Combinatorial properties of frameproof and traceability codes

Abstract. The notion of key privacy for asymmetric encryption schemes was formally de ned by Bellare, Boldyreva, Desai and Pointcheval in 2001: it states that an eavesdropper in possession of a ciphertext is not able to tell which speci c key, out of a set of known public keys, is the one under which the ciphertext was created. Since anonymity can be misused by dishonest users, some situations could require a tracing authority capable of revoking key privacy when illegal behavior is detected. Prior works on traceable anonymous encryption miss a critical point: an encryption scheme may produce a covert channel which malicious users can use to communicate illegally using ciphertexts that trace back to nobody or, even worse, to some honest user. In this paper, we examine subliminal channels in the context of traceable anonymous encryption and we introduce a new primitive termed mediated traceable anonymous encryption that provides con dentiality and anonymity while preventing malicious users to embed subliminal messages in ciphertexts. In our model, all ciphertexts pass through a mediator (or possibly several successive mediators) and our goal is to design protocols where the absence of covert channels is guaranteed as long as the mediator is honest, while semantic security and key privacy hold even if the mediator is dishonest. We give security de nitions for this new primitive and constructions meeting the formalized requirements. Our generic construction is fairly e cient, with ciphertexts that have logarithmic size in the number of group members, while preventing collusions. The security analysis requires classical complexity assumptions in the standard model.

Section: Collusion-secure Codesmentioning

confidence: 99%

Mediated Traceable Anonymous Encryption

Izabachène

Pointcheval

Vergnaud

2010

“…Stinson et al [37] discusses relations between these structures. We choose the language of cover-free families since they have found multiple applications in cryptography (see [20,26,36] for examples).…”

Section: Nonadaptive Group Testing With Cover-free Familiesmentioning

confidence: 99%

Group Testing and Batch Verification

Zaverucha

Stinson

2010

We observe that finding invalid signatures in batches of signatures that fail batch verification is an instance of the classical group testing problem. We present and compare new sequential and parallel algorithms for finding invalid signatures based on group testing algorithms. Of the five new algorithms, three show improved performance for many parameter choices, and the performance gains are especially notable when multiple processors are available.

“…Traitor tracing systems generally fall into two categories: combinatorial, as in [9,23,30,31,13,14,10,27,2,29,28,22], and algebraic, as in [20,3,24,19,11,21,33,8]. The broadcaster's key BK in combinatorial systems can be either secret or public.…”

Section: Introductionmentioning

confidence: 99%

“…Combinatorial systems such as [9,23,30,31,13,14,10,27,2,29,28,22] are typically designed for the secret BK settings, but can be made public-key by replacing the underlying ciphers by public key systems.…”

Section: Introductionmentioning

confidence: 99%

Fully Collusion Resistant Traitor Tracing with Short Ciphertexts and Private Keys

Boneh

Sahai²,

Waters

2006

228

267

We construct a fully collusion resistant tracing traitors system with sublinear size ciphertexts and constant size private keys. More precisely, let N be the total number of users. Our system generates ciphertexts of size O( √ N ) and private keys of size O(1). We first introduce a simpler primitive we call private linear broadcast encryption (PLBE) and show that any PLBE gives a tracing traitors system with the same parameters. We then show how to build a PLBE system with O( √ N ) size ciphertexts. Our system uses bilinear maps in groups of composite order.