Families of finite sets in which no set is covered by the union ofr others

Erdös, P.; Frankl, Péter; Füredi, Zoltán

doi:10.1007/bf02772959

Cited by 392 publications

(200 citation statements)

References 9 publications

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“…We note that a (n, w, 2) CFF is exactly a Sperner family. CFF has been extensively studied by ErdSs et al in [8] and [9]. A trivial CFF is the family consisting of single element subsets, in which n = m. Non-trivial CFFs are those with n > m. A good CFF is the one that for given m and k, n is as large as possible.…”

mentioning

confidence: 99%

New results on multi-receiver authentication codes

Wang

1998

Lecture Notes in Computer Science

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Abstract. Multi-receiver authentication is an extension of traditional point-to-point message authentication in which a sender broadcasts a single authenticated message such that all the receivers can independently verify the authenticity of the message, and malicious groups of up to a given size of receivers can not successfully impersonate the transmitter, or substitute a transmitted message. This paper presents some new resalts on unconditionally secure multi-receiver authentication codes. First we generalize a polynomial construction due to Desmedt, Frankel and Yung, to allow multiple messages be authenticated with each key. Second, we propose a new flexible construction for multi-receiver A-code by combining an A-code and an (n, m, k)-cover-free family. Finally, we introduce the model of malti-receiver A-code with dynamic sender and present an efficient construction for that.Keywords: Authentication code, Multi-receiver authentication code. IntroductionConventional authentication systems deal with point-to-point message authentication. In Simmons' model of unconditionally secure authentication there are three participants: a transmitter (sender), a receiver, and an opponent. The transmitter and the receiver share a secret key and are both assumed honest. The message is sent over a public channel which is subject to active attack. Transmitter and receiver use an authentication code which is a set of authentication functions f, indexed by keys belonging to a set E. To authenticate a message, called a source state and denoted by s E S, transmitter forms a codeword f (e, s) and sends it to the receiver who can verify its authenticity using his knowledge of the key. We are only concerned with sys$ernatic Cartesian A-codes in which the codeword constructed for s using e E E is the concatenation of s and f(e, denotes the set of all tags.

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confidence: 99%

New results on multi-receiver authentication codes

Wang

1998

Lecture Notes in Computer Science

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“…This result shows that if we want the number of channels to be less than n (the number of the required channels in a conventional secret sharing scheme), then the threshold t can not be too large. For example, in [22] the constant c is approximately 1/2, and so if t ≥ n 1/2 then m ≥ n.…”

Section: Channel Efficiencymentioning

confidence: 97%

“…Theorem 4.1 shows that finding the minimum number of channels m for a (t, n)-threshold partial broadcast secret sharing scheme is equivalent to finding an (n, m, t−1)-CFF with minimal m. Constructions and bounds for (n, m, t)-CFF have been studied by numerous authors (see, for example [1,22,[39][40][41]). It has been shown in [35,41] that for any (n, m, t)-CFF with t ≥ 2, m ≥ c t 2 log t log n for some constant c > 0.…”

Section: Channel Efficiencymentioning

confidence: 98%

Secret sharing schemes with partial broadcast channels

Wang

2006

Des Codes Crypt

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In a conventional secret sharing scheme a dealer uses secure point-to-point channels to distribute the shares of a secret to a number of participants. At a later stage an authorised group of participants send their shares through secure point-topoint channels to a combiner who will reconstruct the secret. In this paper, we assume no point-to-point channel exists and communication is only through partial broadcast channels. A partial broadcast channel is a point-to-multipoint channel that enables a sender to send the same message simultaneously and privately to a fixed subset of receivers. We study secret sharing schemes with partial broadcast channels, called partial broadcast secret sharing schemes. We show that a necessary and sufficient condition for the partial broadcast channel allocation of a (t, n)-threshold partial secret sharing scheme is equivalent to a combinatorial object called a cover-free family. We use this property to construct a (t, n)-threshold partial broadcast secret sharing scheme with O(log n) partial broadcast channels. This is a significant reduction compared to n pointto-point channels required in a conventional secret sharing scheme. Next, we consider communication rate of a partial broadcast secret sharing scheme defined as the ratio Communicated by P. Wild.R. Safavi-Naini 6 Des Codes Crypt (2006) 41:5-22 of the secret size to the total size of messages sent by the dealer. We show that the communication rate of a partial broadcast secret sharing scheme can approach 1/O(log n) which is a significant increase over the corresponding value, 1/n, in the conventional secret sharing schemes. We derive a lower bound on the communication rate and show that for a (t, n)-threshold partial broadcast secret sharing scheme the rate is at least 1/t and then we propose constructions with high communication rates. We also present the case of partial broadcast secret sharing schemes for general access structures, discuss possible extensions of this work and propose a number of open problems.

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“…We now show that it is possible to construct a (t, d)-independent family of vectors, for some values of the parameters t and d. We review the concept of a t-cover free family as introduced in [13] and we show that these families of vectors are (t, d)-independent.…”

Section: Lemma 3 Letmentioning

confidence: 98%

Low-randomness constant-round private XOR computations

Blundo

Galdi

Persiano

2006

Int. J. Inf. Secur.

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In this paper we study the randomness complexity needed to distributively perform k XOR computations in a t-private way using constant-round protocols in the case in which the players are honest but curious.We show that the existence of a particular family of subsets allows the recycling of random bits for constantround private protocols. More precisely, we show that after a 1-round initialization phase during which random bits are distributed among n players, it is possible to perform each of the k XOR computations using two rounds of communication.For t ≤ c √ n/ log n, for any c < 1/2, we design a protocol that uses O(kt 2 log n) random bits.

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Families of finite sets in which no set is covered by the union ofr others

Cited by 392 publications

References 9 publications

New results on multi-receiver authentication codes

New results on multi-receiver authentication codes

Secret sharing schemes with partial broadcast channels

Low-randomness constant-round private XOR computations

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