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J. Benaloh. Secret sharing homomorphisms: Keeping shares of a secret secret. In Advances in Cryptology - Proceedings of the 13th Annual International Cryptology Conference 215 (CRYPTO), volume 263 of Lecture Notes in Computer Science (LNCS), pages 251--260. Springer, 1987.

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On Verifiable Function Sharing - Blunden   (Correct)

....of 38 users .4 such that only authorized sets of users can jointly compute the function. This is described in more detail in Chapter 2. A good overview of threshold cryptography can be found in [14] Many of the existing threshold cryptosystems make use of homomorphic threshold sharing schemes [3]. Informally, if is a binary operation on the set of secrets and is a binary operation on the set of shares, then a threshold scheme is homomorphic if it has the property that when si is user Ui s share of k and sti is Ui s share of k2, then si sti is Ui s share of 1.13 Zero Knowledge ....

.... sharing schemes provided cr and or have the same access structure PA It was shown in [7] that homomorphisms of threshold sharing schemes, where no algebraic structure is imposed on the set of secrets or the set of shares, is an extension of the notion of homomorphic threshold sharing schemes [3]. With homomorphic threshold sharing schemes, a binary operation is defined on the set of secrets and a binary operation : on the sets of shares Si such that for a threshold scheme cr = 9,7 ) for all (sl, st) sl, s) output by 9, 52 A homomorphism h: cr x cr cr is defined as ....

J. Benaloh. Secret Sharing Homomorphisms: Keeping Shares of a Secret Secret. In A. Odlyzko, editor, Advances in Cryptology - Crypro'86 (Lecture Notes in Computer Science 263), pages 251-260. Springer-Verlag, 1987.


How to Prove All NP Statements in Zero-Knowledge and a.. - Goldreich, al. (1998)   (17 citations)  (Correct)

....the Public Key of the i th receiver, and sends all encrypted secrets to all receivers. Finally, the sender provides each receiver with a zero knowledge proof that the encrypted messages correspond to the evaluation of a single polynomial over Z 182 (note that this is a NP statement) Recently, Benaloh has presented a much more efficient solution based on the intrac tability of quadratic residuosity [Bena] 4.3 Proving that a String is Pseudorandom The notion of a pseudorandom bit generator, suggested by Blum and Micali [BM] and Yao [Y] is central to cryptography. A pseudorandom bit ....

.... each receiver with a zero knowledge proof that the encrypted messages correspond to the evaluation of a single polynomial over Z 182 (note that this is a NP statement) Recently, Benaloh has presented a much more efficient solution based on the intrac tability of quadratic residuosity [Bena] 4.3 Proving that a String is Pseudorandom The notion of a pseudorandom bit generator, suggested by Blum and Micali [BM] and Yao [Y] is central to cryptography. A pseudorandom bit generator is an efficient deterministic program which stretches a randomly selected n bit long seed into a longer ....

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Benaloh, (Cohen) J.D., "Secret Sharing Homomorphisms: Keeping Shares of a Secret Secret", these proceedings.


Privacy-preserving Distributed Mining of Association Rules .. - Kantarcioglu, Clifton (2002)   (31 citations)  (Correct)

....a straightforward technique from the cryptographic community. The basic idea is each party divides its input into n parts, and send the n 1 pieces to di#erent sites. To reveal any parties input, n 1 party must collude. The following is a brief summary of the protocol, details can be found in [15]. A slightly more e#cient version can be found in [16] 1. Each site i randomly chooses n elements such that x i = j=1 z i,j mod m where x i is the input of site i. Site i sends z i,j to site j. 2. Every site i computes w i = j=1 z j,i mod m and sends w i to site n. 3. Site n computes ....

J. Benaloh, (Cohen), "Secret sharing homomorphisms: Keeping shares of a secret secret," in Advances in Cryptography - Crypto86 (proceedings), A.M. Odlyzko (ed.), SpringerVerlag, Lecture Notes in Computer Science,Vol.263, 1987, pp. 251--260.


