In "Memory Leakage-Resilient Encryption based on Physically Unclonable Functions" (ASIACRYPT2009), the authors use a construction based on a PUF and a Fuzzy Extractor and argue that this yields a Memory-leakage resilient encryption.
The definition of a Fuzzy Extractor is the following:
A $\left(m,n,\delta,\mu_{FE},\epsilon_{FE}\right)$-fuzzy extractor $\mathsf{E}$ is a pair of randomized procedures, "generate" $\mathsf{Gen}:\{0,1\}^m\to\{0,1\}^n\times\{0,1\}^{*}$ and "reproduce" $\mathsf{Rep}:\{0,1\}^m\to\{0,1\}^*\times\{0,1\}^{n}$.
The correctness property guarantees that for $(z,\omega)\leftarrow\mathsf{Gen}(y)$ and $y'\in\{0,1\}^m$ with $\mathsf{dist}\left(y,y'\right)\leqslant\delta$, then $\mathsf{Rep}\left(y',\omega\right)=z$. If $\mathsf{dist}\left(y,y'\right)>\delta$, then no guarantee is provided about the output of $\mathsf{Rep}$.
The security property guarantees that for any distribution $\mathbb{D}$ on $\{0,1\}^m$ of min-entropy $\mu_{FE}$, the string $z$ is nearly uniform even for those who observe $\omega$: if $(z,\omega)\leftarrow\mathsf{Gen}(\mathbb{D})$, then it holds that $SD\left((z,\omega),\left(\mathbb{U}_n,\omega\right)\right)\leqslant\epsilon_{FE}$.
Where $\mathbb{U}_n$ is the uniform distribution on $[n]$. From my understanding, the authors then define an encryption scheme based on $\mathsf{Gen}\circ\Pi$, where $\Pi$ is a PUF. They model the resources the adversary get access to by the helper data, namely $\omega$.
However, I don't understand why is this model realistic. In a memory-leakage situation, the adversary should be able to learn information on the plaintext. Though they argue that this is the case when usign Fuzzy Extractors, I can't convince myself that this model isn't a tautology. Of course, if the adversary is only given some helper data that looks random anyway because of the security guarantee of the Fuzzy Extractor, surely the model is secure.
Hence my question: why do we consider the Fuzzy-Extractors to be a good model for memory leakage?
