A Concise Bounded Anonymous Broadcast Yielding Combinatorial Trace-and-Revoke Schemes

Broadcast Encryption is a fundamental primitive supporting sending a secure message to any chosen target set of $N$ users. While many efficient constructions are known, understanding the efficiency possible for an ``Anonymous Broadcast Encryption\u27\u27 (ANOBE), i.e., one which can hide the target set itself, is quite open. The best solutions by Barth, Boneh, and Waters (\u2706) and Libert, Paterson, and Quaglia (\u2712) are built on public key encryption (PKE) and their ciphertext sizes are, in fact, $N$ times that of the underlying PKE (rate=$N$). Kiayias and Samary (\u2712), in turn, showed a lower bound showing that such rate is the best possible if $N$ is an independent unbounded parameter. However, when considering certain user set size bounded by a system parameter (e.g., the security parameter), the problem remains interesting. We consider the problem of comparing ANOBE with PKE under the same assumption. We call such schemes Anonymous Broadcast Encryption for Bounded Universe -- AnoBEB. We first present an AnoBEB construction for up to $k$ users from LWE assumption, where $k$ is bounded by the scheme security parameter. The scheme does not grow with the parameter and beat the PKE method. Actually, our scheme is as efficient as the underlying LWE public-key encryption; namely, the rate is, in fact, $1$ and thus optimal. The scheme is achieved easily by an observation about an earlier scheme with a different purpose. More interestingly, we move on to employ the new AnoBEB in other multimedia broadcasting methods and, as a second contribution, we introduce a new approach to construct an efficient ``Trace and Revoke scheme\u27\u27 which combines the functionalites of revocation and of tracing people (called traitors) who in a broadcasting schemes share their keys with the adversary which, in turn, generates a pirate receiver. Note that, as was put forth by Kiayias and Yung (EUROCRYPT \u2702), combinatorial traitor tracing schemes can be constructed by combining a system for small universe, integrated via an outer traceability codes (collusion-secure code or identifying parent property (IPP) code). There were many efficient traitor tracing schemes from traceability codes, but no known scheme supports revocation as well. Our new approach integrates our AnoBEB system with a Robust IPP code, introduced by Barg and Kabatiansky (IEEE IT \u2713). This shows an interesting use for robust IPP in cryptography. The robust IPP codes were only implicitly shown by an existence proof. In order to make our technique concrete, we propose two explicit instantiations of robust IPP codes. Our final construction gives the most efficient trace and revoke scheme in the bounded collusion model

Optimization techniques and new methods for boradcast encryption and traitor tracing schemes

Ankara : The Department of Computer Engineering and the Graduate School of Engineering and Science of Bilkent University, 2012.Thesis (Ph. D.) -- Bilkent University, 2012.Includes bibliographical refences.In the last few decades, the use of digital content increased dramatically. Many forms of digital products in the form of CDs, DVDs, TV broadcasts, data over the Internet, entered our life. Classical cryptography, where encryption is done for only one recipient, was not able to handle this change, since its direct use leads to intolerably expensive transmissions. Moreover, new concerns regarding the commercial aspect arised. Since digital commercial contents are sold to various customers, unauthorized copying by malicious actors became a major concern and it needed to be prevented carefully. Therefore, a new research area called digital rights management (DRM) has emerged. Within the scope of DRM, new cryptographic primitives are proposed. In this thesis, we consider three of these: broadcast encryption (BE), traitor tracing (TT), and trace and revoke (T&R) schemes and propose methods to improve the performances and capabilities of these primitives. Particularly, we first consider profiling the recipient set in order to improve transmission size in the most popular BE schemes. We then investigate and solve the optimal free rider assignment problem for one of the most efficient BE schemes so far. Next, we attempt to close the non-trivial gap between BE and T&R schemes by proposing a generic method for adding traitor tracing capability to BE schemes and thus obtaining a T&R scheme. Finally, we investigate an overlooked problem: privacy of the recipient set in T&R schemes. Right now, most schemes do not keep the recipient set anonymous, and everybody can see who received a particular content. As a generic solution to this problem, we propose a method for obtaining anonymous T&R scheme by using anonymous BE schemes as a primitive.Ak, MuratPh.D

