Charles H. Bennett and Peter W. Shor. Quantum information theory. IEEE Transactions on Information Theory, 44(6):2724--2742, 1998.  Home/Search   Document Not in Database   Summary   Related Articles   Check

....Alice and Bob may initially share an arbitrary number of quantum bits which are in some pure state that is independent of the inputs. This is known as communication with prior entanglement [8, 7] or in informationtheoretic terms, as communication over an entanglementassisted quantum channel [3]. The complexity of a quantum (or classical) protocol is the number of qubits (respectively, bits) exchanged between the two players. We say a protocol computes a function f : X Y ## 0, 1 with # 0 error if, for any input x X, y Y , the probability that the two players compute f(x, y) ....

C. Bennett and P. Shor. Quantum information theory. IEEE Transactions on Information Theory, IT-44(6):2724--2742, 1998.

....[76] as a building block. Oblivious transfer protocols may rely on base assumptions involving Diffie Hellman [70] channel noise [26] or quantum properties [25] These solutions are too inefficient or are inapplicable to RFID devices. However, leveraging channel noise for privacy amplification [8] may be an intriguing possibility for RFID. The List Intersection Problem and its relation to RFID leads to two open questions. First, are there oblivious transfer protocols appropriate for low cost RFID devices Second, are there other efficient solutions to the List Intersection problem relying ....

Charles H. Bennett, Gilles Brassard, Claude Crepeau, and Ueli Maurer. Generalized Privacy Amplification. IEEE Transaction on Information Theory, 41(6):1915.

....partial information. Eavesdropping may occur, even with significantly improved hardware, through either multiple photon splitting or by intercepting and resending some bits, but not enough to reveal the presence of the eavesdropper. To overcome this problem, Bennett, Brassard, Crdpeau, and Maurer [BBCM95] developed a privacy amplification procedure that distills a secure key by removing Eve s information with an arbitrarily high probability. During the privacy amplification phase of the protocol, Eve s information is removed. The first step in privacy amplification is for Alice and Bob to use ....

Charles H. Bennett, Gilles Brassard, Claude Cr5peau, and Ueli M. Maurer. Generalized privacy amplification. IEEE Transactions on Information Theory, 41(6):1915-1923, November 1995.

.... ffl K(a b) is the complexity of ha; bi, the usual notation for this is K(a; b) ffl K(a b) minfK(a) K(b)g O(1) ffl K( a b) b a) maxfK(bja) K(ajb)g O(log K(a; b) The lower bound K( a b) b a) maxfK(bja) K(ajb)g Gamma O(1) is obvious, the upper bound was proven in [2]. ffl K( a c) b c) maxfK(cja) K(cjb)g O(log K(a; b; c) where K(a; b; c) denotes the complexity of hha; bi; ci. The lower bound here is also evident: K( a c) b c) maxfK(cja) K(cjb)g Gamma O(1) the upper bound was established in the paper [8] The complexity of all other ....

C.H. Bennett, P. G'acs, M. Li, P. Vitanyi and W. Zurek. Information Distance, IEEE transactions on Information Theory, Vol. 44, No. 4, 1407--1423.

....Knapsack [24] and its modifications. Though many cryptographers have been pessimistic about combinatorial cryptography after the breakdown of the Knapsack type PKC s by Shamir [30] Brickell [9] Lagarias [22] Odlyzko [26] Vaudenay [35] and others, and after the appearance of Brassard theorem [8], there may still be some hopes as Koblitz has noted in [21] The other systems that are worth to mention are the quantum cryptography proposed by Bennet and Brassard [4] and the lattice cryptography proposed by Goldreich, Goldwasser and Halevi [18] Another approach is to use hard problems in ....

G. Brassard, A note on the complexity of cryptography, IEEE Transactions on Information Theory 25 (1979), 232-233.

.... Many reduction results for oblivious transfer (e.g. 8, 10, 14 16, 18, 20] Secret key agreement by public discussion from noisy channels as discussed in the previous section can be interpreted as the reduction of key agreement to a certain type of noisy source. Privacy amplification [6, 5], an important sub protocol in unconditional key agreement, can be interpreted as the reduction of key agreement to a setting in which Alice and Bob share the same string, but where Eve has some arbitrary unknown type information about the string with the only constraint being an upper bound on ....

