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131
A generalisation, a simplification and some applications of Paillier's probabilistic publickey system
 LNCS
, 2001
"... We propose a generalisation of Paillier’s probabilistic public key system, in which the expansion factor is reduced and which allows to adjust the block length of the scheme even after the public key has been fixed, without loosing the homomorphic property.We show that the generalisation is as secu ..."
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Cited by 226 (2 self)
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We propose a generalisation of Paillier’s probabilistic public key system, in which the expansion factor is reduced and which allows to adjust the block length of the scheme even after the public key has been fixed, without loosing the homomorphic property.We show that the generalisation is as secure as Paillier’s original system. We construct a threshold variant of the generalised scheme as well as zeroknowledge protocols to show that a given ciphertext encrypts one of a set of given plaintexts, and protocols to verify multiplicative relations on plaintexts. We then show how these building blocks can be used for applying the scheme to efficient electronic voting. This reduces dramatically the work needed to compute the final result of an election, compared to the previously best known schemes. We show how the basic scheme for a yes/no vote can be easily adapted to casting a vote for up to t out of L candidates.The same basic building blocks can also be adapted to provide receiptfree elections, under appropriate physical assumptions. The scheme for 1 out of L elections can be optimised such that for a certain range of parameter values, a ballot has size only O(log L) bits.
Efficient generation of shared RSA keys
 Advances in Cryptology  CRYPTO 97
, 1997
"... We describe efficient techniques for a number of parties to jointly generate an RSA key. At the end of the protocol an RSA modulus N = pq is publicly known. None of the parties know the factorization of N. In addition a public encryption exponent is publicly known and each party holds a share of the ..."
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Cited by 151 (5 self)
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We describe efficient techniques for a number of parties to jointly generate an RSA key. At the end of the protocol an RSA modulus N = pq is publicly known. None of the parties know the factorization of N. In addition a public encryption exponent is publicly known and each party holds a share of the private exponent that enables threshold decryption. Our protocols are efficient in computation and communication. All results are presented in the honest but curious settings (passive adversary).
Robust Threshold DSS Signatures
, 1996
"... . We present threshold DSS (Digital Signature Standard) signatures where the power to sign is shared by n players such that for a given parameter t ! n=2 any subset of 2t + 1 signers can collaborate to produce a valid DSS signature on any given message, but no subset of t corrupted players can forg ..."
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Cited by 149 (12 self)
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. We present threshold DSS (Digital Signature Standard) signatures where the power to sign is shared by n players such that for a given parameter t ! n=2 any subset of 2t + 1 signers can collaborate to produce a valid DSS signature on any given message, but no subset of t corrupted players can forge a signature (in particular, cannot learn the signature key). In addition, we present a robust threshold DSS scheme that can also tolerate n=3 players who refuse to participate in the signature protocol. We can also endure n=4 maliciously faulty players that generate incorrect partial signatures at the time of signature computation. This results in a highly secure and resilient DSS signature system applicable to the protection of the secret signature key, the prevention of forgery, and increased system availability. Our results significantly improve over a recent result by Langford from CRYPTO'95 that presents threshold DSS signatures which can stand much smaller subsets of corrupted player...
The Round Complexity of Secure Protocols
, 1990
"... ) Donald Beaver Harvard University Silvio Micali y MIT Phillip Rogaway y MIT Abstract In a network of n players, each player i having private input x i , we show how the players can collaboratively evaluate a function f(x 1 ; : : : ; xn ) in a way that does not compromise the privacy of the pla ..."
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Cited by 121 (4 self)
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) Donald Beaver Harvard University Silvio Micali y MIT Phillip Rogaway y MIT Abstract In a network of n players, each player i having private input x i , we show how the players can collaboratively evaluate a function f(x 1 ; : : : ; xn ) in a way that does not compromise the privacy of the players' inputs, and yet requires only a constant number of rounds of interaction. The underlying model of computation is a complete network of private channels, with broadcast, and a majority of the players must behave honestly. Our solution assumes the existence of a oneway function. 1 Introduction Secure function evaluation. Assume we have n parties, 1; : : : ; n; each party i has a private input x i known only to him. The parties want to correctly evaluate a given function f on their inputs, that is to compute y = f(x 1 ; : : : ; xn ), while maintaining the privacy of their own inputs. That is, they do not want to reveal more than the value y implicitly reveals. Secure function evaluat...
