Buyer-Seller Watermarking (BSW) Protocols Geong Sen Poh 31 Oct 2006

2 Outline Introduction  Motivation  Development of BSW  Goals, Methodology and Assumptions Protocols  Memon-Wong Protocol (MW)  Lei et al. Protocol (Lei)  Zhang et al. Protocol (Zhang) Analysis of Zhang et al. Protocol Summary

3 Motivation How can the seller identifies buyers that illegally distributed songs, movies etc.?  The seller can embeds unique watermarks… songs, movies etc. £££££ Seller Buyer Distributes copies

4 Motivation BUT… The seller is the entity that generates and embeds the watermark into a digital work If illegal copies are found and a buyer is identified through the embedded watermark, the buyer can claim that he/she is framed by the seller since the seller can embed the buyer’s watermark into any digital work. SO… Buyer-Seller Watermarking Protocol

5 Development of BSW MW Choi Attack I Goi Attack I Choi II Goi Attack II Lei Zhang IWDW ACNS IEEE EUC IEEE IEE Ju 2003ICISC

6 Goals No Framing  An honest buyer should not be falsely accused by a malicious seller or other buyers No Repudiation  The buyer accused of reselling an unauthorised copy should not be able to claim that the copy was created by the seller or a security breach of the seller’s system Traceability  A buyer who has illegally distributed digital works can be traced Collusion Tolerance  An attacker should not be able to find, generate, or delete the fingerprint by comparing the marked copies, even if they have access to a large number of copies Anonymity  A buyer should be able to buy anonymously Unlinkability  Given two marked digital works, no one can decide whether or not they were bought by the same buyer B. M. Goi, R. C.-W. Phan, Y. Yang, F. Bao, R. H. Deng and M. U. Siddiqi, Cryptanalysis of Two Anonymous Buyer-Seller Watermarking Protocols and an Improvement for True Anonymity, ACNS 2004, LNCS 3089, pp , 2004

7 Methodology Interactive Protocol  Registration  Buy and Sell  Identification and Arbitration Seller does not know the watermark Buyer does not know the embedded watermark

8 Principals Involved Buyer (B) Seller (S) Certificate Authority (CA)  Fully trusted  Issues certificates to WCA, A, B, and S Watermark Certificate Authority (WCA)  Fully trusted  Issues and certifies buyer’s watermark Arbiter (A)  Fully trusted  Resolves dispute between B and S

9 Assumptions Each of the principals involved (e.g. buyer and seller) has a CA certified public and private key pair, (PK i, SK i ) for i the identity of the principal The public-key encryption algorithm is homomorphic

10 Homomorphic Encryption E(x) + E(y) = E(x + y) E(x)  E(y) = E(x  y) Example: RSA Paillier homomorphic encryption (in Zhang Protocol): E(x)  E(y) = E(x + y) If the public key is: n,e then: E(x 1 )  E(x 2 ) = x 1 e x 2 e mod n = (x 1 x 2 ) e mod n = E(x 1  x 2 )

11 MW Protocol WCA SB O’ = O * W S σ(E PKB (W B )) = E PKB (σ(W B )) E PKB (O’) * E PKB (σ(W B )) = E PKB (O’ * σ(W B )) Request watermark E PKB (W B ), Sign WCA (E PKB (W B )) B = Buyer S = Seller WCA = Watermark Certificate Authority O = Original Work O’ = Marked Work W k = k’s Watermark E PKB (W B ), Sign WCA (E PKB (W B )) σ = Random permutation of degree n * = Embedding algorithm E k (.) = Encrypt with k’s public key Sign k (.) = Sign with k’s private key E PKB (O’ * σ(W B )) D SKB (E PKB (O’ * σ(W B ))) = O’ * σ(W B ) Generate W B Registration, Buy and Sell S does not know the watermark B does not know the embedded watermark

12 MW Protocol A SB Request private key Private key σ, E PKB (W B ), Sign WCA (E PKB (W B )), Y B = Buyer S = Seller A = Arbiter WCA = Watermark Certificate Authority O = Original Work O’, O” = Marked Work Y = Illegal copy W k = k’s Watermark σ = Random permutation of degree n * = Embedding algorithm E k (.) = Encrypt with k’s public key Sign k (.) = Sign with k’s private key On discovering an illegal copy of O’, say Y, S can determine B by detecting σ(W B ) embedded using a watermark detection algorithm and search the buyer details from his database. Identification and Arbitration

13 Issue with MW MW Protocol achieved:  No Framing  No repudiation  Traceability But…  No anonymity,  No unlinkability for the buyers

14 Lei Protocol CAB pk B Cert CA (pk B ) Generate (sk B,pk B ) Generate cert CA (pk B ) B = Buyer S = Seller O = Original Work O’, O” = Marked Work W k = k’s Watermark ARG = An agreement between the buyer and the seller * = Embedding algorithm E k (.) = Homomorphic encrypt with k’s public key D k (.) = Homomorphic decrypt with k’s private key Sign k (.) = Sign with k’s private key (sk B,pk B ), (sk’, pk’) = Buyer generated random key pair Registration Anonymous key pair

