# Short 3-Secure Fingerprinting Codes for Copyright Protection Francesc Sebé and Josep Domingo-Ferrer Dept. of Computer Engineering and Mathematics Universitat.

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Short 3-Secure Fingerprinting Codes for Copyright Protection Francesc Sebé and Josep Domingo-Ferrer Dept. of Computer Engineering and Mathematics Universitat Rovira i Virgili Tarragona, 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 100 1 0 100 0 0 001 0 0 ?0? ? 0

Collusion strategy In a 3-collusion p-majority strategy 11 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 a1a1 a2a2 a3a3 invariant minor(a 3 ) minor(a 2 ) minor(a 1 )

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 a1a1 a2a2 a3a3 0001111 00001111 00001111 00001111 aiai

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 a1a1 a2a2 a3a3 0b(t,2 n-2,1-p) b(t,2 n-2,p) d(a 1,a coll ) a coll

3-Collusions in DH(n) 0000000 00000000 00000000 00000000 0000000 00000000 11111111 11111111 0000000 11111111 00000000 11111111 a1a1 a2a2 a3a3 0001111 00001111 00001111 00001111 a a coll d(a coll,a)

Distance distribution d 2 =minimum distance to colluding codewords d 6 =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 0.00.60.70.80.91.0 DH(7) 1.00.5·10 -3 0.1·10 -3 0.1·10 -6 0.7·10 -14 0.0 DH(8) 1.00.17·10 -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’ 1111 1111 0000 0000 0000 1111 0000 0000 0000 1111 0000 0000 0000 ‘0’ 0000 0000 0000 0000 1111 0000 0000 0000 1111 0000 0000 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

Collusions over SC(d,t) p-majoritary strategy Probability of majoritary decoding

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’  1

Comparison vs Boneh-Shaw For not too large number of buyers, our proposal (with SC(5,5)) generates shorter codes nºbuyersOur lengthBS length 512 1,024.... 32,768 65,536 131,072 28,105 56,265.... 1,802,185 3,604,425 7,208,905 5,148,000 5,269,992.... 5,883,888 6,006,780 6,129,816

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.http://www.acet.es/english/2003/index.htm

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.

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