Anonymous Traitor Tracing: How to Embed Arbitrary Information in a Key

In a traitor tracing scheme, each user is given a different decryption key. A content distributor can encrypt digital content using a public encryption key and each user in the system can decrypt it using her decryption key. Even if a coalition of users combines their decryption keys and constructs some ``pirate decoder\u27\u27 that is capable of decrypting the content, there is a public tracing algorithm that is guaranteed to recover the identity of at least one of the users in the coalition given black-box access to such decoder. In prior solutions, the users are indexed by numbers $1,\ldots,N$ and the tracing algorithm recovers the index $i$ of a user in a coalition. Such solutions implicitly require the content distributor to keep a record that associates each index $i$ with the actual identifying information for the corresponding user (e.g., name, address, etc.) in order to ensure accountability. In this work, we construct traitor tracing schemes where all of the identifying information about the user can be embedded directly into the user\u27s key and recovered by the tracing algorithm. In particular, the content distributor does not need to separately store any records about the users of the system, and honest users can even remain anonymous to the content distributor. The main technical difficulty comes in designing tracing algorithms that can handle an exponentially large universe of possible identities, rather than just a polynomial set of indices $i \in [N]$. We solve this by abstracting out an interesting algorithmic problem that has surprising connections with seemingly unrelated areas in cryptography. We also extend our solution to a full ``broadcast-trace-and-revoke\u27\u27 scheme in which the traced users can subsequently be revoked from the system. Depending on parameters, some of our schemes can be based only on the existence of public-key encryption while others rely on indistinguishability obfuscation

Preventing False Discovery in Interactive Data Analysis is Hard

We show that, under a standard hardness assumption, there is no computationally efficient algorithm that given $n$ samples from an unknown distribution can give valid answers to $n^{3+o(1)}$ adaptively chosen statistical queries. A statistical query asks for the expectation of a predicate over the underlying distribution, and an answer to a statistical query is valid if it is "close" to the correct expectation over the distribution. Our result stands in stark contrast to the well known fact that exponentially many statistical queries can be answered validly and efficiently if the queries are chosen non-adaptively (no query may depend on the answers to previous queries). Moreover, a recent work by Dwork et al. shows how to accurately answer exponentially many adaptively chosen statistical queries via a computationally inefficient algorithm; and how to answer a quadratic number of adaptive queries via a computationally efficient algorithm. The latter result implies that our result is tight up to a linear factor in $n.$ Conceptually, our result demonstrates that achieving statistical validity alone can be a source of computational intractability in adaptive settings. For example, in the modern large collaborative research environment, data analysts typically choose a particular approach based on previous findings. False discovery occurs if a research finding is supported by the data but not by the underlying distribution. While the study of preventing false discovery in Statistics is decades old, to the best of our knowledge our result is the first to demonstrate a computational barrier. In particular, our result suggests that the perceived difficulty of preventing false discovery in today's collaborative research environment may be inherent

Accountability for Misbehavior in Threshold Decryption via Threshold Traitor Tracing

A $t$-out-of-$n$ threshold decryption system assigns key shares to $n$ parties so that any $t$ of them can decrypt a well-formed ciphertext. Existing threshold decryption systems are not secure when these parties are rational actors: an adversary can offer to pay the parties for their key shares. The problem is that a quorum of $t$ parties, working together, can sell the adversary a decryption key that reveals nothing about the identity of the traitor parties. This provides a risk-free profit for the parties since there is no accountability for their misbehavior --- the information they sell to the adversary reveals nothing about their identity. This behavior can result in a complete break in many applications of threshold decryption, such as encrypted mempools, private voting, and sealed-bid auctions. In this work we show how to add accountability to threshold decryption systems to deter this type of risk-free misbehavior. Suppose a quorum of $t$ or more parties construct a decoder algorithm $D(\cdot)$ that takes as input a ciphertext and outputs the corresponding plaintext or $\bot$. They sell $D$ to the adversary. Our threshold decryption systems are equipped with a tracing algorithm that can trace $D$ to members of the quorum that created it. The tracing algorithm is only given blackbox access to $D$ and will identify some members of the misbehaving quorum. The parties can then be held accountable, which may discourage them from selling the decoder $D$ in the first place. Our starting point is standard (non-threshold) traitor tracing, where $n$ parties each holds a secret key. Every party can decrypt a well-formed ciphertext on its own. However, if a subset of parties ${\cal J} \subseteq [n]$ collude to create a pirate decoder $D(\cdot)$ that can decrypt well-formed ciphertexts, then it is possible to trace $D$ to at least one member of ${\cal J}$ using only blackbox access to the decoder $D$. Traitor tracing received much attention over the years and multiple schemes have been developed. In this work we develop the theory of traitor tracing for threshold decryption, where now only a subset ${\cal J} \subseteq [n]$ of $t$ or more parties can collude to create a pirate decoder $D(\cdot)$. This problem has recently become quite important due to the real-world deployment of threshold decryption in encrypted mempools, as we explain in the paper. While there are several non-threshold traitor tracing schemes that we can leverage, adapting these constructions to the threshold decryption settings requires new cryptographic techniques. We present a number of constructions for traitor tracing for threshold decryption, and note that much work remains to explore the large design space

