Towards joint decoding of binary Tardos fingerprinting codes

The class of joint decoder of probabilistic fingerprinting codes is of utmost importance in theoretical papers to establish the concept of fingerprint capacity. However, no implementation supporting a large user base is known to date. This article presents an iterative decoder which is, as far as we are aware of, the first practical attempt towards joint decoding. The discriminative feature of the scores benefits on one hand from the side-information of previously accused users, and on the other hand, from recently introduced universal linear decoders for compound channels. Neither the code construction nor the decoder make precise assumptions about the collusion (size or strategy). The extension to incorporate soft outputs from the watermarking layer is straightforward. An extensive experimental work benchmarks the very good performance and offers a clear comparison with previous state-of-the-art decoders.Comment: submitted to IEEE Trans. on Information Forensics and Security. - typos corrected, one new plot, references added about ECC based fingerprinting code

A construction of traceability set systems with polynomial tracing algorithm

© 2021 IEEE. Personal use of this material is permitted. Permission from IEEE must be obtained for all other uses, in any current or future media, including reprinting/republishing this material for advertising or promotional purposes,creating new collective works, for resale or redistribution to servers or lists, or reuse of any copyrighted component of this work in other works.A family F of w-subsets of a finite set X is called a set system with the identifiable parent property if for any w-subset contained in the union of some t sets, called traitors, of F at least one of these sets can be uniquely determined, i.e. traced. A set system with traceability property (TSS, for short) allows to trace at least one traitor by minimal distance decoding of the corresponding binary code, and hence the complexity of tracing procedure is of order O(M), where M is the number of users or the code's cardinality. We propose a new construction of TSS which is based on the old Kautz-Singleton concatenated construction with algebraic-geometry codes as the outer code and Guruswami-Sudan decoding algorithm. The resulting codes (set systems) have exponentially many users (codevectors) M and polylog(M) complexity of code construction and decoding, i.e. tracing traitors. This is the first construction of traceability set systems with such properties.Peer ReviewedPostprint (author's final draft

Contribution to the construction of fingerprinting and watermarking schemes to protect mobile agents and multimedia content

The main characteristic of fingerprinting codes is the need of high error-correction capacity due to the fact that they are designed to avoid collusion attacks which will damage many symbols from the codewords. Moreover, the use of fingerprinting schemes depends on the watermarking system that is used to embed the codeword into the content and how it honors the marking assumption. In this sense, even though fingerprinting codes were mainly used to protect multimedia content, using them on software protection systems seems an option to be considered. This thesis, studies how to use codes which have iterative-decoding algorithms, mainly turbo-codes, to solve the fingerprinting problem. Initially, it studies the effectiveness of current approaches based on concatenating tradicioanal fingerprinting schemes with convolutional codes and turbo-codes. It is shown that these kind of constructions ends up generating a high number of false positives. Even though this thesis contains some proposals to improve these schemes, the direct use of turbo-codes without using any concatenation with a fingerprinting code as inner code has also been considered. It is shown that the performance of turbo-codes using the appropiate constituent codes is a valid alternative for environments with hundreds of users and 2 or 3 traitors. As constituent codes, we have chosen low-rate convolutional codes with maximum free distance. As for how to use fingerprinting codes with watermarking schemes, we have studied the option of using watermarking systems based on informed coding and informed embedding. It has been discovered that, due to different encodings available for the same symbol, its applicability to embed fingerprints is very limited. On this sense, some modifications to these systems have been proposed in order to properly adapt them to fingerprinting applications. Moreover the behavior and impact over a video produced as a collusion of 2 users by the YouTube’s s ervice has been s tudied. We have also studied the optimal parameters for viable tracking of users who have used YouTube and conspired to redistribute copies generated by a collusion attack. Finally, we have studied how to implement fingerprinting schemes and software watermarking to fix the problem of malicious hosts on mobile agents platforms. In this regard, four different alternatives have been proposed to protect the agent depending on whether you want only detect the attack or avoid it in real time. Two of these proposals are focused on the protection of intrusion detection systems based on mobile agents. Moreover, each of these solutions has several implications in terms of infrastructure and complexity.Els codis fingerprinting es caracteritzen per proveir una alta capacitat correctora ja que han de fer front a atacs de confabulació que malmetran una part important dels símbols de la paraula codi. D'atra banda, la utilització de codis de fingerprinting en entorns reals està subjecta a que l'esquema de watermarking que gestiona la incrustació sigui respectuosa amb la marking assumption. De la mateixa manera, tot i que el fingerprinting neix de la protecció de contingut multimèdia, utilitzar-lo en la protecció de software comença a ser una aplicació a avaluar. En aquesta tesi s'ha estudiat com aplicar codis amb des codificació iterativa, concretament turbo-codis, al problema del rastreig de traïdors en el context del fingerprinting digital. Inicialment s'ha qüestionat l'eficàcia dels enfocaments actuals en la utilització de codis convolucionals i turbo-codis que plantegen concatenacions amb esquemes habituals de fingerprinting. S'ha demostrat que aquest tipus de concatenacions portaven, de forma implícita, a una elevada probabilitat d'inculpar un usuari innocent. Tot i que s'han proposat algunes millores sobre aquests esquemes , finalment s'ha plantejat l'ús de turbocodis directament, evitant així la concatenació amb altres esquemes de fingerprinting. S'ha demostrat que, si s'utilitzen els codis constituents apropiats, el rendiment del turbo-descodificador és suficient per a ser una alternativa aplicable en entorns amb varis centenars d'usuaris i 2 o 3 confabuladors . Com a codis constituents s'ha optat pels codis convolucionals de baix ràtio amb distància lliure màxima. Pel que fa a com utilitzar els codis de fingerprinting amb esquemes de watermarking, s'ha estudiat l'opció d'utilitzar sistemes de watermarking basats en la codificació i la incrustació informada. S'ha comprovat que, degut a la múltiple codificació del mateix símbol, la seva aplicabilitat per incrustar fingerprints és molt limitada. En aquest sentit s'ha plantejat algunes modificacions d'aquests sistemes per tal d'adaptar-los correctament a aplicacions de fingerprinting. D'altra banda s'ha avaluat el comportament i l'impacte que el servei de YouTube produeix sobre un vídeo amb un fingerprint incrustat. A més , s'ha estudiat els paràmetres òptims per a fer viable el rastreig d'usuaris que han confabulat i han utilitzat YouTube per a redistribuir la copia fruït de la seva confabulació. Finalment, s'ha estudiat com aplicar els esquemes de fingerprinting i watermarking de software per solucionar el problema de l'amfitrió maliciós en agents mòbils . En aquest sentit s'han proposat quatre alternatives diferents per a protegir l'agent en funció de si és vol només detectar l'atac o evitar-lo en temps real. Dues d'aquestes propostes es centren en la protecció de sistemes de detecció d'intrusions basats en agents mòbils. Cadascuna de les solucions té diverses implicacions a nivell d'infrastructura i de complexitat.Postprint (published version

