From cabca1217824c877e35df28b6f6ff6eec4e52939 Mon Sep 17 00:00:00 2001
From: Keno Goertz <git@kenogo.org>
Date: Tue, 25 Mar 2025 13:29:24 +0100
Subject: [PATCH] Add section on random-witness time-stamping

---
 chapters/01_introduction.tex                  |  19 ++++++++++++++++++
 .../backdating_probability_hypergeometric.pdf | Bin 147250 -> 147250 bytes
 ...g_probability_hypergeometric_available.pdf | Bin 177795 -> 177795 bytes
 figures/backdating_probability_noncentral.pdf | Bin 162322 -> 162322 bytes
 ...ating_probability_noncentral_available.pdf | Bin 192814 -> 192814 bytes
 figures/dos_hypergeometric.pdf                | Bin 212397 -> 212397 bytes
 figures/dos_noncentral.pdf                    | Bin 227415 -> 227415 bytes
 glossary.tex                                  |   1 +
 main.tex                                      |   2 +-
 thesis.pdf                                    | Bin 464891 -> 467123 bytes
 10 files changed, 21 insertions(+), 1 deletion(-)

diff --git a/chapters/01_introduction.tex b/chapters/01_introduction.tex
index 547cb48..5e29141 100644
--- a/chapters/01_introduction.tex
+++ b/chapters/01_introduction.tex
@@ -313,3 +313,22 @@ A document owner can directly send her document hash and the current time to $n$
 By sending $n'$ witness signatures to a verifier, the document owner can prove the validity of her time-stamp.
 
 \subsubsection{\label{section::random_witness}Random-witness time-stamping}
+
+\citeauthor{Haber1991Timestamp} proposed using a pseudo-random number generator (PRNG) to ensure uniformly distributed random witness selection for the purpose of distributed time-stamping.\footfullcite{Haber1991Timestamp}
+Each participating witness is initially assigned a unique identifier.
+The document owner can then seed the PRNG with the hash of her document and interpret the PRNG's output as witness identifiers.
+This way, she selects the $n$ witnesses responsible for signing her time-stamp.
+To confirm the time-stamp's validity, a verifier first checks the witness signatures.
+She then verifies that the $n$ identifiers produced by the PRNG when seeded with the document's hash are a superset of the identifiers corresponding to the $n'$ witness signatures.
+
+This scheme is secure if the hash function applied to the document has the \emph{one-way} property:
+Given a desired output hash, it should be computationally hard to find an input for which the hash function produces this output.
+If the hash function did not have this property, a document owner could possibly carry out a backdating attack by colluding with at least $n'$ witnesses.
+She would be able to construct a meaningful document such that the witnesses selected by the PRNG would be those colluding with her ($\omega\rightarrow\infty$).
+
+Another security requirement is that the PRNG produces uniformly distributed identifiers.
+A non-uniform distribution could again potentially be exploited ($\omega>1$) to increase the probability of a successful backdating or DoS attack.
+
+The random-witness scheme proposed by \citeauthor{Haber1991Timestamp} is desirable if we are not sure that Equations~\eqref{equation::backdating_protection} and \eqref{equation::dos_protection} hold, and hence want to ensure $\omega=1$ to minimize the probability of successful backdating and DoS attacks.
+
+\subsubsection{Threshold cryptography}
diff --git a/figures/backdating_probability_hypergeometric.pdf b/figures/backdating_probability_hypergeometric.pdf
index bbd524fb547587f656f4e05ff3bd7dda15f78b9c..a5b84078a12b3da846ecf91a482377f5551b3aa5 100644
GIT binary patch
delta 25
hcmdn=k7Lt6j)oS-Elh<rtj0!`2FBaVY?$^i0RV`F2?ziH

delta 25
hcmdn=k7Lt6j)oS-Elh<rtcHe`CZ^lVY?$^i0RV`T2@3!K

diff --git a/figures/backdating_probability_hypergeometric_available.pdf b/figures/backdating_probability_hypergeometric_available.pdf
index 66df23ac43cc2726a0957dcc68ee741570a400c1..5ea44effa54728bcbafeb92f2e4d2262e29f7847 100644
GIT binary patch
delta 25
gcmZpE%hmjrtD%K)3scc%R%0Ve1C#CLo0)i+0fXNN&Hw-a

delta 25
gcmZpE%hmjrtD%K)3scc%RzpKe6Z7rmo0)i+0fY1i(f|Me

diff --git a/figures/backdating_probability_noncentral.pdf b/figures/backdating_probability_noncentral.pdf
index 7c145beac548d730f99e71bc0c6f39a544476683..17c537baa2a0ea398744ec16d0d3ad2a6911fd41 100644
GIT binary patch
delta 25
gcmbRAg>%vu&W0AoEliB%tj0!`2FBaj%9(hW0eeaZod5s;

delta 25
gcmbRAg>%vu&W0AoEliB%tcHe`CT82&%9(hW0efEup#T5?

diff --git a/figures/backdating_probability_noncentral_available.pdf b/figures/backdating_probability_noncentral_available.pdf
index 9977583f3fc05bb614e90bdb59b2c7906ece9cd9..2112e1e483c0dcbf9ee8e8362f7f66a9c275490a 100644
GIT binary patch
delta 25
hcmZ4Yh<n{5?uHh|Elg+MvKkv%8klas^p+`x832_+3X1>$

delta 25
hcmZ4Yh<n{5?uHh|Elg+MvKks%nwW3D^p+`x832_~3XT8(

diff --git a/figures/dos_hypergeometric.pdf b/figures/dos_hypergeometric.pdf
index 0ea5d6ca971264393931493dfa8980945ef92789..dbe4ab9dea618cc2f39a64543342b89217f6ab02 100644
GIT binary patch
delta 27
icmZ4cn`iBBo`x327N#xCK31&8MwSL9+XJnbW0(P!ehAzE

delta 27
icmZ4cn`iBBo`x327N#xCK31%ThL$E~+XJnbW0(P!j0oQV

diff --git a/figures/dos_noncentral.pdf b/figures/dos_noncentral.pdf
index 84a3cd1d770285542e1b4b0e923e9486c9d32f91..88af066ce9f82402cbad67b02ee3b4b5b21d9e51 100644
GIT binary patch
delta 27
jcmccqf%p0c-i8*&7N#xC%Su>{jVujJwy!Q>Uc(Fks2B>A

delta 27
jcmccqf%p0c-i8*&7N#xC%Su=c4J}Q~wy!Q>Uc(Fks3r=R

diff --git a/glossary.tex b/glossary.tex
index dac3917..fb1b27f 100644
--- a/glossary.tex
+++ b/glossary.tex
@@ -27,5 +27,6 @@
 }
 
 \newacronym{dos}{DoS}{Denial of Service}
+\newacronym{prng}{PRNG}{Pseudo-Random Number Generator}
 \newacronym{tsa}{TSA}{Time-Stamp Authority}
 \newacronym{ttp}{TTP}{Trusted Third Party}
diff --git a/main.tex b/main.tex
index 9a21d04..7804393 100644
--- a/main.tex
+++ b/main.tex
@@ -95,7 +95,7 @@
 \pagenumbering{roman} % start roman page numbers from here (optional)
 \section*{Appendix} \label{Appendix}
 \addcontentsline{toc}{section}{Appendix}    % adds entry to table of contents
-\selbstaendigkeitserklaerung{\today}
+\selbstaendigkeitserklaerung{1. Januar 1970}
 %\input{chapters/xxx}                       % add in case you have additional images/tables
 \end{document}
 %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
diff --git a/thesis.pdf b/thesis.pdf
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