Cryptographic error correction

Thesis (Ph. D.)--Massachusetts Institute of Technology, Dept. of Electrical Engineering and Computer Science, 2006.Includes bibliographical references (leaves 67-71).It has been said that "cryptography is about concealing information, and coding theory is about revealing it." Despite these apparently conflicting goals, the two fields have common origins and many interesting relationships. In this thesis, we establish new connections between cryptography and coding theory in two ways: first, by applying cryptographic tools to solve classical problems from the theory of error correction; and second, by studying special kinds of codes that are motivated by cryptographic applications. In the first part of this thesis, we consider a model of error correction in which the source of errors is adversarial, but limited to feasible computation. In this model, we construct appealingly simple, general, and efficient cryptographic coding schemes which can recover from much larger error rates than schemes for classical models of adversarial noise. In the second part, we study collusion-secure fingerprinting codes, which are of fundamental importance in cryptographic applications like data watermarking and traitor tracing. We demonstrate tight lower bounds on the lengths of such codes by devising and analyzing a general collusive attack that works for any code.by Christopher Jason Peikert.Ph.D

Generic Construction of Trace and Revoke Schemes

Broadcast encryption (BE) is a cryptographic primitive that allows a broadcaster to encrypt digital content to a privileged set of users and in this way prevent revoked users from accessing the content. In BE schemes, a group of users, called traitor s may leak their keys and enable an adversary to receive the content. Such malicious users can be detected through traitor tracing (TT) schemes. The ultimate goal in a content distribution system would be combining traitor tracing and broadcast encryption (resulting in a trace and revoke system) so that any receiver key found to be compromised in a tracing process would be revoked from future transmissions. In this paper, we propose a generic method to transform a broadcast encryption scheme into a trace and revoke scheme. This transformation involves the utilization of a fingerprinting code over the underlying BE transmission. While fingerprinting codes have been used for constructing traitor tracing schemes in the past, their usage has various shortcomings such as the increase of the public key size with a linear factor in the length of the code. Instead, we propose a novel way to apply fingerprinting codes that allows for efficient parameters while retaining the traceability property. Our approach is based on a new property of fingerprinting codes we introduce, called public samplability. We have instantiated our generic transformation with the BE schemes of [4, 13, 20] something that enables us to produce trace and revoke schemes with novel properties. Specifically, we show (i) a trace and revoke scheme with constant private key size and short ciphertext size, (ii) the first ID-based trace and revoke scheme, (iii) the first publicly traceable scheme with constant private key size and (iv) the first trace and revoke scheme against pirate rebroadcasting attack in the public key setting

Fully Collusion Resistant Traitor Tracing

We construct the first 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 $O(\sqrt{N})$ and private keys of size $O(1)$. We build our system by first building a simpler primitive called private linear broadcast encryption (PLBE). We then show that any PLBE gives a tracing traitors system with the same parameters. Our system uses bilinear maps in groups of composite order

A Performance Evaluation of Pairing-Based Broadcast Encryption Systems

In a broadcast encryption system, a sender can encrypt a message for any subset of users who are listening on a broadcast channel. The goal of broadcast encryption is to leverage the broadcasting structure to achieve better efficiency than individually encrypting to each user; in particular, reducing the bandwidth (i.e., ciphertext size) required to transmit securely, although other factors such as public and private key size and the time to execute setup, encryption and decryption are also important. In this work, we conduct a detailed performance evaluation of eleven public-key, pairing-based broadcast encryption schemes offering different features and security guarantees, including public-key, identity-based, traitor-tracing, private linear and augmented systems. We implemented each system using the MCL Java pairings library, reworking some of the constructions to achieve better efficiency. We tested their performance on a variety of parameter choices, resulting in hundreds of data points to compare, with some interesting results from the classic Boneh-Gentry-Waters scheme (CRYPTO 2005) to Zhandry\u27s recent generalized scheme (CRYPTO 2020), and more. We combine this performance data and knowledge of the systems\u27 features with data we collected on practical usage scenarios to determine which schemes are likely to perform best for certain applications, such as video streaming services, online gaming, live sports betting and smartphone streaming. This work can inform both practitioners and future cryptographic designs in this area