National Institute of Standards and Technology における超伝導研究及び生活

Usually, a proof of a theorem contains more knowledge than the mere fact that the theorem is true. For instance, to prove that a graph is Hamiltonian it suffices to exhibit a Hamiltonian tour in it; however, this seems to contain more knowledge than the single bit Hamiltonian/non-Hamiltonian.In this paper a computational complexity theory of the “knowledge” contained in a proof is developed. Zero-knowledge proofs are defined as those proofs that convey no additional knowledge other than the correctness of the proposition in question. Examples of zero-knowledge proof systems are given for the languages of quadratic residuosity and 'quadratic nonresiduosity. These are the first examples of zero-knowledge proofs for languages not known to be efficiently recognizable.

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The knowledge complexity of interactive proof-systems

This paper is brief tutorial on a technique for structuring security proofs as sequences games.

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Sequences of games: a tool for taming complexity in security proofs.

An important open problem in the area of Traitor Tracing is designing a scheme with constant expansion of the size of keys (users' keys and the encryption key) and of the size of ciphertexts with respect to the size of the plaintext. This problem is known from the introduction of Traitor Tracing by Chor, Fiat and Naor. We refer to such schemes as traitor tracing with constant transmission rate. Here we present a general methodology and two protocol constructions that result in the first two public-key traitor tracing schemes with constant transmission rate in settings where plaintexts can be calibrated to be sufficiently large. Our starting point is the notion of copyrighted function which was presented by Naccache, Shamir and Stern. We first solve the open problem of discrete-log-based and public-key-based copyrighted function. Then, we observe the simple yet crucial relation between (public-key) copyrighted encryption and (public-key) traitor tracing, which we exploit by introducing a generic design paradigm for designing constant transmission rate traitor tracing schemes based on copyrighted encryption functions. Our first scheme achieves the same expansion efficiency as regular ElGamal encryption. The second scheme introduces only a slightly larger (constant) overhead, however, it additionally achieves efficient black-box traitor tracing (against any pirate construction).

Traitor Tracing with constant transmission rate

This paper shows a generic and simple conversion from weak asymmetric and symmetric encryption schemes into an asymmetric encryption scheme which is secure in a very strong sense- indistinguishability against adaptive chosen-ciphertext attacks in the random oracle model. In particular, this conversion can be applied efficiently to an asymmetric encryption scheme that provides a large enough coin space and, for every message, many enough variants of the encryption, like the ElGamal encryption scheme.

Secure integration of asymmetric and symmetric encryption schemes

Traitor tracing schemes are of major importance for secure distribution of digital content. They indeed aim at protecting content providers from colluding users to build pirate decoders. If such a collusion happens, at least one member of the latter collusion will be detected. Several solutions have already been proposed in the literature, but the most important problem to solve remains having a very good cipher-text/plaintext rate. At Eurocrypt '02, Kiayias and Yung proposed the first scheme with such a constant rate, but still not optimal. In this paper, granted bilinear maps, we manage to improve it, and get an almost optimal scheme, since this rate is asymptotically 1. Furthermore, we introduce a new feature, the public traceability, which means that the center can delegate the tracing capability to any untrusted person. This is not the first use of bilinear maps for traitor tracing applications, but among the previous proposals, only one has remained unbroken: we present an attack by producing an anonymous pirate decoder. We furthermore explain the flaw in their security analysis. For our scheme, we provide a complete proof, based on new computational assumptions, related to the bilinear Diffie-Hellman ones, in the standard model.

Public traceability in traitor tracing schemes

Traitor tracing schemes are of major importance for secure distribution of digital content. They indeed aim at protecting content providers from colluding users to build pirate decoders. If such a collusion happens, at least one member of the latter collusion will be detected. Several solutions have already been proposed in the literature, but the most important problem to solve remains having a very good ciphertext/plaintext rate. At Eurocrypt '02, Kiayias and Yung proposed the first scheme with such a constant rate, but still not optimal. In this paper, granted bilinear maps, we manage to improve it, and get an “almost” optimal scheme, since this rate is asymptotically 1. Furthermore, we introduce a new feature, the “public traceability”, which means that the center can delegate the tracing capability to any “untrusted” person. This is not the first use of bilinear maps for traitor tracing applications, but among the previous proposals, only one has remained unbroken: we present an attack by producing an anonymous pirate decoder. We furthermore explain the flaw in their security analysis. For our scheme, we provide a complete proof, based on new computational assumptions, related to the bilinear Diffie-Hellman ones, in the standard model.

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We consider a situation where multiple parties, owning data that have to be frequently updated, agree to share weighted sums of these data with some aggregator, but where they do not wish to reveal their individual data, and do not trust each other We combine techniques from Private Stream Aggregation (PSA) and Functional Encryption (FE), to introduce a primitive we call Decentralized Multi-Client Functional Encryption (DMCFE), for which we give a practical instantiation for Inner Product functionalities This primitive allows various senders to non-interactively generate ciphertexts which support inner-product evaluation, with functional decryption keys that can also be generated non-interactively, in a distributed way, among the senders Interactions are required during the setup phase only We prove adaptive security of our constructions, while allowing corruptions of the clients, in the random oracle model

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Decentralized Multi-Client Functional Encryption for Inner Product

Probabilistic symmetric encryption have already been widely studied, from a theoretical point of view. Nevertheless, many applications require length-preserving encryption, to be patched at a minimal cost to include privacy without modifying the format (e.g. encrypted filesystems). In this paper, we thus consider the security notions for length-preserving, deterministic and symmetric encryption schemes, also termed ciphers: semantic security under lunchtime and challenge-adaptive adversaries. We furthermore provide some relations for this notion between different models of adversaries, and the more classical security notions for ciphers: pseudo-random permutations (PRP) and super pseudo-random permutations (SPRP).

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About the security of ciphers (semantic security and pseudo-random permutations)

We consider designing public-key broadcast encryption schemes with constant-size secret keys and ciphertexts, achieving chosen-ciphertext security. We first argue that known CPA-to-CCA transforms currently do not yield such schemes. We then propose a scheme, modifying a previous selective CPA secure proposal by Boneh, Gentry, and Waters. Our scheme has constant-size secret keys and ciphertexts, and we prove that it is selective chosen-ciphertext secure based on standard assumptions. Our scheme has ciphertexts that are shorter than those of the previous CCA secure proposals. Then, we propose a second scheme that provides the functionality of both broadcast encryption and revocation schemes simultaneously using the same set of parameters. Finally, we show that it is possible to prove our first scheme adaptive chosen-ciphertext secure under reasonable extensions of the bilinear Diffie---Hellman exponent and the knowledge-of-exponent assumptions. We prove both of these extended assumptions in the generic group model. Hence, our scheme becomes the first to achieve constant-size secret keys and ciphertexts (both asymptotically optimal) and adaptive chosen-ciphertext security at the same time.

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Duong Hieu Phan

Papers

Public traceability in traitor tracing schemes

Public traceability in traitor tracing schemes

Decentralized Multi-Client Functional Encryption for Inner Product

About the security of ciphers (semantic security and pseudo-random permutations)

Adaptive CCA broadcast encryption with constant-size secret keys and ciphertexts