Adi Shamir: How to share a secret, Communications of the ACM, 22(1), pp612613, 1979.  Home/Search   Document Not in Database   Summary   Related Articles   Check

....shares anonymously. h2 Fig. 1. Publishing Publisher: To publish a document (see Figure 2) the publisher P splits it into n 1 shares hi, any k 1 of which can be combined to form the whole document again. This can be done using one of the standard algorithms like Shamir s secret sharing [Sha79]. He then generates n 1 keys ki and encrypts each share with the corresponding key. He now picks n q 1 peers ao. an at random to act as forwarders and constructs onions 2 to send (via the anonymous connections layer) each of them the encrypted share h ki, the corresponding key ki and a ....

A. Shamin How to share a secret. Communications of the ACM, 22:612 613, 1979.

....and number of queries to the decryption share generation oracles are bounded by t and q D , respectively. We describe our threshold cryptosystem from the GDH group = K, E, D, V, SC) 3.2. 1 Preliminary Shamir s Secret Sharing Scheme We use Shamir s (t, n) threshold secret sharing scheme [31] to share a private key. More precisely, it can be described as follows. Setup: Let q be a prime and 1 n q. Let x ZZ # q be a secret to share. A dealer picks a 1 , a 2 , a t 1 at random from ZZ # q , sets a 0 = x and define a polynomial P oly(X) The dealer transfers the ....

A. Shamir: How to Share a Secret, Communications of the ACM, Vol. 22, 1979, pages 612--613.

....up with a DFA, it then transfers its atoms to the DFA. For simplicity, we assume that there is only one DFA. If the DFA has sufficient atoms, it declares that the intrusion threshold Theta has been reached and therefore it deploys a PA. This is similar to the threshold schemes discussed in [5], in that below the threshold level of Theta, one can assume no knowledge, but at or above Theta, the game is up. In this paper we do not discuss how Theta is determined, nor do we discuss the case where, below Theta, the DFA has no knowledge of an intrusion. In addition, we have made further ....

A. Shamir: How to Share a Secret, Communications of the ACM, 22(11): 612-613, November 1979. 16

.... [23] the computational power of interactive Turing machines was studied in [17, 19] Roughly speaking, the theory leads to a generalization of standard computability theory to the case of in nite computations, recently referred to as a theory of super recursive algorithms and computation in [2]. The results from [17, 19] indicate that merely adding interactive properties and allowing endless computations does not break the computational barrier of Turing machines. The resulting devices are not computationally more powerful than classical Turing machines because each of their ....

....of non classical computability theory to arti cial living systems. The main result explaining the emergence of a super Turing computing potential in such systems justi es the approach, and concretely proves what is often speculated on in informal explanations (cf. 23] or, more recently [2]) It also points to the increasing role that computer science will play in problems related to understanding the nature of the emergence of the mechanisms of life and of intelligence in particular (cf. 26] The above results also point to quite realistic instances in which the classical ....

M. Burgin: How we know what technology can do, Communications of the ACM 44 (2001) 83-88.

....n pieces of information called shares or shadows are assigned to a secret key K in such a way that 1. the secret key can be reconstructed from certain authorised groups of shares and 2. the secret key cannot be reconstructed from unauthorised groups of shares. 2. 1 Threshold Schemes Shamir [14], states that threshold schemes can be very helpful in the management of cryptographic keys. To protect data, we would encrypt it. However to protect the encryption key we need a di#erent method. The most secure key management scheme keeps the key in a single place. This sort of scheme may not ....

....sort of scheme may not always be appropriate, for instance in a single case of misfortune the key may be rendered unaccessable. An obvious solution to this may be to make multiple copies of the key. This however also increases the risk associated in keeping multiple keys secret. By using Shamir s [14] threshold scheme concept we can get a very robust key managment scheme. In some applications the trade o# is not between secrecy and reliability, but between safety and convenience [14] If for example we were a company that needed to digitally sign all cheques and if each executive is given a ....

[Article contains additional citation context not shown here]

Shamir, A., How to Share a Secret (1979) Communications of the ACM, vol.22, no. 11

....of the form 1; ff i ; ff t Gamma1 i and ff i 6= ff j if i 6= j. It is easy to see that M t;n can be viewed as a span program computing f t;n , with root a = 10 Delta Delta Delta 0) In this case the associated secret sharing scheme (as defined in Section 4. 2) is identical to Shamir s [21]. To see that (K; M t;n ; a) has multiplication, observe that the product h = f Deltag of any two polynomials f; g 2 K[X] both of degree at most t Gamma 1, can be interpolated given n points if 2t n 1. In particular, if we are given distinct values P 1 ; P n 2 Kn0, and the evaluations ....

A. Shamir: How to Share a Secret, Communications of the ACM 22 (1979) 612--613.

....subsets of them are quali ed to reconstruct the secret while other subsets have no information about it. The collection of quali ed subsets is called the access structure. The secret sharing scheme has to satisfy some properties which will be made more precise below. Shamir s secret sharing scheme [14] has the properties we need. Our main result uses a proof of knowledge P , an access structure for n participants, and a secret sharing scheme S for the access structure dual to to build a new protocol, in which the prover shows that he knows solutions to a subset of n problem instances ....

....requirement 5 is satis ed it is called smooth. It is natural to ask if for any family of monotone access structures there is a family of smooth secret sharing schemes. This question is easy to answer in case of threshold structures. In that case it is clear that Shamir s secret sharing scheme [14] can be used. This scheme is even ideal, i.e. the shares are of the same length as the secret. Given d or more shares, the secret s can be found, whereas with d 1 or fewer shares, s is completely unknown. The following alternative to Shamir s scheme (which is also ideal) can lead to more ecient ....

