preliminary
enrollment phase before chip deployment. After enrollment, CRPs are no
longer accessible from off chip, disabling the test port that previously
scanned out the CRPs.
PUFs can be categorized into two
classes. Weak PUFs exhibit a number
of CRPs that are approximately linear
with the PUF silicon area or the number of available PUF bit cells. The limited availability of CRPs in weak PUFs
mandates that CRPs are not disclosed
in plain over the insecure channel,
and they should instead be encrypted
or used as cryptokeys (i.e., the PUF

Entropy (b)

generation, as discussed in the following sections.

0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9
Pr (X = 0)
Shannon Entropy

Min-Entropy

FIGURE 3: The Shannon entropy and min-entropy versus Pr[0] as well as numerical examples of targets to keep the effective key-length degradation lower than 1 b in a 256-bit key.

In-Field Operation
(Use Shared Secret)
01101
Challenge

PUF
Die 1

1011010010
Response

Enrollment
(Preliminary
Secret Sharing)
FIGURE 4: The PUF operation at enrollment and in field.

IEEE SOLID-STATE CIRCUITS MAGAZINE

SU M M E R 2 0 19

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IEEE Solid-States Circuits Magazine - Summer 2019

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