C. H. Bennett, G. Brassard, C. Cr'epeau, and U. M. Maurer, Generalized privacy amplification, IEEE Transactions on Information Theory , vol. 41, no. 6, pp.

....other s information. During the second phase, information reconciliation, Alice and Bob agree on a mutual string S by using error correction techniques, and in the third phase, privacy amplification, the partial secret S is transformed into a shorter, highly secret string S 0 . Bennett et al. [1] have shown that the length of S 0 can be nearly H 2 (SjZ = z) the R enyi entropy of S when given Eve s complete knowledge Z = z about S. Privacy amplification, which was first introduced by Bennett et al. 2] can alternatively be seen as a special case of secret key agreement from common ....

....h(2 ) 0) or Y is simulatable by Z with respect to X (and r Delta (1 Gamma ) Gamma Gamma h( 0) then there exists no strong (PXY Z ; r; ffi) protocol for any ffi 1. 3 Privacy Amplification 3. 1 Protocol Definition Privacy amplification, introduced in [2] and generalized in [1], is the technique of transforming a partially secret string into a highly secret but shorter string, and corresponds to the special case of secret key agreement for which X = Y = S holds with probability 1. The following definition is a strengthened version of the general definition in Section ....

C. H. Bennett, G. Brassard, C. Cr'epeau, and U. M. Maurer, Generalized privacy amplification, IEEE Transactions on Information Theory , Vol. 41, Nr. 6, 1995.

....the algorithm can also be viewed as computing the OR function: it can determine whether at least one of the input bits is 1. 3 Quantum Communication The area of quantum information theory deals with the properties of quantum information and its communication between different parties. We refer to [11,44] for general surveys, and will here restrict ourselves to explaining two important primitives: teleportation [8] and superdense coding [9] These pre date quantum communication complexity and show some of the power of quantum communication. We first show how teleporting a qubit works. Alice has a ....

C. H. Bennett and P. W. Shor. Quantum information theory. IEEE Transactions on Information Theory, 44(6):2724--2742, 1998.

.... hashing, authentication, resiliency against correlation attacks, pseudorandomness, block ciphers, derandomization, two point based sampling, zero knowledge, span programs, testing of combinatorial circuits, intersecting codes, oblivious transfer, interactive proof systems, resiliency (see [19, 16, 18, 17, 1, 11, 25, 10, 6, 9, 7, 13, 16]) A basic notion underlying these concepts are families of ffl Gammabiased random variables. The Weil Carlitz Uchiyama bound and several constructions from the influential papers by Naor and Naor [18] and by Alon, Goldreich, Hastad and Peralta [1] provide families of ffl Gammabiased random ....

Brassard, G., Cr'epeau, C., Santha,M.: Oblivious transfers and intersecting codes, IEEE Transactions on Information Theory 42 (1996), 1769-1780

....Results on Nonlinear Zigzag Functions D. R. Stinson Computer Science and Engineering Department University of Nebraska Lincoln, NE 68588 March 13, 1997 Abstract Zigzag functions were defined by Brassard, Cr epeau and S antha [1] in connection with an application to the construction of oblivious transfers (a useful tool in cryptographic protocols) They proved that linear zigzag functions are equivalent to self intersecting codes, which have been studied by several researchers. In this paper, we begin an investigation of ....

....(linear or nonlinear) zigzag functions. In particular, we prove some bounds (i.e. necessary conditions for existence of zigzag functions) which generalize known bounds for linear zigzag functions. 1 Introduction and Definitions Zigzag functions were defined by Brassard, Cr epeau and S antha [1]. We review basic concepts and definitions now. Let F q denote the finite field with q elements. Suppose that f : F q ) n (F q ) m , where n m. Let I f1; ng. We say that f is unbiased with respect to I if for all possible choices for (x i : i 2 I) 2 (F q ) jIj , and for every ....

