QKD WIP

chapter-qkd/chapter.tex

@@ -1,7 +1,7 @@
-\documentclass[12pt,a4paper,notitlepage]{report}
+\documentclass[12pt,a4paper,notitlepage,twoside]{report}
 \usepackage[ngerman, english]{babel}
 \usepackage[utf8]{inputenc}
-\usepackage[a4paper, top=2cm, bottom=3.5cm, left=3.5cm, right=5cm]{geometry}
+\usepackage[a4paper, top=2cm, bottom=3.5cm, inner=3.5cm, outer=5cm]{geometry}
 % Matti remarkable tablet special size
 %\usepackage[paperwidth=15cm, paperheight=244mm, top=1cm, bottom=1cm, left=5mm, right=5mm]{geometry}
 \usepackage[T1]{fontenc}
@@ -182,6 +182,44 @@ algorithm can easily be compensated by doubling key size. Longer key sizes requi
 additional bits and result in slightly slower operation of the cipher, but this additional cost is easily manageable
 even without any improvement in today's hardware.
 
+\textcite{impagliazzoPersonalViewAveragecase1995} provided a colloquial but useful analysis characterizing the
+implications of which kinds of hard problems are solvable in practice, based on the observation that the fact that an
+\emph{average} problem out of a class like $NP$ is solvable does not mean that most, or even many \emph{practical}
+problems are solvable. \textcite{impagliazzoPersonalViewAveragecase1995} was published after Shor's algorithm was
+discovered, and before Grover's algorithm was published. Impagliazzo foresaw that fast quantum algorithms could threaten
+public-key security, and their analysis remains relevant facing the outlook of quantum computing today.
+
+Impagliazzo proposes a set of five scenarios that provide increasingly extensive computational hardness properies,
+dubbed \emph{Algorithmica}, \emph{Heuristica}, \emph{Pessiland}, \emph{Minicrypt}, and \emph{Cryptomania}. In
+Algorithmica, $P = NP$. In Heuristica, $P \ne NP$, but $NP$ problems are only intractable in the worst case, and
+tractable on average. In Pessiland, problems exist that are hard on average, but there are no one-way functions and thus
+there is no way to efficiently sample solved instances of hard problems.
+
+The next scenario, Minicrypt is frequently cited in cryptographic works. In it, one-way functions exist, but there is no
+public key cryptography. Minicrypt aligns well with a world in which fast quantum algorithms exist that solve the
+computational problems underlying public-key cryptosystems. Impagliazzo's last scenario is Cryptomania, which extends
+Minicrypt with public-key cryptography and aligns with the world view that is commonly assumed in cryptography today.
+
+In Mincrypt, we assume that all computational problems that are amenable to public key cryptography fall. However, it is
+not specified \emph{how} specifically this fall will happen---whether it will be classically, or by quantum
+algorithms---leading to two sub-variants of the Minicrypt scenario. The pessimistic sub-variant is one where classical
+algorithms solving all those problems are discovered. This scenario leads to identical conclusions to those Impagliazzo
+drew. However, if we base our Minicrypt assumption instead on the availability of \emph{quantum } algorithms for these
+problems, and thus on quantum computers being both powerful enough and generally available, we end up with an
+interesting spin on the original Minicrypt scenario that recently has garnered some academic attention, receiving the
+name Mini\textbf{Q}Crypt\cite{griloObliviousTransferMiniQCrypt2021, barootiPublicKeyEncryptionQuantum2023}. In
+MiniQCrypt, on one hand, conventional public key cryptography falls before quantum computers, but the key observation is
+that on the other hand, we can then use those quantum computers to do \emph{quantum} cryptography, re-gaining some of
+what we lost. The (im)possibility results for MiniQCrypt are nuanced, and provide something between the intact
+conventional public-key cryptography in Cryptomania, and the total absence of it in classical Minicrypt.
+
+In the discourse on quantum computing and its application to cryptography, it is important to be mindful of which
+security notion the authors of some source, or the implementors of some device base their work on. Especially in
+academic work, Pessiland assumptions are often implicitly made. In this model, we can use neither public-key nor
+symmetric cryptography. In this framework, secret key rate becomes paramount because it is assumed that QKD keys will be
+used with an information-theoretically secure encryption scheme, requiring a never-ending secret key stream. Key
+expansion functions are based on one-way-functions, which are unavailable here.
+
 \section{The Practical Security Implications of Quantum Computing}
 \label{qc-practical-implications}
 
@@ -273,8 +311,7 @@ disadvantage of doing that is that it consumes a fraction of the system's precio
 this point there is ongoing research\todo{citations on ongoing research} on both systems based on symmetric MACs and
 systems using information-theoretically secure MACs, with commercial systems often choosing the
 latter\cite{bibakQuantumKeyDistribution2021} owing to the low secure key rates that are the state of the art.
-
-% \textcite{impagliazzoPersonalViewAveragecase1995}
+\todo{Finish this section}
 
 \subsection{The Technical Implementation of QKD}