A. Shamir: How to Share a Secret, Communications of the ACM 22 (1979) 612-613.

....key before they start sending messages to each other. Every user has his own two keys; the public key is publicly announced and the private key is kept secret. Several public key cryptosystems have been proposed since 1976; here we concentrate our attention on the most popular one namely the RSA [32]. In fact the techniques were rst discovered at CESG in the early 1970s by James Ellis, who called them NonSecret Encryption [33] In 1973, building on Ellis idea, C. Cocks designed what we now call RSA [34] and in 1974 M. Williamson proposed what is essentially known today as the Die Hellman ....

R. L. Rivest, A. Shamir and L. M. Adleman, Communication of the ACM 21 120 (1978).

....of them are qualified to reconstruct the secret while other subsets have no information about it. The collection of qualified subsets is called the access structure. The secret sharing scheme has to satisfy some properties which will be made more precise below. Shamir s secret sharing scheme [14] has the properties we need. Our main result uses a proof of knowledge P, an access structure Gamma for n participants, and a secret sharing scheme S for the access structure dual to Gamma to build a new protocol, in which the prover shows that he knows solutions to a subset of n problem ....

....requirement 5 is satisfied it is called smooth. It is natural to ask if for any family of monotone access structures there is a family of smooth secret sharing schemes. This question is easy to answer in case of threshold structures. In that case it is clear that Shamir s secret sharing scheme [14] can be used. This scheme is even ideal, i.e. the shares are of the same length as the secret. Given d or more shares, the secret s can be found, whereas with d Gamma 1 or fewer shares, s is completely unknown. The following alternative to Shamir s scheme (which is also ideal) can lead to more ....

A. Shamir: How to Share a Secret, Communications of the ACM 22 (1979) 612--613.

....of them are qualified to reconstruct the secret while other subsets have no information about it. The collection of qualified subsets is called the access structure. The secret sharing scheme has to satisfy some properties which will be made more precise below. Shamir s secret sharing scheme [13] has the properties we need. Our main result uses a proof of knowledge P, an access structure Gamma for n participants, and a secret sharing scheme S for the access structure dual to Gamma to build a new protocol, in which the prover shows that he knows some subset of n secrets. More precisely, ....

....requirement 5 is satisfied it is called smooth. It is natural to ask if for any family of monotone access structures there is a family of smooth secret sharing schemes. This question is easy to answer in case of threshold structures. In that case it is clear that Shamir s secret sharing scheme [13] can be used. This scheme is even ideal, i.e. the shares are of the same length as the secret. In Shamir s scheme, the secret is an element in a finite field GF (q) A secret is shared by choosing a random polynomial f(X) ff d Gamma1 X d Gamma1 Delta Delta Delta ff 1 X s, where s is ....

A. Shamir: How to Share a Secret, Communications of the ACM 22 (1979) 612--613.

....researchers have investigated perfect secret sharing schemes extensively so far [1] 16] Let s review the history of perfect secret sharing schemes. An access structure Gamma is defined as the family of all access sets. 1. First, k; n) threshold schemes were proposed by Shamir and Blakley [1][2]. 2. Later, more general access structures were considered. It was shown that Gamma is an access structure of a perfect secret sharing scheme if and only if Gamma is monotone [3] The meaning of monotone is as follows. If A can recover S, then any set A which contains A can also recover S. ....

A.Shamir : How to share a secret. Communications of the ACM, 22, (11), pp.612613 (1979)

....University, Poland. # Basic Research in Computer Science, center of the Danish National Research Foundation 1 Introduction In this paper, we consider three related problems, namely secret sharing (SS) verifiable secret sharing (VSS) and multiparty computation (MPC) SS was introduced by Shamir[16] and generalized by Itoh et al. 11] a Dealer has a secret s and distributes a set of shares s 1 , s n to n players, such that s can be reconstructed only by certain qualified subsets of players while unqualified subsets have no information about s. The collection of qualified sets is ....

A. Shamir: How to Share a Secret, Communications of the ACM 22 (1979) 612--613.

....researchers have investigated perfect secret sharing schemes extensively so far [1] 16] Let s review the history of perfect secret sharing schemes. An access structure Gamma is defined as the family of all access sets. 1. First, k; n) threshold schemes were proposed by Shamir and Blakley [1][2]. 2. Later, more general access structures were considered. It was shown that Gamma is an access structure of a perfect secret sharing scheme if and only if Gamma is monotone [3] The meaning of monotone is as follows. If A can recover S, then any set A 0 which contains A can also recover S. ....

A.Shamir : How to share a secret. Communications of the ACM, 22, (11), pp.612613 (1979)

No context found.

Adi Shamir: How to share a secret, Communications of the ACM, 22(1), pp612613, 1979.

No context found.

Adi Shamir: How to share a secret, Communications of the ACM, 22(1), pp612613, 1979.

No context found.

Shamir A: How to share a secret. Communications of the ACM 22(11):612--613 (1979)

No context found.

A. Shamir: How to Share a Secret, Communications of the ACM, volume 22, issue 11, pp. 612-613. ACM Press, November 1979.

No context found.

Adi Shamir: How to share a secret. Communications of the ACM, 24(11), July 1979, pp. 612-613.

No context found.

A. Shamir: How to share a secret. Communications of the ACM, vol.22, no.11, pp.612-- 613, November 1979.

No context found.

A. Shamir: How to share a secret, Communications of the ACM, vol.22, no.11, pp. 612--613, 1979.

No context found.

Shamir, A., How to Share a Secret (1979) Communications of the ACM, vol.22, no. 11

Online articles have much greater impact   More about CiteSeer.IST   Add search form to your site   Submit documents   Feedback  

CiteSeer.IST - Copyright Penn State and NEC