Journal Article•
Traitor Tracing with constant transmission rate
TL;DR: This work presents 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 sufficientlylarge.
Abstract: 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).
Citations
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04 May 2003
TL;DR: This paper shows how to substantially lower the degree of these equations by multiplying them by well-chosen multivariate polynomials, and is able to break Toyocrypt in 249 CPU clocks, with only 20 Kbytes of keystream, the fastest attack proposed so far.
Abstract: A classical construction of stream ciphers is to combine several LFSRs and a highly non-linear Boolean function f. Their security is usually analysed in terms of correlation attacks, that can be seen as solving a system of multivariate linear equations, true with some probability. At ICISC'02 this approach is extended to systems of higher-degree multivariate equations, and gives an attack in 292 for Toyocrypt, a Cryptrec submission. In this attack the key is found by solving an overdefined system of algebraic equations. In this paper we show how to substantially lower the degree of these equations by multiplying them by well-chosen multivariate polynomials. Thus we are able to break Toyocrypt in 249 CPU clocks, with only 20 Kbytes of keystream, the fastest attack proposed so far. We also successfully attack the Nessie submission LILI-128, within 257 CPU clocks (not the fastest attack known). In general, we show that if the Boolean function uses only a small subset (e.g. 10) of state/LFSR bits, the cipher can be broken, whatever is the Boolean function used (worst case). Our new general algebraic attack breaks stream ciphers satisfying all the previously known design criteria in at most the square root of the complexity of the previously known generic attack.
997 citations
26 May 2013
TL;DR: This work describes plausible lattice-based constructions with properties that approximate the sought-after multilinear maps in hard-discrete-logarithm groups, and shows an example application of such multi-linear maps that can be realized using the approximation.
Abstract: We describe plausible lattice-based constructions with properties that approximate the sought-after multilinear maps in hard-discrete-logarithm groups, and show an example application of such multi-linear maps that can be realized using our approximation. The security of our constructions relies on seemingly hard problems in ideal lattices, which can be viewed as extensions of the assumed hardness of the NTRU function.
817 citations
20 Dec 2004
TL;DR: GCM is shown to be the most efficient mode of operation for high speed packet networks, by using a realistic model of a network crypto module and empirical data from studies of Internet traffic in conjunction with software experiments and hardware designs.
Abstract: The recently introduced Galois/Counter Mode (GCM) of operation for block ciphers provides both encryption and message authentication, using universal hashing based on multiplication in a binary finite field. We analyze its security and performance, and show that it is the most efficient mode of operation for high speed packet networks, by using a realistic model of a network crypto module and empirical data from studies of Internet traffic in conjunction with software experiments and hardware designs. GCM has several useful features: it can accept IVs of arbitrary length, can act as a stand-alone message authentication code (MAC), and can be used as an incremental MAC. We show that GCM is secure in the standard model of concrete security, even when these features are used. We also consider several of its important system-security aspects.
505 citations
18 Nov 2002
TL;DR: This paper formalizes and investigates the authenticated-encryption with associated-data (AEAD) problem, and studies two simple ways to turn an authenticated-Encryption scheme that does not support associated- data into one that does: nonce stealing and ciphertext translation.
Abstract: When a message is transformed into a ciphertext in a way designed to protect both its privacy and authenticity, there may be additional information, such as a packet header, that travels alongside the ciphertext (at least conceptually) and must get authenticated with it. We formalize and investigate this authenticated-encryption with associated-data (AEAD) problem. Though the problem has long been addressed in cryptographic practice, it was never provided a definition or even a name. We do this, and go on to look at efficient solutions for AEAD, both in general and for the authenticated-encryption scheme OCB. For the general setting we study two simple ways to turn an authenticated-encryption scheme that does not support associated-data into one that does: nonce stealing and ciphertext translation. For the case of OCB we construct an AEAD-scheme by combining OCB and the pseudorandom function PMAC, using the same key for both algorithms. We prove that, despite "interaction" between the two schemes when using a common key, the combination is sound. We also consider achieving AEAD by the generic composition of a nonce-based, privacy-only encryption scheme and a pseudorandom function.