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G. Brassard, C. Cr'epeau and M. S'antha. Oblivious transfers and intersecting codes. IEEE Transactions on Information Theory 42 (1996), 1769--1780.

.... the security assumptions for oblivious transfer were considered previously by Cr epeau and Kilian [CK88] Research on reductions from Gamma 2 1 Delta OT k string OT to bitwise Gamma 2 1 Delta OT has for a long time concentrated on using self intersecting codes for the constructions [BCS96], but recent work by Brassard and Cr epeau [BC97] shows that the reduction can be done much more efficiently using privacy amplification [BBR86, ILL89, BBCM95] This technique allows to weaken the security assumptions for Bob, permitting him not only to read one of the two bits, but also the XOR ....

....In generalized OT, Alice has input bits b 0 and b 1 , Bob chooses any function f : f0; 1g 2 f0; 1g and obtains f(b 0 ; b 1 ) but Alice does not learn f . Our reductions follow the information theoretic definitions of unconditional security for oblivious transfer and other multiparty protocols [BCS96, BC97, DPP96], but formal treatment lies not in the scope of this paper. Informally, an OT protocol is correct if it accomplishes the transmission of information between honest parties. The protocol is private if a malicious party cannot obtain information about the honest party s input beyond the ....

Gilles Brassard, Claude Cr'epeau, and Mikl'os S'antha, Oblivious transfers and intersecting codes, IEEE Transactions on Information Theory 42 (1996), no. 6, 1769--1780.

....communication. We list below some of the areas in need of development: ffl Quantum protocols need to be extended to a computer network setting. See [102] and [115] ffl More sophisticated error correction and detection techniques need to be implemented in quantum protocols. See [6] 13] and [18]. ffl There is a need for greater understanding of intrusion detection in the presence of noise. The no cloning theorem of Appendix A of this paper and the no detection implies no information theorem of Appendix B of this paper simply do not provide a complete picture. See [55] ffl There ....

Bennett, C.H., G. Brassard, C. Crepeau, and U.M. Maurer, IEEE Transactions on Information Theory, 1995.

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C.H. Bennett, G. Brassard, C. Cr'epeau, and U.M. Maurer. Generalized Privacy Amplification. IEEE Transaction on Information Theory, Volume 41, Number 6, November 1995, pp. 1915--1923.

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C. H. Bennett, G. Brassard, C. Crepeau, and U. Maurer. Generalized privacy ampli cation. IEEE Transaction on Information Theory, 41(6):1915-1923, 1995.

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C.H. Bennett, P. Gacs, M. Li, P.M.B. Vitanyi, and W. Zurek, Information Distance, IEEE Transactions on Information Theory, 44:4(1998), 1407--1423.

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C. H. Bennett, G. Brassard, C. Crepeau, and U. Maurer. Generalized privacy ampli cation. IEEE Transaction on Information Theory, 41(6):1915-1923, 1995. 10

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C. H. Bennett, G. Brassard, C. Crepeau, and U. M. Maurer, Generalized privacy amplification, IEEE Transactions on Information Theory , Vol. 41, No. 6, pp. 1915.

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C. H. Bennett, G. Brassard, C. Cr'epeau, and U. M. Maurer. Generalized privacy amplification. IEEE Transactions on Information Theory, 41(6):1915--1923, 1995. 19

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C. H. Bennett, G. Brassard, C. Crepeau, and U. M. Maurer, Generalized privacy amplification, IEEE Transactions on Information Theory , Vol. 41, Nr. 6, pp. 1915.

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C.H. Bennett, P. Gacs, M. Li, P.M.B. Vitanyi, and W. Zurek, Information Distance, IEEE Transactions on Information Theory, 44:4(1998), 1407--1423.

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C.H. Bennett, P. Gacs, M. Li, P.M.B. Vitanyi, and W. Zurek. Information Distance, IEEE Transactions on Information Theory, 44:4(1998), 1407--1423.