Gossip Codes for Fingerprinting: Construction, Erasure Analysis and Pirate Tracing

This work presents two new construction techniques for q-ary Gossip codes from tdesigns and Traceability schemes. These Gossip codes achieve the shortest code length specified in terms of code parameters and can withstand erasures in digital fingerprinting applications. This work presents the construction of embedded Gossip codes for extending an existing Gossip code into a bigger code. It discusses the construction of concatenated codes and realisation of erasure model through concatenated codes.Comment: 28 page

Almost separating and almost secure frameproof codes over q-ary alphabets

The final publication is available at Springer via http://dx.doi.org/10.1007/s10623-015-0060-zIn this paper we discuss some variations of the notion of separating code for alphabets of arbitrary size. We show how the original definition can be relaxed in two different ways, namely almost separating and almost secure frameproof codes, yielding two different concepts. The new definitions enable us to obtain codes of higher rate, at the expense of satisfying the separating property partially. These new definitions become useful when complete separation is only required with high probability, rather than unconditionally. We also show how the codes proposed can be used to improve the rate of existing constructions of families of fingerprinting codes.Peer ReviewedPostprint (author's final draft

On codes for traceability schemes: constructions and bounds

A traceability or fingerprinting scheme is a cryptographic scheme that facilitates the identification of the source of leaked information. In a fingerprinting setting, a distributor delivers copies of a given content to a set of authorized users. If there are dishonest members (traitors) among them, the distributor can deter plain redistribution of the content by delivering a personalized, i.e., marked, copy to each user. The set of all user marks is known as a fingerprinting code. There is, however, another threat. If several traitors collude to create a copy that is a combination of theirs, then the pirated copy generated will contain a corrupted mark, which may obstruct the identification of traitors. This dissertation is about the study and analysis of codes for their use in traceability and fingerprinting schemes, under the presence of collusion attacks. Moreover, another of the main concerns in the present work will be the design of identification algorithms that run efficiently, i.e., in polynomial time in the code length. In Chapters 1 and 2, we introduce the topic and the notation used. We also discuss some properties that characterize fingerprinting codes known under the names of separating, traceability (TA), and identifiable parent property (IPP), which will be subject of research in the present work. Chapter 3 is devoted to the study of the Kötter-Vardy algorithm to solve a variety of problems that appear in fingerprinting schemes. The concern of the chapter is restricted to schemes based on Reed-Solomon codes. By using the Kötter-Vardy algorithm as the core part of the identification processes, three different settings are approached: identification in TA codes, identification in IPP codes and identification in binary concatenated fingerprinting codes. It is also discussed how by a careful setting of a reliability matrix, i.e., the channel information, all possibly identifiable traitors can be found. In Chapter 4, we introduce a relaxed version of separating codes. Relaxing the separating property lead us to two different notions, namely, almost separating and almost secure frameproof codes. From one of the main results it is seen that the lower bounds on the asymptotical rate for almost separating and almost secure frameproof codes are greater than the currently known lower bounds for ordinary separating codes. Moreover, we also discuss how these new relaxed versions of separating codes can be used to show the existence of families of fingerprinting codes of small error, equipped with polynomial-time identification algorithms. In Chapter 5, we present explicit constructions of almost secure frameproof codes based on weakly biased arrays. We show how such arrays provide us with a natural framework to construct these codes. Putting the results obtained in this chapter together with the results from Chapter 4, shows that there exist explicit constructions of fingerprinting codes based on almost secure frameproof codes with positive rate, small error and polynomial-time identification complexity. We remark that showing the existence of such explicit constructions was one of the main objectives of the present work. Finally, in Chapter 6, we study the relationship between the separating and traceability properties of Reed-Solomon codes. It is a well-known result that a TA code is an IPP code, and that an IPP code is a separating code. The converse of these implications is in general false. However, it has been conjectured for some time that for Reed-Solomon codes all three properties are equivalent. Giving an answer to this conjecture has importance in the