490 citations
02 Dec 2009
TL;DR: This work demonstrates how the framework that is used for creating efficient number-theoretic ID and signature schemes can be transferred into the setting of lattices and is able to shorten the length of the signatures that are produced by Girault's factoring-based digital signature scheme.
Abstract: We demonstrate how the framework that is used for creating efficient number-theoretic ID and signature schemes can be transferred into the setting of lattices. This results in constructions of the most efficient to-date identification and signature schemes with security based on the worst-case hardness of problems in ideal lattices. In particular, our ID scheme has communication complexity of around 65,000 bits and the length of the signatures produced by our signature scheme is about 50,000 bits. All prior lattice-based identification schemes required on the order of millions of bits to be transferred, while all previous lattice-based signature schemes were either stateful, too inefficient, or produced signatures whose lengths were also on the order of millions of bits. The security of our identification scheme is based on the hardness of finding the approximate shortest vector to within a factor of $\tilde{O}(n^2)$ in the standard model, while the security of the signature scheme is based on the same assumption in the random oracle model. Our protocols are very efficient, with all operations requiring $\tilde{O}(n)$ time.
We also show that the technique for constructing our lattice-based schemes can be used to improve certain number-theoretic schemes. In particular, we are able to shorten the length of the signatures that are produced by Girault's factoring-based digital signature scheme ([10][11][31]).
478 citations
References
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23 Aug 1985
TL;DR: A new signature scheme is proposed, together with an implementation of the Diffie-Hellman key distribution scheme that achieves a public key cryptosystem that relies on the difficulty of computing discrete logarithms over finite fields.
Abstract: A new signature scheme is proposed, together with an implementation of the Diffie-Hellman key distribution scheme that achieves a public key cryptosystem. The security of both systems relies on the difficulty of computing discrete logarithms over finite fields.
7,514 citations
19 Aug 2001
TL;DR: In this paper, the Subset-Cover framework is proposed for the stateless receiver case, where the users do not (necessarily) update their state from session to session, and sufficient conditions that guarantee the security of a revocation algorithm in this class are provided.
Abstract: We deal with the problem of a center sending a message to a group of users such that some subset of the users is considered revoked and should not be able to obtain the content of the message. We concentrate on the stateless receiver case, where the users do not (necessarily) update their state from session to session. We present a framework called the Subset-Cover framework, which abstracts a variety of revocation schemes including some previously known ones. We provide sufficient conditions that guarantees the security of a revocation algorithm in this class.
We describe two explicit Subset-Cover revocation algorithms; these algorithms are very flexible and work for any number of revoked users. The schemes require storage at the receiver of log N and 1/2 log2 N keys respectively (N is the total number of users), and in order to revoke r users the required message lengths are of r log N and 2r keys respectively. We also provide a general traitor tracing mechanism that can be integrated with any Subset-Cover revocation scheme that satisfies a "bifurcation property". This mechanism does not need an a priori bound on the number of traitors and does not expand the message length by much compared to the revocation of the same set of traitors.
The main improvements of these methods over previously suggested methods, when adopted to the stateless scenario, are: (1) reducing the message length to O(r) regardless of the coalition size while maintaining a single decryption at the user's end (2) provide a seamless integration between the revocation and tracing so that the tracing mechanisms does not require any change to the revocation algorithm.
1,277 citations
19 Aug 2001
TL;DR: In this article, it was shown that the Boneh-Franklin (BF) scheme and the Kurosawa-Desmedt (KDS) scheme have no black-box traceability in the self-protecting model when the number of traitors is super-logarithmic.