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C.H. Bennett, P. Gacs, M. Li, P.M.B. Vitanyi, and W. Zurek. Information Distance, IEEE Transactions on Information Theory, 44:4(1998), 1407--1423.

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C.H. Bennett, P. G acs, M. Li, P. Vit anyi, and W. Zurek, Information Distance. IEEE Transactions on Information Theory, 44:4(July 1998), 1407-1423.

....is interested in one of them. After the execution of the protocol, the Receiver gets the secret she wishes to recover, obtaining at the same time no information on the others, while the Sender does not know which secret the Receiver has recovered. All these forms were shown to be equivalent [11, 9, 15], and Kilian in [30] showed that the OT is a complete primitive, in the sense that it can be used as building block for any secure function evaluation (multi party computation) A variety of slightly different definitions and implementations can be found in the literature as well as papers ....

.... can be found in the literature as well as papers addressing issues such as the relation of the OT with other cryptographic primitives, the assumptions required to implement such a concept, reductions among more complex forms of OT to simpler ones and applicative environments (e.g. [15, 11, 23, 19, 3, 21, 22, 16, 29, 36, 28], just to name few examples) Our Contribution. In this paper we study unconditionally secure distributed oblivious transfer protocols, introduced in [34] in order to strengthen the security of protocols designed for electronic auctions [36] We present an analysis and some new results: lower ....

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G. Brassard, C. Crep'eau, and M. S'antha, Oblivious Transfer and Intersecting Codes, IEEE Transaction on Information Theory, Special Issue in Coding and Complexity, Vol. 42, No. 6, pp. 1769-1780, 1996. 32

....distance, and so on. Such a metric would be able to simultaneously detect all similarities between pieces that other effective metrics can detect. Rather surprisingly, such a universal metric indeed exists. It was developed in [9, 10, 11] based on the information distance of [12, 3]. Roughly speaking, two objects are deemed close if we can significantly compress one given the information in the other, the idea being that if two pieces are more similar, then we can more succinctly describe one given the other. Here compression is based on the ideal mathematical notion of ....

....compression techniques. We lose theoretical optimality in some cases, but gain an efficiently computable similarity metric intended to approximate the theoretical ideal. In contrast, a later and partially independent compression based approach of [1, 2] for building language trees while citing [12, 3] is by ad hoc arguments about empirical Shannon entropy and Kullback Leibler distance resulting in non metric distances. Earlier research has demonstrated that this new universal similarity metric works well on concrete examples in very different application fields the first completely ....

C.H. Bennett, P. Gacs, M. Li, P.M.B. Vitanyi, and W. Zurek. Information Distance, IEEE Transactions on Information Theory, 44:4(1998), 1407--1423.

....plagiarism in student programming assignments [32] and phylogeny of chain letters in [5] We plan a further test on arti cially generated data, where we know the right answer beforehand. Related Work: Together with our coauthors, we have studied various forms of information distance in [4] and [21] in the past. The information distance studied in [23, 4] and subsequently investigated in [22, 16, 26, 28, 35] is universal and has other nice properties. This distance essentially says that the distance between two objects is the length of the shortest program (or amount of energy) ....

....phylogeny of chain letters in [5] We plan a further test on arti cially generated data, where we know the right answer beforehand. Related Work: Together with our coauthors, we have studied various forms of information distance in [4] and [21] in the past. The information distance studied in [23, 4], and subsequently investigated in [22, 16, 26, 28, 35] is universal and has other nice properties. This distance essentially says that the distance between two objects is the length of the shortest program (or amount of energy) that is needed to transform the two objects into each other. But ....

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C.H. Bennett, P. Gacs, M. Li, P.M.B. Vitanyi, and W. Zurek, Information Distance, IEEE Transactions on Information Theory, 44:4(1998), 1407-1423.