Verifiable Secret Redistribution for archive systems - Wong, Wang, Wing (2002)   (2 citations)  (Correct)

....Desmedt surveys other sharing schemes [12] Our VSR protocol expands on the concept embodied in VSS schemes, that of protecting shareholders from a faulty dealer. Chor et al. present a scheme in which the dealer and shareholders perform an interactive secure distributed computation [11] Benaloh [3], Gennaro and Micali [20, 21] Goldreich et al. [23] and Rabin and Ben Or [34, 36] propose schemes in which the dealer and shareholders participate in an interactive zero knowledge proof of validity; the schemes of Gennaro and Micali and of Rabin and BenOr are information theoretically secure. ....

J. C. Benaloh. Secret sharing homomorphisms: Keeping shares of a secret secret. In Proc. of CRYPTO 1986.


Reshufflable And laziness tolerant mental card game protocol - Kurosawa, Katayama, Ogata (1997)   (Correct)

....problem and a plaintext m takes a value of 0 or 1. 3] generalized it to m = 0; 1; r Gamma 1 by using the r th residue problem, where r is a prime number. 9] further generalized it to any r. By combining a secret sharing scheme with the probabilistic encryption scheme of [3] [2] showed an efficient verifiable secret sharing scheme and a fault tolerant election scheme. We apply this technique to a mental card game protocol. We suppose that there are N players. Numbers from 0 to 51 will be used to describe the cards. 2. Public key of each player We use the 53rd residue ....

J. Benaloh, "Secret sharing homomorphisms: Keeping shares of a secret secret", Proc. CRYPTO'86, pp.251--260, 1987


Unconditional Privacy in Social Choice - Felix Brandt Computer   (Correct)

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J. Benaloh. Secret sharing homomorphisms: Keeping shares of a secret secret. In Advances in Cryptology - Proceedings of the 13th Annual International Cryptology Conference 215 (CRYPTO), volume 263 of Lecture Notes in Computer Science (LNCS), pages 251--260. Springer, 1987.


General Secret Sharing Based on the Chinese - Remainder Theorem Sorin (2006)   (Correct)

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J. Benaloh. Secret sharing homomorphisms: Keeping shares of a secret secret. In A. M. Odlyzko, pages 251--260. Springer-Verlag, 1987.


Verifiable Secret Redistribution - Theodore Wong Jeannette   (Correct)

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J. C. Benaloh. Secret sharing homomorphisms: Keeping shares of a secret secret. In A. M. Odlyzko, editor, Proc. of CRYPTO 1986.


Unknown -   (Correct)

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J. C. Benaloh. Secret sharing homomorphisms: Keeping shares of a secret secret. In Proc. of CRYPTO 1986, the 6th Ann. Intl. Cryptology Conf., vol. 263 of Lecture Notes in Computer Science, pp. 213--222. 1987.


Verifiable Secret Redistribution for - Threshold Sharing Schemes   (Correct)

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Josh Cohen Benaloh. Secret sharing homomorphisms: Keeping shares of a secret secret. In Andrew M. Odlyzko, editor, Proc. of CRYPTO 1986, the 6th Ann. Intl. Cryptology Conf., volume 263 of Lecture Notes in Computer Science, pages 213--222. Intl. Assoc. for Cryptologic Research, Springer-Verlag, 1987.


Secure Distributed Data-Mining and Its Application to.. - Roughan, Zhang (2006)   (Correct)

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J. Benaloh. Secret sharing homomorphisms: Keeping shares of a secret secret. In Proc. Advances in Cryptology (CRYPTO '86), pages 251--260, 1987.


Batch Verification of Validity of Bids in - Homomorphic Auction Kun (2005)   (Correct)

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J. Cohen Benaloh. Secret sharing homomorphisms: keeping shares of a secret secret. In CRYPTO '86, pages 251--260, Berlin, 1986. Springer-Verlag. Lecture Notes in Computer Science Volume 263.


Verifiable Threshold Sharing of a Large Secret Safe-Prime - Maged Hamada Ibrahim (2005)   (Correct)

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Josh C. Benaloh, Secret sharing homomorphisms: keeping shares of a secret secret, proceedings on Advances in cryptology---CRYPTO '86, pp. 251--260, 1987.


Privacy Preserving k means clustering over Vertically Partitioned .. - Vaidya (2003)   (2 citations)  (Correct)

No context found.

Josh Cohen Benaloh. Secret sharing homomorphisms: Keeping shares of a secret secret. In A.M. Odlyzko, editor, Advances in Cryptography - CRYPTO86: Proceedings, volume 263, pages 251--260. Springer-Verlag, Lecture Notes in Computer Science, 1986.