Abstract: We present a new generic black-box traitor tracing model in which the pirate-decoder employs a self-protection technique. This mechanism is simple, easy to implement in any (software or hardware) device and is a natural way by which a pirate (an adversary) which is black-box accessible, may try to evade detection. We present a necessary combinatorial condition for black-box traitor tracing of self-protecting devices. We constructively prove that any system that fails this condition, is incapable of tracing pirate-decoders that contain keys based on a superlogarithmic number of traitor keys. We then combine the above condition with specific properties of concrete systems. We show that the Boneh-Franklin (BF) scheme as well as the Kurosawa-Desmedt scheme have no black-box tracing capability in the self-protecting model when the number of traitors is superlogarithmic, unless the ciphertext size is as large as in a trivial system, namely linear in the number of users. This partially settles in the negative the open problem of Boneh and Franklin regarding the general black-box traceability of the BF scheme: at least for the case of superlogarithmic traitors. Our negative result does not apply to the Chor-Fiat-Naor (CFN) scheme (which, in fact, allows tracing in our self-protecting model); this separates CFN black-box traceability from that of BF. We also investigate a weaker form of black-box tracing called single-query "black-box confirmation." We show that, when suspicion is modeled as a confidence weight (which biases the uniform distribution of traitors), such single-query confirmation is essentially not possible against a self-protecting pirate-decoder that contains keys based on a superlogarithmic number of traitor keys.
1,132 citations
Journal Article•
TL;DR: This work constructively proves that any system that fails this condition, is incapable of tracing pirate-decoders that contain keys based on a superlogarithmic number of traitor keys, and investigates a weaker form of black-box tracing called single-query "black-box confirmation."
Abstract: We present a new generic black-box traitor tracing model in which the pirate-decoder employs a self-protection technique. This mechanism is simple, easy to implement in any (software or hardware) device and is a natural way by which a pirate (an adversary) which is black-box accessible, may try to evade detection. We present a necessary combinatorial condition for black-box traitor tracing of self-protecting devices. We constructively prove that any system that fails this condition, is incapable of tracing pirate-decoders that contain keys based on a superlogarithmic number of traitor keys. We then combine the above condition with specific properties of concrete systems. We show that the Boneh-Franklin (BF) scheme as well as the Kurosawa-Desmedt scheme have no black-box tracing capability in the self-protecting model when the number of traitors is superlogarithmic, unless the ciphertext size is as large as in a trivial system, namely linear in the number of users. This partially settles in the negative the open problem of Boneh and Franklin regarding the general black-box traceability of the BF scheme: at least for the case of superlogarithmic traitors. Our negative result does not apply to the Chor-Fiat-Naor (CFN) scheme (which, in fact, allows tracing in our self-protecting model); this separates CFN black-box traceability from that of BF. We also investigate a weaker form of black-box tracing called single-query black-box confirmation. We show that, when suspicion is modeled as a confidence weight (which biases the uniform distribution of traitors), such single-query confirmation is essentially not possible against a self-protecting pirate-decoder that contains keys based on a superlogarithmic number of traitor keys.
1,098 citations
Additional excerpts
...(see [KY01a]) TTS Scheme 1 ∼ 2 ∼ 1 ∼ 3 Ω(l) = t ? TTS Scheme 2 ∼ 3 ∼ 2 ∼ 4 Ω(l) = t √...
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04 May 2003
TL;DR: This paper shows how to substantially lower the degree of these equations by multiplying them by well-chosen multivariate polynomials, and is able to break Toyocrypt in 249 CPU clocks, with only 20 Kbytes of keystream, the fastest attack proposed so far.
Abstract: A classical construction of stream ciphers is to combine several LFSRs and a highly non-linear Boolean function f. Their security is usually analysed in terms of correlation attacks, that can be seen as solving a system of multivariate linear equations, true with some probability. At ICISC'02 this approach is extended to systems of higher-degree multivariate equations, and gives an attack in 292 for Toyocrypt, a Cryptrec submission. In this attack the key is found by solving an overdefined system of algebraic equations. In this paper we show how to substantially lower the degree of these equations by multiplying them by well-chosen multivariate polynomials. Thus we are able to break Toyocrypt in 249 CPU clocks, with only 20 Kbytes of keystream, the fastest attack proposed so far. We also successfully attack the Nessie submission LILI-128, within 257 CPU clocks (not the fastest attack known). In general, we show that if the Boolean function uses only a small subset (e.g. 10) of state/LFSR bits, the cipher can be broken, whatever is the Boolean function used (worst case). Our new general algebraic attack breaks stream ciphers satisfying all the previously known design criteria in at most the square root of the complexity of the previously known generic attack.
997 citations