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Marius Drechsler 2024-08-21 21:23:33 +02:00
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content/introduction.typ
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#import "@preview/glossarium:0.4.1": *
#import "@preview/bob-draw:0.1.0": *
= Introduction
#gls("puf", display: "Physical unclonable functions (PUF)")
In the field of cryptography, @puf devices are a popular tool for key generation and storage.
In general, a @puf describes a kind of circuit that issues due to minimal deviations in the manufacturing process slightly different behaviours during operation.
Since the behaviour of one @puf device is now only reproducible on itself and not on a device of the same type with the same manufacturing process, it can be used for secure key generation and/or storage.\
To improve the reliability of the keys generated and stored using the @puf, various #glspl("hda") have been introduced.
The general operation of a @puf with a @hda can be divided into two separate stages: _enrollment_ and _reconstruction_.
During enrollment, a @puf readout $v$ is generated upon which helper data $h$ is generated.
At reconstruction, a slightly different @puf readout $v^*$ is generated.
Using the helper data $h$ the new @puf readout $v^*$ can be improved to be less deviated from $v$ as before.
This process of helper-data generation is generally known as _Fuzzy Commitment_.
Previous works already introduced different #glspl("hda") with various strategies.
The simplest form of helper-data one could generate is reliability information for every @puf bit.
Here, the @hda marks unreliable @puf bits that are then either discarded during reconstruction or rather corrected using a repetition code after the quantization process.
Going on, publications @tmhd1, @tmhd2 and @smhd already introduced a metric-based @hda.
These #glspl("hda") generate helper data during enrollment to define multiple quantizers for the reconstruction phase to minimize the risk of bit errors.
As a newly proposed @hda, we will propose a method to shape the input values of a @puf to better fit inside the bounds of a multi-bit quantizer.
We will explore the question which of these two #glspl("hda") provides the better performance for higher order bit cases using the least amount of helper-data bits possible.
== Notation
To ensure a consistent notation of functions and ideas, we will now introduce some conventions
To ensure a consistent notation of functions and ideas, we will now introduce some conventions and definitions.
Random distributed variables will be notated with a capital letter, i.e. $X$, its realization will be the corresponding lower case letter, $x$.
Vectors will be written in bold text: $bold(k)$ represents a vector of quantized symbols.
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=== Tilde-Domain<tilde-domain>
AS also described in @smhd, we will use a CDF to transform the real PUF values into the Tilde-Domain
As also described in @smhd, we will use a CDF to transform the real PUF values into the Tilde-Domain
This transformation can be performed using the function $xi = tilde(x)$. The key property of this transformation is the resulting uniform distribution of $x$.
Considering a normal distribution, the CDF is defined as