![](bg6.png)
ing attack. This led to our discovery of an attack on
the recently published HZ protocol that had not pre-
viously been identified, as described in Section 5.
In Section 6 we justified why the buyer must not
be left to ensure that a unique key pair is used in each
transaction as it is in their interest to use duplicates.
We therefore conclude that the seller must verify the
uniqueness of key pairs unless such action becomes
unmanageable wherein an alternative approach to as-
suring key uniqueness must be proposed.
REFERENCES
Barni, M. and Bartolini, F. (2004). Watermarking Systems
Engineering. Marcel Dekker, Inc.
Deng, M. and Preneel, B. (2008). Attacks on two buyer-
seller watermarking protocols and an improvement for
revocable anonymity. Electronic Commerce and Secu-
rity, International Symposium, 0:923–929.
Hu, Y. and Zhang, J. (2009). A secure and efficient buyer-
seller watermarking protocol. Journal of Multimedia,
4(3):161–168.
Ibrahim, I. M., El-Din, S. H. N., and Hegazy, A. F. A.
(2007). An effective and secure buyer seller water-
marking protocol. In Third International Symposium
on Information Assurance and Security, pages 21–28.
Ju, H. S., Kim, H. J., Lee, D. H., and Lim, J. I. (2003). An
anonymous buyer-seller watermarking protocol with
anonymity control. In International Conference on In-
formation Security and Cryptology, pages 421–432.
Lei, C. L., Yu, P. L., Tsai, P. L., and Chan, M. H. (2004).
An efficient and anonymous buyer-seller watermark-
ing protocol. IEEE Transactions on Image Process-
ing, 13(12):1618–1626.
Mauw, S. and Bos, V. (2001). Drawing Message Sequence
Charts with L
A
T
E
X. TUGBoat, 22(1-2):87–92.
Memon, N. and Wong, P. W. (2001). A buyer seller water-
marking protocol. IEEE Transactions on Image Pro-
cessing, 10(4):643–649.
Poh, G. S. and Martin, K. M. (2007). A framework for
design and analysis of asymmetric fingerprinting pro-
tocols. In Third International Symposium on Informa-
tion Assurance and Security, pages 457–461.
Poh, G. S. and Martin, K. M. (2008). On the (in)security
of two buyer-seller watermarking protocols. In SE-
CRYPT 2008 - International Conference on Security
and Cryptography, pages 253–260.
Qiao, L. and Nahrstedt, K. (1998). Watermarking schemes
and protocols for protecting rightful ownership and
customer’s rights. Journal of Visual Communication
and Image Representation, 9(3):194–210.
Shao, M. H. (2007). A privacy-preserving buyer-seller wa-
termarking protocol with semi-trust third party. In
Trust, Privacy and Security in Digital Business, pages
44–53.
Williams, D. M., Treharne, H., Ho, A. T. S., and Culnane, C.
(2008a). Using a formal analysis technique to identify
an unbinding attack on a buyer-seller watermarking
protocol. In 10th ACM Workshop on Multimedia and
Security, pages 205–214.
Williams, D. M., Treharne, H., Ho, A. T. S., and Waller, A.
(2008b). Formal analysis of two buyer-seller water-
marking protocols. In 7th International Workshop on
Digital Watermarking, pages 278–292.
APPENDIX
The following notation is used throughout.
• A set of all agents
• WM, CV sets of all watermarks and cover material re-
spectively
• PK set of all public keys
• KP
∗
set of all one-time key pairs
• b, s, t, ca variables to model agents, respectively buyers,
sellers, trusted third parties and certification authorities
• w, c variables to model watermarks and content taken
from the set of all watermarks WM and set of all digital
content CV, respectively
• (pk
a
, sk
a
) public-secret key pair belonging to agent a
• wk
s
watermarking key belonging to seller s
• arg(c) common agreement identifying content c
• C
sk
ca
(a, pk
a
) digital certificate binding an agent to their
public key signed under sk
ca
• C
sk
ca
(pk
a
) anonymous certificate signed under sk
ca
• S
sk
a
(m) message m signed under sk
a
• E
pk
a
(m) message m encrypted under pk
a
• W
wk
s
(c, w) watermark w embedded within c using wa-
termarking key wk
s
Lowercase values are considered variable whereas
those in uppercase are concrete. Protocols are pre-
sented as message sequence charts (Mauw and Bos,
2001) in conjunction with this notation.
SECRYPT 2010 - International Conference on Security and Cryptography
446