The main threat against fingerprinting systems is collusion attacks. The attack most commonly assumed in the literature is a combination of averaging the collusion fingerprints and additive noise. In this correspondence, we demonstrate that the recently proposed fingerprinting scheme of Kuribayashi's is very vulnerable to certain nonlinear collusion attacks.

Keywords: data compression;fingerprint identification;image coding; image denoising;image watermarking; Kuribayashi fingerprinting scheme;additive noise; collusion fingerprints;fingerprinting systems; nonlinear collusion attacks;Additive noise; Detectors;Discrete cosine transforms; Educational institutions;Interference;Transform coding; Watermarking;Fingerprinting;collusion attack;watermarking

We formalize a new attack model for collusion secure codes, incorporating attacks on the underlying watermarking scheme as well as cut-and-paste attacks traditionally considered for collusion secure codes. We use this model to analyze the collusion resistance of two versions of the Tardos code, both for binary and nonbinary alphabets. The model allows us to consider different signal processing attacks on the content, namely the addition of noise and averaging attacks. The latter may result in content segments that have multiple watermarks embedded. We study two versions of the q-ary Tardos code in which the accusation method has been modified so as to allow for the detection of multiple symbols in the same content segment. We show that both variants yield efficient codes in the new model, parametrized for realistic attacker strengths.

Keywords: fingerprint identification;image watermarking;Tardos fingerprinting codes;accusation method;binary alphabets;collusion resistance;collusion secure codes;combined digit model;content segment;cut-and-paste attacks;nonbinary alphabets;q-ary Tardos code;signal processing attacks;watermarking scheme;Analytical models;Detectors;Mathematical model;Noise;Watermarking;Collusion attacks;fingerprinting;watermarking

The Deletion-Insertion Correcting Code construction proposed by Davey and MacKay consists of an inner code that recovers synchronization and an outer code that provides substitution error protection. The inner code uses low-weight codewords which are added (modulo two) to a pilot sequence. The receiver is able to synchronise on the pilot sequence in spite of the changes introduced by the added codeword. The original bit-level formulation of the inner decoder assumes that all bits in the sparse codebook are identically and independently distributed. Not only is this assumption inaccurate, but it also prevents the use of soft a- priori input to the decoder. We propose an alternative symbol-level inner decoding algorithm that takes the actual codebook into account. Simulation results show that the proposed algorithm has an improved performance with only a small penalty in complexity, and it allows other improvements using inner codes with larger minimum distance.

Keywords: turbo codes;Davey-MacKay construction;alternative symbol-level inner decoding algorithm;deletion-insertion correcting code construction;improved decoding algorithm;inner decoder;nonbinary codes;pilot sequence;sparse codebook;substitution error protection;turbo codes;Communications Society;Decoding;Delta modulation;Demodulation;Error correction codes;Iterative algorithms;Partial transmit sequences;Peer to peer computing;Turbo codes;Watermarking

We introduce a new attack model for collusion-secure codes, called the combined digit model, which represents signal processing attacks against the underlying watermarking level better than existing models. In this paper, we analyze the performance of two variants of the Tardos code and show that both variants can accommodate the new model and resist collusion attacks with only a modest increase in code length as compared to the results for the commonly used restricted digit model.

Keywords: codes;watermarking;Tardos fingerprinting codes;collusion-secure codes;combined digit model;restricted digit model;signal processing;watermarking level;Codes;Data security;Fingerprint recognition;Forensics;Information security;Performance analysis;Resists;Signal processing;Signal processing algorithms;Watermarking

The Davey-MacKay construction is a deletion-insertion correcting code scheme consisting of an inner code that functions as a pilot sequence to which the receiver seeks to synchronize, and an outer code that provides error protection. We analyse the performance of the inner code in isolation, arguing that these codes provide unequal protection, and demonstrate empirically that the error rate is dependent on the date symbol values. We also propose modifications to the code construction that alleviate this asymmetry. Simulation results show that these codes have an improved performance with no penalty.

Keywords: error correction codes;Davey-MacKay construction;code construction;deletion-insertion correcting code scheme;error protection code;inner code;outer code;Decoding;Delta modulation;Error analysis;Error correction codes;Information theory;Parity check codes;Partial transmit sequences;Performance analysis;Protection;Watermarking

In this paper we consider the use of q-ary turbo codes on abstract q-ary channels. Simulations show that our 16-ary codes perform well on the q-ary symmetric channel. This validates their suitability as outer codes in non-binary applications. We also compare with the performance of same codes on conventional PSK and QAM modulation, and demonstrate an application of these codes to the insertion/deletion channel.

