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Published in:
2006 | OriginalPaper | Chapter
Obtaining Asymptotic Fingerprint Codes Through a New Analysis of the Boneh-Shaw Codes
Authors : Marcel Fernandez, Josep Cotrina
Published in: Information Security and Cryptology
Publisher: Springer Berlin Heidelberg
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A fingerprinting code is a set of codewords that are embedded in each copy of a digital object with the purpose of making each copy unique. If the fingerprinting code is
c
-secure with
ε
error, then the decoding of a pirate word created by a coalition of at most
c
dishonest users, will expose at least one of the guilty parties with probability 1–
ε
.
The Boneh-Shaw fingerprinting codes are
n
-secure codes with
ε
error, where
n
also denotes the number of authorized users. Unfortunately, the length the Boneh-Shaw codes should be of order
O
(
n
3
log(
n
/
ε
)), which is prohibitive for practical applications. In this paper, we prove that the Boneh-Shaw codes are (
c
<
n
)-secure for lengths of order
O
(
nc
2
log(
n
/
ε
)).
Moreover we show how to use these codes to construct binary fingerprinting codes with length
L
=
O
(
c
6
log
c
log
n
), with probability of error
O
(1/
n
)=
exp
(–Ω(
L
)), and identification algorithm of complexity
poly
(log
n
)=
poly
(
L
). These results improve in some aspects the best known schemes and with a much more simple construction.