IEEE Consumer Electronics Magazine - January/February 2022 - 11

Figure 3. Illustration of the rotation process in RAFV for both legitimate and Chaff points. (a) Fully constructed
fuzzy vault with five quadrants. (b) Overview of the top right quadrant of the vault before rotation. (c) Overview
of the top right quadrant of the vault after rotation.
random number generator which will randomly
choose which quadrant shall be rotated next.
The order of rotation has a significant impact on
the obscured vault as each rotation carried out
will fundamentally change the result. An illustration
of the rotation applied to the content of a
vault is shown in Figure 3. The first subfigure
[see Figure 3(a)] shows a fully constructed fuzzy
vault divided into five quadrants where there
is a set of legitimate points (highlighted in blue)
on a polynomial and chaff points (highlighted
in red) that are used to conceal the secret. The
second subfigure [see Figure 3(b)] depicts a
close up of the top-right quadrant of the vault
where its center point has been marked and a
rotation direction has been assigned to it. The
final subfigure [see Figure 3(c)] shows the same
quadrant after90 rotation has been applied,
where the rotated legitimate and Chaff points
are highlighted using the same color as their corresponding
original points but with increased
transparency.
To be able to recover the locked fuzzy vault,
the receiver should know the number of layers
present within the vault in addition to how many
rotations have been carried out. This information
must be communicated to the receiver,
alongside the obfuscated locked vault, and be
sent as plain text in a message appended to the
fuzzy vault. This is because such information
does not give the adversaries any advantage in
their attempts to recover the vault. Once this
information is obtained, the receiver can divide
the vault the same way the sender did in addition
to assigning the RSSI values and rotation
January/February 2022
order to each quadrant. The only difference,
however, is that the receiver must swap 90 rotation
with90 and vice versa in addition to
reversing the order of rotation.
Security Analysis of RAFV
Two parameters can be used to calculate the
size of the search space an adversary may face
when attempting to directly brute force the rotation
of the vault. These two parameters are the
number of quadrants assigned a unique RSSI bit
and the number of rotations carried out during
the locking phase. The search space can be calculated
using the following equation:
Searchspace ¼ 2n rn
(1)
where n is the number of quadrants and r is the
number of rotations. For example, an RAFVbased
vault that is locked using 85 quadrants
and 32 rotations would yield 285 3285
=
3:15 10153. However, whilst the search space is
exponentially large it is ultimately limited by the
size of the key agreed upon by the sender and
receiver within the RSSI reconciliation because
this key determines the rotation. Therefore, an
appropriate sized key must be picked to ensure
strong bit-security for the scheme to function.
For example, a 128-b key that has been agreed
upon by the two BAN nodes will ensure sufficient
protection against brute force attack as an
adversary would, on average, have to search half
of the key space, e.g., 2127, and use each key to
generate its rotation pattern and attempt the
unlocking process in full. As mentioned earlier in
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IEEE Consumer Electronics Magazine - January/February 2022

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