A Verifiable Secret Shuffle and its Application to E-Voting - Neff (2001)   (8 citations)  (Correct)

No context found.

J. Benaloh. Secret Sharing Homomorphisms: Keeping Shares of a Secret Secret. Advances in Cryptology - CRYPTO '86, Lecture Notes in Computer Science, pp. 251-260, Springer-Verlag, Berlin, 1987.


(Im)Possibility of Unconditionally Privacy-Preserving Auctions - Brandt, Sandholm (2004)   (Correct)

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J. Benaloh. Secret sharing homomorphisms: Keeping shares of a secret secret. In Advances in Cryptology - Proceedings of the 13th Annual International Cryptology Conference (CRYPTO), volume 263 of Lecture Notes in Computer Science (LNCS), pages 251--260. Springer, 1987.


Privacy Preserving Regression Modelling via Distributed.. - Sanil, Karr, Reiter, Lin (2004)   (Correct)

No context found.

J. Benaloh. Secret sharing homomorphisms: Keeping shares of a secret sharing. In A. M. Odlyzko, editor, CRYPTO86. Springer Verlag, 1987. Lecture Notes in Computer Science No. 263.


(Im)Possibility of Unconditionally Privacy-Preserving Auctions - Brandt, Sandholm (2004)   (Correct)

No context found.

J. Benaloh. Secret sharing homomorphisms: Keeping shares of a secret secret. In Advances in Cryptology - Proceedings of the 13th Annual International Cryptology Conference (CRYPTO), volume 263 of Lecture Notes in Computer Science (LNCS), pages 251--260. Springer, 1987.


Towards Fault-Tolerant and Secure On-Line Services - Zhou (2001)   (3 citations)  (Correct)

No context found.

J. C. Benaloh. Secret sharing homomorphisms: Keeping shares of a secret secret. In A. M. Odlyzko, editor, Advances in CryptologyCrypto'86, Conference on the Theory and Applications of Cryptographic Techniques, Santa Barbara, CA USA, 1986.


A Verifiable Secret Sharing Scheme with Statistical.. - Tang, Liu, Wang (2003)   (Correct)

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J.C Benaloh, Secret Sharing Homomorphisms: Keeping Shares of a Secret. Proc of CRYPTO'86, Berlin: Springer, 1986.


(Im)Possibility of Unconditionally Privacy-Preserving Auctions - Brandt, Sandholm (2004)   (Correct)

No context found.

J. Benaloh. Secret sharing homomorphisms: Keeping shares of a secret secret. In Advances in Cryptology - Proceedings of the 13th Annual International Cryptology Conference (CRYPTO), volume 263 of Lecture Notes in Computer Science (LNCS), pages 251--260. Springer, 1987.


Protecting Secret Keys with Personal Entropy - Ellison, Hall, Milbert, Schneier (1999)   (8 citations)  (Correct)

No context found.

J. Benaloh, \Secret Sharing Homomorphisms: Keeping Shares of a Secret Secret," Proc. of CRYPTO '86, Springer-Verlag, pp. 251-260.


Verifiable Mixing (Shuffling) of ElGamal Pairs - Neff (2004)   (1 citation)  (Correct)

No context found.

J. Benaloh. Secret Sharing Homomorphisms: Keeping Shares of a Secret Secret. Advances in Cryptology - CRYPTO '86, Lecture Notes in Computer Science, pp. 251-260, Springer-Verlag, Berlin, 1987.


Internet Voting: Concerns and Solutions - Wu, Sankaranarayana   (Correct)

No context found.

J. Benaloh, "Secret Sharing Homomorphisms: Keeping Shares of a Secret Secret", Advances in Cryptology - CRYPTO '86, Springer-Verlag, 251-260, 1987.


A Verifiable Secret Shuffle and its Application to E-Voting - Neff (2001)   (8 citations)  (Correct)

No context found.

J. Benaloh. Secret Sharing Homomorphisms: Keeping Shares of a Secret Secret. Advances in Cryptology - CRYPTO '86, Lecture Notes in Computer Science, pp. 251-260, Springer-Verlag, Berlin, 1987.

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