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? 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Januar 1970} %\input{chapters/xxx} % add in case you have additional images/tables \end{document} %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% diff --git a/thesis.pdf b/thesis.pdf index 490bb8f38e930f403eac7d480245b16bd15f143b..da4f6229c870633ed78dadab76e78fab69faa318 100644 GIT binary patch delta 90229 zcmZ^rb9CI@+wNmER%11`)!4Re+h{VeJ+YmJjT$z#Z98dfCnxRm!~3pt&Oi6M*5-BZ z+3P#AKeK0^f8f=1;Z=7*fU>6uzCxjaF|wrOok39n=G0_kGZ>NE&VOuL5az!1I;`Fp zCuJ{VC?S>eA`|tZVxh~d+$^|1NU#%2)|C^mb43eY^q-GCc!mML_Ifsb0dhv3@qNqV zbN_yYmDC-c9D|xolviMKNL7?c>6$$`FsvaXoapMG3&k(4AKNKL`a4*u7BQTYUYX#t z4M^T10O1v6ELzu{NOhT9x4wlL+G89zvMCJ9pD8K4<cqWDJ=naXwAgepphI9%AcBg% z6_@L}vPj$KCrzxM)*Kx@qLqQys^qvUNVIF#Bf^6N!!%VzBgzoFI@}}X$#>LWb(`-K zUor!i%-8Cw`KHWlp^H*xsa?}vgXK4>rCaC&_;fllPp58;mtQuf-s8MR50};JlhdjL zwXjC)EweOu<Bf}3o|1vTbR#n(fvMx{za-lK&4h<z2uC`xZ!E?+syWuzXk4Kp(j)Ja zEytp&&YD&0^XEC_0-TK}-v&)1{n<fd+Xe*wm6s!&UXz|3R0u2YM;wQ5cfRmFJ&k8w 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