Keywords: channel coding;phase shift keying;quadrature amplitude modulation;turbo codes;PSK modulation;QAM modulation;insertion/deletion channel;nonbinary turbo codes;q-ary channels;q-ary turbo codes;Construction industry;Decoding;Delta modulation;Error analysis;Modulation;Turbo codes;Watermarking;deletion-insertion correcting codes;non-binary codes;q-ary symmetric channel;turbo codes

With a digital fingerprinting scheme, a vendor of digital copies of copyrighted material marks each individual copy with a unique fingerprint. If an illegal copy appears, it can be traced back to one or more guilty pirates due to this fingerprint. A coalition of pirates may combine their copies to produce an unauthorized copy with a false, hybrid fingerprint. It is often assumed in the literature that the members of the collusion will make equal contributions to the hybrid fingerprint, because nobody will accept an increased risk of being caught. We argue that no such assumption is valid a priori, and we show that a published solution by Sebe and Domingo-Ferrer can be broken by breaking the assumption.

Keywords: copyright;fingerprint identification;image coding;copyrighted material;digital copy protection;digital fingerprinting scheme;hybrid fingerprint;illegal copying;Collusion-attack;collusion-secure code (CSC);digital fingerprinting;scattering codes

Digital fingerprinting is a forensic method against illegal copying. The distributor marks each individual copy with a unique fingerprint. If an illegal copy appears, it can be traced back to one or more guilty pirates due to this fingerprint. To work against a coalition of several pirates, the fingerprinting scheme must be based on a collusion-secure code. This paper addresses binary collusion-secure codes in the setting of Boneh and Shaw (1995/1998). We prove that the Boneh-Shaw scheme is more efficient than originally proven, and we propose adaptations to further improve the scheme. We also point out some differences between our model and others in the literature.

Keywords: binary codes;copy protection;Boneh-Shaw fingerprinting;binary collusion-secure codes;forensic method;illegal copying;Copyright protection;Councils;Data security;Fingerprint recognition;Forensics;Law;Legal factors;Legislation;Marketing and sales;Motion pictures;Collusion-secure codes;copyright protection;digital fingerprinting (FP);traitor tracing

We compute the second support weight distribution of the Kasami codes.

Keywords: Galois fields, dual codes, linear codes GF, Galois field, Kasami code, SWD, dual code, linear code, support weight distribution

Separating codes find applications in many fields including automata theory and digital fingerprinting. It is known that the Kerdock code of sufficient order is (2,1)- and (2,2)-separating, but the separating weight is only known by a lower bound due to Sagalovich. In this correspondence, we prove that the lower bound on the (2,1)-separating weight is met with equality.

Keywords: automata theory;binary codes;linear codes;(2, 1)-separating weight;automata theory;binary Kerdock code;digital fingerprinting;linear codes;separating codes;Binary codes;Councils;Hamming distance;Informatics;65;Fingerprinting;Kerdock code;linear codes over;separating systems

We show how to compute the support weight distribution A/sub i//sup r/ for r/spl ges/k-d/sub 2//sup /spl perp//+3, where d/sub 2//sup /spl perp// is the second minimum support weight of a code, provided the weight enumerator of the dual code is known.

Keywords: dual codes dual code, support weight distribution, weight enumerator

The combinatorial concept of separating systems has numerous applications, such as automata theory, digital fingerprinting, group testing, and hashing. In this correspondence, we derive upper bounds on the size of codes with various separating properties.

Keywords: combinatorial mathematics;error correction codes;automata theory;combinatorial concept;digital finger printing;error-correcting codes;group testing;hashing;separating codes;separating system;superimposed codes;upper bound;Cryptography;Cyclic redundancy check;Error-correcting codes;hashing;separating systems;superimposed codes

The theory of separating systems has been applied in different areas of science and technology such as automata synthesis, technical diagnosis, and authenticating ownership claims. Constructions of (2,2)-separating systems derived from error-correcting codes are given, together with bounds on their parameters based on distance considerations.

Keywords: concatenated codes;error correction codes;linear codes;2,2-separating systems;bounds;concatenated codes;copyright protection;distance considerations;error-correcting codes;linear codes;watermarking;Linear code;Sufficient conditions;Terminology;Watermarking

We present the relation between product codes and projective multisets, and give a lower bound on the greedy weights of product codes

Keywords: linear codes;set theory;greedy weights;linear codes;lower bound;product codes;projective multisets;Councils;Informatics;Linear code;Product codes;Subspace constraints;Tensile stress

The weight of a code is the number of coordinate positions where no codeword is zero. The rth minimum weight dr is the least weight of an r-dimensional subcode. Wei and Yang (1993) gave a conjecture about the minimum weights for some product codes. In this article, we find a relation between product codes and the Segre embedding of a pair of projective systems, and we use this to prove the conjecture

Keywords: linear codes;set theory;Segre embedding;coordinate positions;linear code;minimum weight;minimum weights;product codes;projective multiset;projective systems;subcode;weight hierarchy;Informatics;Linear code;Product codes;Tensile stress;Vectors

We use projective multisets (projective systems) to find upper bounds on the weight hierarchies for a special class of codes, namely the extremal non-chain codes. Several code constructions exist meeting the bounds with equality

Keywords: linear codes;code constructions;extremal nonchain codes;higher weights;linear codes;projective multisets;projective systems;upper bounds;weight hierarchies;Algebra;Binary codes;Galois fields;Hamming weight;Informatics;Upper bound