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Ported everything to typst now

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Marius Drechsler 2024-07-17 21:26:25 +02:00
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content/introduction.typ
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@ -13,11 +13,14 @@ Vectors will be written in bold test: $bold(k)$ represents a vector of quantized
We will call a quantized symbol $k$. $k$ consists of all possible binary symbols, i.e. $0, 01, 110$.
A quantizer will be defined as a function $cal(Q)(x, bold(a))$ that returns a quantized symbol $k$.
We also define the following special quantizers for metric based HDAs:
A quantizer used during the enrollment phase is defined by a calligraphic $cal(E)$.
For the reconstruction phase, a quantizer will be defined by a calligraphic $cal(R)$
@example-quantizer shows the curve of a 2-bit quantizer that receives $tilde(x)$ as input. In the case, that the value of $tilde(x)$ equals one of the four bounds, the quantized value is chosen randomly from the relevant bins.
#figure(
include("../graphics/quantizers/two-metric-enroll.typ"),
include("../graphics/quantizers/two-bit-enroll.typ"),
caption: [Example quantizer function]) <example-quantizer>
For the S-Metric Helper Data Method, we introduce a function
@ -28,8 +31,12 @@ where s determines the amount of metrics and m the bit width of the symbols.
=== Tilde-Domain<tilde-domain>
AS also described in REFSMHD, we will use a CDF to transform the real PUF values into the Tilde-Domain
This transformation can be performed using the function $sym(xi) = tilde(x)$. The key property of this transformation is the resulting uniform distribution of $x$.
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
$ sym(xi)(frac(x - sym(mu))(sym(sigma))) = frac(1)(2)[1 + erf(frac(x - sym(mu))(sym(sigma) sqrt(2)))] $
$ xi(frac(x - mu, sigma)) = frac(1, 2)[1 + \e\rf(frac(x - mu, sigma sqrt(2)))] $
=== ECDF
The eCDF is constructed through sorting the empirical measurements of a distribution @dekking2005modern. Although less accurate, this method allows a more simple and less computationally complex way to transform real valued measurements into the Tilde-Domain. We will mainly use the eCDF in @chap:smhd because of the difficulty of finding an analytical description for the CDF of a Gaussian-Mixture.