15 Lei Protocol WCA SB Generate (sk ’,pk ’ ) for this transaction s = Sign sk’ (ARG) Generate Cert pkB (pk’) B = Buyer S = Seller WCA = Watermark Certificate Authority O = Original Work O’, O” = Marked Work W k = k’s Watermark ARG = An agreement between the buyer and the seller * = Embedding algorithm E k (.) = Homomorphic encrypt with k’s public key D k (.) = Homomorphic decrypt with k’s private key Sign k (.) = Sign with k’s private key (sk B,pk B ), (sk’, pk’) = Buyer generated random key pair Cert CA (pk B ), Cert pkB (pk’), ARG, s O’ = O * W S E pk’ (O’ * W B ) E pk’ (O’) * E pk’ (W B ) = E pk’ (O’ * W B ) Cert pkB (pk’), ARG, s, O’ E pk’ (W B ), E WCA (W B ), S WCA, pk’, s Generate W B S WCA = Sign WCA (W B ) D sk’ (E pk’ (O’ * σ(W B ))) = O’ * σ(W B ) Buy and Sell Unlinkable key pair S & B do not know the watermark

16 Lei Protocol The B Identity B X 1 (sk 1, pk 1 ) Y 11 (sk 11, pk 11 ) X 2 (sk 2, pk 2 ) X n (sk n, pk n ) Y 1m (sk 1m, pk 1m ) Y 21 (sk 21, pk 21 ) Y 2k (sk 2k, pk 2k ) Y n1 (sk n1, pk n1 ) Y nt (sk nt, pk nt ) Linkable, to X 1 Unlinkable, S knows is from X 1 S knows is from X 2 S does not know X 1 links to X 2 S does not know X 1,X 2,…,X n link to B

17 Lei Protocol Identification and Arbitration S = Seller A = Arbiter WCA = Watermark Certificate Authority O = Original Work O’, O” = Marked Work Y = Illegal Copy W k = k’s Watermark ARG = An agreement between the buyer and the seller * = Embedding algorithm Det(.,.) = Detection algorithm E k (.) = Homomorphic encrypt with k’s public key D k (.) = Homomorphic decrypt with k’s private key Sign k (.) = Sign with k’s private key (sk B,pk B ), (sk’, pk’) = Buyer generated random key pair A S WCA E WCA (W B ) WBWB O’, Y, Cert CA (pk B ), Cert pkB (pk’), ARG, s, E pk’ (W B ), E WCA (W B ), S WCA W’ = Det(Y) W’ = W B ? On discovering an illegal copy of O’, say Y, S carries out the following steps:

18 Zhang Protocol Similar to Lei Protocol except that there is no WCA No need WCA to generate and certify watermark:  S generates his part of the watermark  B generates his part of the watermark  The final watermark embedded in the digital work is the combination of S and B’s watermarks

19 Zhang Protocol CAB pk B Cert CA (pk B ) Generate (sk B,pk B ) Generate cert CA (pk B ) B = Buyer CA = Certificate Authority O = Original Work O’, O” = Marked Work O f = Illegal Copy W k = k’s Watermark ARG = An agreement between the buyer and the seller SEC i = Secret string of i * = Embedding algorithm E k (.) = Homomorphic encrypt with k’s public key D k (.) = Homomorphic decrypt with k’s private key Sign k (.) = Sign with k’s private key (sk B,pk B ), (sk’, pk’) = Buyer generated random key pair Registration

20 Zhang Protocol SB Generate (sk ’,pk ’ ) for this transaction Generate a secret SEC B e = E pk’ (SEC B ) s = Sign sk’ (E pk’ (SEC B ), ARG) Generate Cert pkB (pk’) B = Buyer S = Seller O = Original Work O’, O” = Marked Work O f = Illegal Copy W k = k’s Watermark ARG = An agreement between the buyer and the seller SEC i = Secret string of i * = Embedding algorithm E k (.) = Homomorphic encrypt with k’s public key D k (.) = Homomorphic decrypt with k’s private key Sign k (.) = Sign with k’s private key (sk B,pk B ), (sk’, pk’) = Buyer generated random key pair Cert CA (pk B ), Cert pkB (pk’), ARG, e, s O’ = O * W S E pk’ (W B ) = E pk’ (SEC S )(E pk’ (SEC B ) = E pk’ (SEC S + SEC B ) E pk’ (O’) * E pk’ (W B ) = E pk’ (O’ + W B ) E pk’ (O’ * W B ) D sk’ (E pk’ (O’ + W B )) = O’ + W B Buy and Sell

21 Zhang Protocol B = Buyer S = Seller A = Arbiter CA = Certificate Authority O = Original Work O’ = Marked Work Y = Illegal Copy W k = k’s Watermark ARG = An agreement between the buyer and the seller SEC i = Secret string of i * = Embedding algorithm Det(.,.) = Detection algorithm E k (.) = Homomorphic encrypt with k’s public key D k (.) = Homomorphic decrypt with k’s private key Sign k (.) = Sign with k’s private key (sk B,pk B ), (sk’, pk’) = Buyer generated random key pair A S CA Cert CA (pk B ), Cert pkB (pk’), e SEC B O’, Y, Cert CA (pk B ), Cert pkB (pk’), ARG, e, s, SEC S Found Y Compute W B = SEC S + SEC B W’ = Det(Y) W’ = W B ? B e = E pk’ (SEC B ) SEC B D sk’ (E pk’ (SEC B )) = SEC B Identification and Arbitration

22 Analysis of Zhang et al. Protocols Issues  Buyer can remove his part of the watermark easily since… O’ + W B = O’ + SEC S + SEC B and Buyer knows SEC B, to remove… O’ + SEC S + SEC B – SEC B

23 Summary The motivation of BSW The proposals to date  MW, Lei and Zhang The issues  No formal security model, protocols designed in ad hoc manner Current focus  To continue analyse other proposals (Ju, Choi, Goi), with issues when parties collude with each others (Seller colludes with WCA etc.)

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