field of fingerprinting, because a proper characterization of these properties is directly related to an upper bound on the code rate i.e., the maximum users that a fingerprinting scheme can allocate. In this chapter we investigate the equivalence between these properties, and provide a positive answer for a large number of families of Reed-Solomon codes.Un sistema de trazabilidad o de fingerprinting es un mecanismo criptogr afi co que permite identi car el origen de informaci on que ha sido fi ltrada. En el modelo de aplicación de estos sistemas, un distribuidor entrega copias de un determinado contenido a un conjunto de usuarios autorizados. Si existen miembros deshonestos (traidores) entre ellos, el distribuidor puede disuadir que realicen una redistribuci on ingenua del contenido entregando copias personalizadas, es decir, marcadas, a cada uno de los usuarios. El conjunto de todas las marcas de usuario se conoce como c ódigo de fingerprinting. No obstante, existe otra amenaza m as grave. Si diversos traidores confabulan para crear una copia que es una combinación de sus copias del contenido, entonces la copia pirata generada contendr a una marca corrompida que di ficultar a el proceso de identificaci on de traidores. Esta tesis versa sobre el estudio y an alisis de c odigos para su uso en sistemas de trazabilidad o de fi ngerprinting bajo la presencia de ataques de confabulaci on. Otra de las cuestiones importantes que se tratan es el diseño de algoritmos de identi caci on e ficientes, es decir, algoritmos que se ejecuten en tiempo polin omico en la longitud del c odigo. En los Cap tulos 1 y 2 presentamos el tema e introducimos la notaci on que utilizaremos. Tambi en presentaremos algunas propiedades que caracterizan los c odigos de fi ngerprinting, conocidas bajo los nombres de propiedad de separaci on, propiedad identi cadora de padres (IPP) y propiedad de trazabilidad (TA), que est an sujetas a estudio en este trabajo. El Cap tulo 3 est a dedicado al estudio del algoritmo de decodi caci on de lista con informaci on de canal de Kötter-Vardy en la resoluci on de determinados problemas que aparecen en sistemas de fingerprinting. El ambito de estudio del cap ítulo son sistemas basados en c odigos de Reed-Solomon. Empleando el algoritmo de Kötter-Vardy como parte central de los algoritmos de identifi caci on, se analizan tres propuestas en el cap ítulo: identi caci on en c odigos TA, identifi caci on en c odigos IPP e identifi caci on en c odigos de fingerprinting binarios concatenados. Tambi en se analiza c omo mediante un cuidadoso ajuste de una matriz de abilidad, es decir, de la informaci on del canal, se pueden encontrar a todos los traidores que es posible identi car e ficientemente. En el Capí tulo 4 presentamos una versi on relajada de los c odigos separables. Relajando la propiedad de separaci on nos llevar a a obtener dos nociones diferentes: c odigos cuasi separables y c odigos cuasi seguros contra incriminaciones. De los resultados principales se puede observar que las cotas inferiores de las tasas asint oticas para c odigos cuasi separables y cuasi seguros contra incriminaciones son mayores que las cotas inferiores actualmente conocidas para c odigos separables ordinarios. Adem as, tambi en estudiamos como estas nuevas familias de c odigos pueden utilizarse para demostrar la existencia de familias de c odigos de ngerprinting de baja probabilidad de error y dotados de un algoritmo de identi caci on en tiempo polin omico. En el Capí tulo 5 presentamos construcciones expl citas de c odigos cuasi seguros contra incriminaciones, basadas en matrices de bajo sesgo. Mostramos como tales matrices nos proporcionan una herramienta para construir dichos c odigos. Poniendo en com un los resultados de este cap tulo con los del Capí tulo 4, podemos ver que, bas andonos en c odigos cuasi seguros contra incriminaciones, existen construcciones expl ícitas de c odigos de fi ngerprinting de tasa positiva, baja probabilidad de error y con un proceso de identi caci on en tiempo polin omico. Demostrar que existen dichas construcciones expl citas era uno de los principales objetivos de este trabajo. Finalmente, en el Capí tulo 6, estudiamos la relaci on existente entre las propiedades de separaci on y trazabilidad de los c odigos de Reed-Solomon. Es un resultado bien conocido el hecho que un c odigo TA es un c odigo IPP, y que un c odigo IPP es un c odigo separable. Las implicaciones en el sentido opuesto son falsas en general. No obstante, existe una conjetura acerca de la equivalencia de estas tres propiedades en el caso de cóodigos de Reed-Solomon. Obtener una respuesta a esta conjetura es de una importancia relevante en el campo del fi ngerprinting, puesto que la caracterización de estas propiedades est a directamente relacionada con una cota superior en la tasa del c odigo, es decir, con el n umero de usuarios que puede gestionar un sistema de fi ngerprinting. En este cap ítulo investigamos esta equivalencia y proporcionamos una respuesta afirmativa para un gran n umero de familias de c odigos de Reed-Solomon. Los resultados obtenidos parecen sugerir que la conjetura es cierta