....is interested in one of them. After the execution of the protocol, the receiver gets the secret she wishes to recover, obtaining at the same time no information on the others, while the Sender does not know which secret the receiver has recovered. All these forms were shown to be equivalent [9, 7, 13], and Kilian in [24] showed that the OT is a complete primitive, in the sense that it can be used as building block for any secure function evaluation (multi party computation) A variety of slightly di erent de nitions and implementations can be found in the literature as well as papers ....

.... can be found in the literature as well as papers addressing issues such as the relation of the OT with other cryptographic primitives, the assumptions required to implement such a concept, reductions among more complex forms of OT to simpler ones and applicative environments (e.g. [13, 9, 17, 16, 3, 14, 23, 26, 22], just to name few examples) Our Contribution. In this paper we study unconditionally secure distributed oblivious transfer protocols, introduced in [25] in order to strengthen the security of protocols designed for electronic auctions [26] We present an analysis and some new results: lower ....

G. Brassard, C. Crepeau, and M. Santha, Oblivious Transfer and Intersecting Codes, IEEE Transaction on Information Theory, special issue in coding and complexity, Vol. 42, No. 6, pp. 1769-1780, 1996.

....to achieve the cryptographic primitives of Bit Commitment and Oblivious Transfer based on the existence of a Binary Symmetric Channel. Our protocols respectively require sending O(n) and ) bits through the BSC. These results are based on a technique known as Generalized Privacy Amplification [1] that allow two people to extract secret information from partially compromised data. 1 Introduction The cryptographic power of a noisy channel has been demonstrated by Wyner [20] who showed that two honest parties, say Alice and Bob, can exchange a secret key on which an eavesdropper Eve may ....

....Symmetric Channel of better quality than a similar Channel connecting them to Eve. Maurer [17] has later showed that even if Eve s Channel is better but independent of the Channel between Alice and Bob, the same result is possible. More recently, a result of Bennett, Brassard, Cr epeau and Maurer [1] provides a technique called Generalized Privacy Amplification to ensure that Eve s information is an arbitrary small fraction of a bit under the same conditions. But cryptography is no longer interested solely in protecting communications. As a result of public key cryptography [10] a large ....

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C.H. Bennett, G. Brassard, C. Cr'epeau, and U.M. Maurer. Generalized Privacy Amplification. IEEE Transaction on Information Theory, Volume 41, Number 6, to appear November 1995.

....Waterloo Ontario, N2L 3G1, Canada dstinson uwaterloo.ca Abstract. In this paper we show some efficient and unconditionally secure oblivious transfer reductions. Our main tool is a class of functions that generalizes the Zig zag functions, introduced by Brassard, Crep eau, and S antha in [6]. We show necessary and sufficient conditions for the existence of such generalized functions, and some characterizations in terms of well known combinatorial structures. Moreover, we point out an interesting relation between these functions and ramp secret sharing schemes where each share is ....

....in such a way that S does not know which of the n secrets R has received R does not receive any information on the other secrets S holds. We will refer to such a protocol as to an Gamma n 1 Delta OT . All the oblivious transfer definitions [24, 16, 5] were shown to be equivalent [12, 4, 13, 6]. Moreover, Kilian, in [21] showed that the oblivious transfer is complete; in other words, it can be used to construct any other cryptographic protocol. Due to the importance 1 Recently, it has been pointed out that Wiesner independently developed a similar concept in 1970, unpublished until ....

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G. Brassard, C. Crep'eau, and M. S'antha, Oblivious Transfer and Intersecting Codes, IEEE Transaction on Information Theory, special issue in coding and complexity, Vol. 42, No. 6, pp. 1769-1780, 1996.

....ng: 40 Why do we only consider these particular errors A quantum code can correct any one qubit error if and only if it can correct the errors X(u j ) Y (u j ) and Z(u j ) for all j. This follows from the fact that the matrices I; X; Y; Z span the 4 dimensional space of all 2 2 matrices: see [4, 9]. In our set up, the error group E = f X(a)Z(b) a; b 2 V g is an extraspecial 2 group of order 2 2n 1 . Its centre is (E) f Ig, and E = E= E) is a vector space over F . This is the third, and most important, vector space with which we have to deal. See Section 8. We use the notation ....

