Short 3-Secure Fingerprinting Codes for

Copyright Protection

Francesc Sebé and Josep Domingo-Ferrer

Dept. of Computer Engineering and Mathematics

Universitat Rovira i VirgiliTarragona, Spain

Fingerprinting Before selling a product

A mark identifying the buyer is embedded

Later mark recovery from illegal copies allows the dishonest buyer to be identified

As every copy is different, buyers can collude By comparing their copies We focus on collusions of size c=3

Co-orthogonal codes and Fingerprinting We realized that co-orthogonal codes had

not been designed to have a suitable structure to build codewords needed by collusion-secure fingerprinting. A high error-correcting capacity is needed and co-orthogonal codes are not meant for error correction.

As an alternative, we used dual binary Hamming codes and a new class of codes called scattering codes to obtain collusion-secure codes shorter than Boneh-Shaw’s for collusions of size 3.

The marking assumption Colluders can identify and change

marks in detectable positions

1 0 0 1 0

1 0 0 0 0

0 0 1 0 0

? 0 ? ? 0

Collusion strategy In a 3-collusion

p-majority strategy

1

1

0

p 1-p

Our proposal Each buyer is assigned a Binary

Dual Hamming, DH(n), Codeword

The accused buyer will be the one whose codeword is the nearest to the recovered one

Colluders aim By collusion, generate a codeword

that accuses another buyer

nearest

DH(n) properties for 3-collusions

Any set of three codewords can be divided into four zones

0000000 00000000 00000000 00000000

0000000 00000000 11111111 11111111

0000000 11111111 00000000 11111111

a1

a2

a3

invariant minor(a3) minor(a2) minor(a1)

DH(n) properties for 3-collusions With respect to the rest of

codewords*

(*) There is an exception. For simplicity, it is not mentioned.

0000000 00000000 00000000 00000000

0000000 00000000 11111111 11111111

0000000 11111111 00000000 11111111

a1

a2

a3

0001111 00001111 00001111 00001111ai

0000000 00000011 00000011 11111100

3-Collusions in DH(n) After a p-majority 3-collusion

0000000 00000000 00000000 00000000

0000000 00000000 11111111 11111111

0000000 11111111 00000000 11111111

a1

a2

a3

0 b(t,2n-2,1-p)b(t,2n-2,1-p) b(t,2n-2,p) d(a1,acoll)

acoll

t

nncoll ptkbptbKaadpkp )1;2;();2;()),(()( 121

11

3,2,12 ))),((min()( iicoll kaadpkp

3-Collusions in DH(n)0000000 00000000 00000000 00000000

0000000 00000000 11111111 11111111

0000000 11111111 00000000 11111111

a1

a2

a3

0001111 00001111 00001111 00001111a

acoll

d(acoll,a)

532),( Kaad ncoll

t

nn ptkbptbkKp );23;()1;23;()( 335

3,2,16 ))),((min()( iicoll kaadpkp

Distance distribution d2=minimum distance to colluding codewords d6=minimum distance to non-colluding codeword

Successful collusion Probability of a successful collusion

The nearest codeword is not a colluder’s

Colluders can choose p=0 !!!

p

0.0 0.6 0.7 0.8 0.9 1.0

DH(7) 1.0 0.5·10-3 0.1·10-3 0.1·10-6 0.7·10-

14

0.0

DH(8) 1.0 0.17·10-

7

0.1·10-7 0.1·10-13 0.7·10-

28

0.0

Scattering Codes Scattering codes are a new kind of

code Construction and decoding rules

described in the paper Used to control collusion strategy

Scattering Code Example of SC(4,3)

Decoding rules are detailed in the paper

Encodes

‘1’111111111111

1111 0000 0000

0000 1111 0000

0000 0000 1111

0000 0000 00000000 0000 00000000 0000 0000

‘0’000000000000

0000 0000 0000

0000 0000 0000

0000 0000 0000

1111 0000 00000000 1111 00000000 0000 1111

Collusions over SC(d,t) If 3 codewords, all of them encoding a value v

collude, the collusion-generated codeword will decode as v with probability 1.

If 3 codewords, two encoding value v and one value collude with p-majoritary strategy, the collusion-generated codeword will decode as v with high probability

v

Collusions over SC(d,t)

p-majoritary strategy

Probabilityof

majoritarydecoding

3-secure fingerprinting codes Each buyer is assigned a Binary

Dual Hamming, DH(n), Codeword We choose appropiate parameters

d, t and construct SC(d,t). We compose SC(d,t) with DH(n). We permute the bits of the resulting

sequence With a secret key

3-secure fingerprinting codes

Permutation

DH(n)

SC(d,t)p-majoritary

p-majoritary

p’-majoritary, p’ 1

Comparison vs Boneh-Shaw For not too large number of buyers, our proposal

(with SC(5,5)) generates shorter codes

nºbuyers Our length

BS length

5121,024

....32,76865,536

131,072

28,10556,265

....1,802,1853,604,4257,208,905

5,148,0005,269,992

....5,883,8886,006,7806,129,816

Conclusion A construction for 3-secure

fingerprinting codes has been presented

For not too large number of buyers, shorter codewords are obtained

Scientific dissemination Article in IEEE Transactions on Systems, Man and

Cybernetics, 2003 (to appear). Article in Electronics Letters, 2002. Article in Lecture Notes in Computer Science, vol. 2384

(ACISP’2002), 2002. Acceptance rate 36/94. Other papers (CARDIS’2002, Upgrade Journal, etc.). See

Final Report

Research Prize 20 February 2003. J.Domingo-Ferrer and

F.Sebé were awarded the “Salvà i Campillo” Prize for Outstanding Research, a European-wide prize sponsored by the Association of Telecom Engineers of Catalonia. The prize was delivered by the Spanish Minister for Science and Technology.

See http://www.acet.es/english/2003/index.htm for more information on that prize.

Future Research (1) New short codes secure against larger

collusions should be found (follow-up of project CO-ORTHOGONAL?)

Try to use recent results on q-ary traceability codes to build shorter collusion-secure binary fingerprinting codes for collusions of size c. M.Fernandez “A contribution to the design

and efficient decoding of traceability codes”, PhD. Thesis, UPC, Barcelona. Co-advised by J.Domingo-Ferrer. March 2003.

Future research (2) Design of collusion secure fingerprinting

codes is in line with 6th FP priority 2.3.2.7 “Cross-media content for leisure and entertainment”.

URV is involved in 6th FP NoE proposal “Digiright” and is preparing an IP proposal together with Spain’s SDAE, the digital arm of the world’s 3rd largest rights collecting society SGAE.