Properties and evaluation of fingerprinting codes

The concept of data fingerprinting is of paramount importance in the framework of digital content distribution. This project deals with fingerprinting codes, which are used to prevent dishonest users from redistributing copyrighted material. After introducing some basic notions of coding and fingerprinting theory, the project is divided in two parts. In the first part, we present and analyze some of the main existing fingerprinting codes and we also discuss some new constructions. The study is specifically focused on the estimation of the minimum length of the codes, given the design parameters of the system: number of users to allocate, maximum size of the collusions and probability of identification error. Also, we present some theoretical results about the new code construction studied. Finally, we present several simulations, comparing the different codes and estimating what is the minimum-length code in each region. The second part of the project is devoted to the study of the properties of Reed-Solomon codes in the context of fingerprinting. Codes with the traceability (TA) property are of remarkable significance, since they provide an efficient way to identify traitors. Codes with the identifiable parent property (IPP) are also capable of identifying traitors, requiring less restrictive conditions than the TA codes at the expense of not having an efficient decoding algorithm, in the general case. Other codes that have been widely studied but possess a weaker traitor-tracing capability are the secure frameproof codes (SFP). It is a well-known result that TA implies IPP and IPP implies SFP. The converse is in general false. However, it has been conjectured that for Reed-Solomon codes all three properties are equivalent. In this paper we investigate this equivalence, and provide a positive answer for families of Reed-Solomon codes when the number of traitors divide the size of the code fieldAward-winnin

A survey on Traitor Tracing Schemes

When intellectual properties are distributed over a broadcast network, the content is usually encrypted in a way such that only authorized users who have a certain set of keys, can decrypt the content. Some authorized users may be willing to disclose their keys in constructing a pirate decoder which allows illegitimate users to access the content. It is desirable to determine the source of the keys in a pirate decoder, once one is captured. Traitor tracing schemes were introduced to help solve this problem. A traitor tracing scheme usually consists of: a scheme to generate and distribute each user's personal key, a cryptosystem used to protect session keys that are used to encrypt/decrypt the actual content, and a tracing algorithm to determine one source of the keys in a pirate decoder. In this thesis, we survey the traitor tracing schemes that have been suggested. We group the schemes into two groups: symmetric in which the session key is encrypted and decrypted using the same key and asymmetric schemes in which the session key is encrypted and decrypted using different keys. We also explore the possibility of a truly public scheme in which the data supplier knows the encryption keys only. A uniform analysisis presented on the efficiency of these schemes using a set of performance parameters

A study of the separating property in Reed-Solomon codes by bounding the minimum distance

The version of record is available online at: http://dx.doi.org/10.1007/s10623-021-00988-zAccording to their strength, the tracing properties of a code can be categorized as frameproof, separating, IPP and TA. It is known that, if the minimum distance of the code is larger than a certain threshold then the TA property implies the rest. Silverberg et al. ask if there is some kind of tracing capability left when the minimum distance falls below the threshold. Under different assumptions, several papers have given a negative answer to the question. In this paper, further progress is made. We establish values of the minimum distance for which Reed-Solomon codes do not posses the separating property.This work has been supported by the Spanish Government Grant TCO-RISEBLOCK (PID2019-110224RB-I00) MINECO .Peer ReviewedPostprint (published version