Fully Collusion Resistant Traitor Tracing with Short Ciphertexts and Private Keys

Boneh, Dan; Sahai, Amit; Waters, Brent

doi:10.1007/11761679_34

Cited by 228 publications

(269 citation statements)

References 35 publications

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“…These include GrothOstrovsky-Sahai proofs [22,21], the Boneh-Sahai-Waters traitor tracing scheme [10,15], and the functional encryption schemes of Lewko-Okamoto-Sahai-Takashima-Waters [25,33]. Waters also notes that the dual system encryption techniques in [39] used to obtain prime order systems were first instantiated in composite order groups.…”

Section: Introductionmentioning

confidence: 99%

Tools for Simulating Features of Composite Order Bilinear Groups in the Prime Order Setting

Lewko

2012

Lecture Notes in Computer Science

186

206

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In this paper, we explore a general methodology for converting composite order pairingbased cryptosystems into the prime order setting. We employ the dual pairing vector space approach initiated by Okamoto and Takashima and formulate versatile tools in this framework that can be used to translate composite order schemes for which the prior techniques of Freeman were insufficient. Our techniques are typically applicable for composite order schemes relying on the canceling property and proven secure from variants of the subgroup decision assumption, and will result in prime order schemes that are proven secure from the decisional linear assumption. As an instructive example, we obtain a translation of the Lewko-Waters composite order IBE scheme. This provides a close analog of the BonehBoyen IBE scheme that is proven fully secure from the decisional linear assumption. We also provide a translation of the Lewko-Waters unbounded HIBE scheme.

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Section: Introductionmentioning

confidence: 99%

Tools for Simulating Features of Composite Order Bilinear Groups in the Prime Order Setting

Lewko

2012

Lecture Notes in Computer Science

186

206

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“…Many traitor tracing schemes were designed to be secure against a collusion of t users. Fully collusion resistant traitor tracing schemes were proposed based on bilinear groups [6,15,25]. Abdalla et al [1] proposed the concept of identity-based traitor tracing (IBTT) and constructed an IBTT scheme.…”

Section: Related Workmentioning

confidence: 99%

“…The PKBE scheme of Dodis and Fazio [11] can also be a PKTR scheme since their scheme also follows the subset cover framework. Boneh and Waters [7] proposed a fully collusion resistant PKTR scheme based on composite order bilinear groups and proved its adaptive security by combining the PKBE scheme of Boneh et al [5] and the traitor tracing scheme of Boneh et al [6]. The efficiency of this scheme was improved by using prime order bilinear groups [15,26].…”

Section: Related Workmentioning

confidence: 99%

“…Traitor tracing, introduced by Chor, Fiat, and Naor [8], is a mechanism that provides the tracing functionality such that a tracer who is given a pirate decoder can find at least one user who participated to create a pirate decoder by using his private key. PKTR is a mechanism that can find a user suspected to be a traitor and revoke the user permanently [6,7,21]. A PKTR scheme consists of the four algorithm of PKRE and one additional tracing algorithm that calls a pirate decoder as a black-box.…”

Section: A Trace and Revokementioning

confidence: 99%

“…However, the most efficient scheme of this method that combines the layered subset difference (LSD) scheme of Halevy and Shamir [18] and the HIBE scheme of Boneh et al [3] has a demerit such that the size of private keys is O(log 2.5 N) where N is the total number of users in the system. The second method is to combine a private linear broadcast encryption (PLBE) scheme that was introduced by Boneh, Sahai, and Waters [6] and a PKBE scheme [7,15,26]. The PKTR schemes of this method are quite efficient in terms of the ciphertext size since the size of ciphertexts is independent of the size of a receiver set.…”

Section: Introductionmentioning

confidence: 99%

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Public-Key Revocation and Tracing Schemes with Subset Difference Methods Revisited

Lee

Koo

Lee

et al. 2014

Computer Security - ESORICS 2014

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Trace and revoke is broadcast encryption with the traitor tracing functionality. It is a very powerful primitive since it can revoke users whose private keys are compromised by finding them using a tracing algorithm if a pirate decoder is given. Public-key trace and revoke (PKTR) is a special type of trace and revoke such that anyone can run the tracing algorithm and anyone can create an encrypted message by using a public key. Although public-key trace and revoke schemes are attractive tools, the currently known PKTR schemes are a little bit inefficient in terms of the private key size and the public key size compared with public-key broadcast encryption schemes.In this paper, we propose a new technique to construct an efficient PKTR scheme by using the subset cover framework. First, we introduce a new concept of public-key encryption named single revocation encryption (SRE) and propose an efficient SRE scheme in the random oracle model. The universe of SRE consists of many groups and each group consists of many members. A user in SRE is represented as a group that he belongs and a member in the group. In SRE, a sender can create a ciphertext for a specified group where one member in the group is revoked, and a receiver can decrypt the ciphertext if he belongs to the group in the ciphertext and he is not revoked in the group. Second, we show that the subset difference (SD) scheme (or the layered subset difference (LSD) scheme) and an SRE scheme can be combined to construct a PKTR scheme. Our PKTR scheme using the LSD scheme and our SRE scheme has the ciphertext size of O(r), the private key size of O(log 1.5 N), and the public key size of O(1) where N is the total number of users in the system and r is the size of a revoked set. Our PKTR scheme is the first one that achieves the private key size of O(log 1.5 N) and the public key size of O(1).

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Broadcast Encryption and Traitor Tracing

Phan¹

2022

Asymmetric Cryptography

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Fully Collusion Resistant Traitor Tracing with Short Ciphertexts and Private Keys

Cited by 228 publications

References 35 publications

Tools for Simulating Features of Composite Order Bilinear Groups in the Prime Order Setting

Tools for Simulating Features of Composite Order Bilinear Groups in the Prime Order Setting

Public-Key Revocation and Tracing Schemes with Subset Difference Methods Revisited

Broadcast Encryption and Traitor Tracing

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