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authorFlorian Dold <>2017-08-21 00:26:51 +0200
committerFlorian Dold <>2017-08-21 00:26:51 +0200
commita56f6ce2a5b9615b090b7fb2377f974093ba1cb2 (patch)
treeb386f962d0c83665174fc18ecc913de2a8a9fb00 /comparison
parent7ff357a2bc763b83c43cadf557f66838241a7b0b (diff)
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diff --git a/comparison/comparison.tex b/comparison/comparison.tex
index cbe3c7c..2a6506a 100644
--- a/comparison/comparison.tex
+++ b/comparison/comparison.tex
@@ -235,10 +235,19 @@ Reference: \cite{chaum1990}. Introduces offline double spending detection.
Reference: Unpublished, there used to be some references on a mailing list, but they seem to be gone.
+Reference: \cite{brands1993efficient}. Variations of e-cash based on the representation problem.
+In these schemes, divisibility leads to linkability.
+\subsection{Okamoto's Divisible E-Cash}
+Reference: \cite{okamoto1995efficient}. Efficient construction for divisible E-Cash, but multiple independent
+transactions with the same coin are linkable.
\subsection{Compact E-Cash}
Reference: \cite{camenisch2005}. Allows to withdraw $2^\ell$ coins in $O(\ell)$. Either the whole
$2^\ell$ coins must be spent at once, or all coins must be spent separately.
\subsection{Divisible E-Cash Made Practical}
Reference: \cite{canard2015divisible}. Introduces a different coin structure
where there is one global tree and all coins are put on that skeleton.
diff --git a/comparison/literature.bib b/comparison/literature.bib
index dd74588..76e7d8b 100644
--- a/comparison/literature.bib
+++ b/comparison/literature.bib
@@ -137,3 +137,29 @@ doi="10.1007/978-3-319-28166-7_14",
+author="Okamoto, Tatsuaki",
+editor="Coppersmith, Don",
+title="An Efficient Divisible Electronic Cash Scheme",
+bookTitle="Advances in Cryptology --- CRYPT0' 95: 15th Annual International Cryptology Conference Santa Barbara, California, USA, August 27--31, 1995 Proceedings",
+publisher="Springer Berlin Heidelberg",
+address="Berlin, Heidelberg",
+abstract="Recently, several ``divisible'' untraceable off-line electronic cash schemes have been presented [8, 11, 19, 20]. This paper presents the first practical ``divisible'' untraceable1 off-line cash scheme that is ``single-term''2 in which every procedure can be executed in the order of log N, where N is the precision of divisibility, i.e., N = (the total coin value)/(minimum divisible unit value). Therefore, our ``divisible'' off-line cash scheme is more efficient and practical than the previous schemes. For example, when N = 217 (e.g., the total value is about {\$} 1000, and the minimum divisible unit is 1 cent), our scheme requires only about 1 Kbyte of data be transfered from a customer to a shop for one payment and about 20 modular exponentiations for one payment, while all previous divisible cash schemes require more than several Kbytes of transfered data and more than 200 modular exponentiations for one payment.",
+ author = {Brands, Stefan A.},
+ title = {An Efficient Off-line Electronic Cash System Based On The Representation Problem.},
+ year = {1993},
+ source = {\&id=oai%3Ancstrlh%3Aercim_cwi%3Aercim.cwi%2F%2FCS-R9323},
+ publisher = {CWI (Centre for Mathematics and Computer Science)},
+ address = {Amsterdam, The Netherlands, The Netherlands},