C. H. Bennett and P. W. Shor, Quantum information theory, IEEE Transactions on Information Theory (1998).

....Alice and Bob compress the mutual but generally highly insecure string X N to a shorter string S with virtually uniform distribution and about which Eve has essentially no information. Note that Eve s total information about X N consists of Z N and h(X N ) at this point. Bennett et al. [2] have shown that universal hashing allows for distilling a virtually secure string whose length is roughly equal to the R enyi entropy of the original string in Eve s view. Lemma 2 [2] Let W be a random variable with range W, and let G be the random variable corresponding to the random choice, ....

....(Note that Eve s total information about X N consists of Z N and h(X N ) at this point. Bennett et al. 2] have shown that universal hashing allows for distilling a virtually secure string whose length is roughly equal to the R enyi entropy of the original string in Eve s view. Lemma 2 [2] Let W be a random variable with range W, and let G be the random variable corresponding to the random choice, according to the uniform distribution, of a function out of a universal class of functions mapping W to f0; 1g M . Then H(G(W )jG) H 2 (G(W )jG) M Gamma 2 M GammaH 2 (W ) ln 2. ....

C. H. Bennett, G. Brassard, C. Cr'epeau, and U. M. Maurer, Generalized privacy amplification, IEEE Transactions on Information Theory , Vol. 41, No. 6, pp.

....: a Delta x b, is an SU 2 class of hash functions f0; 1g n f0; 1g n with 2 2n elements. It is shown in [12] that ASU 2 classes can be obtained which are close to stronglyuniversal, but substantially smaller. 1. 3 Privacy Amplification by Authenticated Public Discussion Bennett et al. [1] analyzed the privacy amplification technique of [2] under the assumption that the two parties Alice and Bob are connected by an authentic (but otherwise insecure) channel, or equivalently, that the opponent is not able to insert or modify messages without being detected. The idea of this ....

....sends this function to Bob. Then they both compute S 0 : h(S) It was shown that the amount of almost secret key that can be extracted is at least equal to the conditional R enyi entropy H 2 of S, given Eve s knowledge U = u. This fact is an immediate consequence of the following result of [1] which states that if a random variable X is used as the argument of universal hashing, where the output Y is an r bit string, and r is equal to H 2 (X) minus a security parameter, then the resulting string Y has almost maximal Shannon entropy r, given the hash function (which is chosen uniformly ....

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C. H. Bennett, G. Brassard, C. Cr'epeau, and U. M. Maurer, Generalized privacy amplification, IEEE Transactions on Information Theory , Vol. 41, Nr. 6, 1995.

....achieve the cryptographic primitives of Bit Commitment and Oblivious Transfer based on the existence of a Binary Symmetric Channel. Our protocols respectively require sending O(n) and O(n 3 ) bits through the BSC. These results are based on a technique known as Generalized Privacy Amplification [1] that allow two people to extract secret information from partially compromised data. 1 Introduction The cryptographic power of a noisy channel has been demonstrated by Wyner [20] who showed that two honest parties, say Alice and Bob, can exchange a secret key on which an eavesdropper Eve may ....

....Symmetric Channel of better quality than a similar Channel connecting them to Eve. Maurer [17] has later showed that even if Eve s Channel is better but independent of the Channel between Alice and Bob, the same result is possible. More recently, a result of Bennett, Brassard, Cr epeau and Maurer [1] provides a technique called Generalized Privacy Amplification to ensure that Eve s information is an arbitrary small fraction of a bit under the same conditions. But cryptography is no longer interested solely in protecting communications. As a result of public key cryptography [10] a large ....

[Article contains additional citation context not shown here]

C.H. Bennett, G. Brassard, C. Cr'epeau, and U.M. Maurer. Generalized Privacy Amplification. IEEE Transaction on Information Theory, Volume 41, Number 6, to appear November 1995.

.... wire tap channel de Wyner [19] a d abord et e etudi ee de fa con sp ecifique au contexte de la distribution de clef quantique par Bennett, Brassard et Robert [4] et a celui des canaux binaires sym etriques par Maurer [13] puis de fa con plus g en erale par Bennett, Brassard, Cr epeau et Maurer [2, 14]. Il s av ere qu en g en eral, il ne suffit pas a Alice et Bob de connaitre une borne sur la quantit e d information au sens de Shannon donn ee par Z sur X pour choisir une fonction f(X) sur laquelle Eve ne sera que mal inform ee. L on montre dans [2] qu une borne sur l information au sens de ....

....par Bennett, Brassard, Cr epeau et Maurer [2, 14] Il s av ere qu en g en eral, il ne suffit pas a Alice et Bob de connaitre une borne sur la quantit e d information au sens de Shannon donn ee par Z sur X pour choisir une fonction f(X) sur laquelle Eve ne sera que mal inform ee. L on montre dans [2] qu une borne sur l information au sens de R enyi [16] permettra n eanmoins de fournir une telle fonction f . Dans de nombreuses situations une borne sur l information au sens de Shannon permettra d obtenir la meme chose en gaspillant une moindre fraction du secret. Ces r esultats sont bas es sur ....

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C.H. Bennett, G. Brassard, C. Cr'epeau, and U. Maurer. Generalized Privacy Amplification, IEEE Transaction on Information Theory, 1995. `a paraitre.

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Charles H. Bennett and Peter W. Shor. Quantum information theory. IEEE Transactions on Information Theory, 44(6):2724--2742, 1998.

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Charles H. Bennett, Gilles Brassard, Claude Cr epeau, and Ueli M. Maurer. Generalized privacy amplification. IEEE Transactions on Information Theory, 41(6):1915.

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C. Bennett, P. Gacs, M. Li, P. Vitanyi, and W. Zurek. Information distance. IEEE Transactions on Information Theory, 44:4:1407--1423, 1998.

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Charles H. Bennett, Gilles Brassard, Claude Crepeau, and Ueli M. Maurer. Generalized privacy ampli cation. IEEE Transactions on Information Theory, 41(6), 1995.

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G. Brassard, A Note on the Complexity of Cryptography, IEEE Transactions on Information Theory, Vol. IT-25, No. 5, pp. 232-233, 1979.

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C.H. Bennett, G. Brassard, C. Cr'epeau, and U. Maurer. Generalized Privacy Amplification. IEEE Transaction on Information Theory, Volume 41, Number 6, pp. 1915-1923. November 1995.

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G. Brassard, A note on the complexity of cryptography, IEEE Transactions on Information Theory 25 (1979), 232--233.

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Gilles Brassard, Claude Crepeau, and Miklos Santha. Oblivious transfers and intersecting codes. IEEE Transactions on Information Theory, 42(6):1769--1780, 1996.

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C. Bennett, G. Brassard, C. Crepeau, and U. Maurer. Generalized Privacy Amplification. IEEE Transactions on Information Theory, 41(6), pp. 1915-1923, 1995.

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C.H. Bennett, G. Brassard, C. Cr'epeau, and U. Maurer. Generalized privacy amplification. IEEE Transaction on Information Theory, 41(6):1915--1923, Nov. 1995.

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C.H. Bennett, G. Brassard, C. Crepeau, and U. Maurer. Generalized privacy ampli cation. IEEE Transactions on Information Theory, 41(6):1915-1923, 1995.

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Gilles Brassard, Claude Crepeau, and Miklos Santha. Oblivious transfers and intersecting codes. IEEE Transactions on Information Theory, 42(6):1769--1780, 1996.

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C. Bennett, G. Brassard, C. Crepeau, and U. Maurer. Generalized Privacy Amplification. IEEE Transactions on Information Theory, 41(6), pp. 1915-1923, 1995.

No context found.

G. Brassard. A note on the complexity of cryptography. IEEE Transactions on Information Theory, 25:232--233, 1979.

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