Simplified VSS and Fasttrack Multiparty Computations with Applications to Threshold Cryptography
, 1998
"... The goal of this paper is to introduce a simple verifiable secret sharing scheme, to improve the efficiency of known secure multiparty protocols and, by employing these techniques, to improve the efficiency of applications which use these protocols. First we present a very simple Verifiable Secret ..."
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Cited by 118 (6 self)
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The goal of this paper is to introduce a simple verifiable secret sharing scheme, to improve the efficiency of known secure multiparty protocols and, by employing these techniques, to improve the efficiency of applications which use these protocols. First we present a very simple Verifiable Secret Sharing protocol which is based on fast cryptographic primitives and avoids altogether the need for expensive zeroknowledge proofs. This is followed by a highly simplified protocol to compute multiplications over shared secrets. This is a major component in secure multiparty computation protocols and accounts for much of the complexity of proposed solutions. Using our protocol as a plugin unit in known protocols reduces their complexity. We show how to achieve efficient multiparty computations in the computational model, through the application of homomorphic commitments. Finally, we present fasttrack multiparty computation protocols. In a model in which malicious faults are rare we s...
NonInteractive CryptoComputing for NC1
 In 40th Annual Symposium on Foundations of Computer Science
, 1999
"... The area of "computing with encrypted data" has been studied by numerous authors in the past twenty years since it is fundamental to understanding properties of encryption and it has many practical applications. The related fundamental area of "secure function evaluation" has bee ..."
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Cited by 90 (1 self)
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The area of "computing with encrypted data" has been studied by numerous authors in the past twenty years since it is fundamental to understanding properties of encryption and it has many practical applications. The related fundamental area of "secure function evaluation" has been studied since the mid 80's. In its basic twoparty case, two parties (Alice and Bob) evaluate a known circuit over private inputs (or a private input and a private circuit). Much attention has been paid to the important issue of minimizing rounds of computation in this model. Namely, the number of communication rounds in which Alice and Bob need to engage in to evaluate a circuit on encrypted data securely. Advancements in these areas have been recognized as open problems and have remained open for a number of years. In this paper we give a one round, and thus round optimal, protocol for secure evaluation of circuits which is in polynomialtime for NC
Player simulation and general adversary structures in perfect multiparty computation
, 2000
"... The goal of secure multiparty computation is to transform a given protocol involving a trusted party into a protocol without need for the trusted party, by simulating the party among the players. Indeed, by the same means, one can simulate an arbitrary player in any given protocol. We formally defin ..."
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Cited by 84 (12 self)
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The goal of secure multiparty computation is to transform a given protocol involving a trusted party into a protocol without need for the trusted party, by simulating the party among the players. Indeed, by the same means, one can simulate an arbitrary player in any given protocol. We formally define what it means to simulate a player by a multiparty protocol among a set of (new) players, and we derive the resilience of the new protocol as a function of the resiliences of the original protocol and the protocol used for the simulation. In contrast to all previous protocols that specify the tolerable adversaries by the number of corruptible players (a threshold), we consider general adversaries characterized by an adversary structure, a set of subsets of the player set, where the adversary may corrupt the players of one set in the structure. Recursively applying the simulation technique to standard threshold multiparty protocols results in protocols secure against general adversaries. The classical results in unconditional multiparty computation among a set of n players state that, in the passive model, any adversary that corrupts less than n=2 players can be tolerated, and in the active model, any adversary that corrupts less than n=3 players can be tolerated. Strictly generalizing
A verifiable random function with short proofs and keys
 PKC 2005, LNCS
, 2005
"... Abstract. We give a simple and efficient construction of a verifiable random function (VRF) on bilinear groups. Our construction is direct. In contrast to prior VRF constructions [14, 15], it avoids using an inefficient GoldreichLevin transformation, thereby saving several factors in security. Our ..."
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Cited by 75 (3 self)
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Abstract. We give a simple and efficient construction of a verifiable random function (VRF) on bilinear groups. Our construction is direct. In contrast to prior VRF constructions [14, 15], it avoids using an inefficient GoldreichLevin transformation, thereby saving several factors in security. Our proofs of security are based on a decisional bilinear DiffieHellman inversion assumption, which seems reasonable given current state of knowledge. For small message spaces, our VRF’s proofs and keys have constant size. By utilizing a collisionresistant hash function, our VRF can also be used with arbitrary message spaces. We show that our scheme can be instantiated with an elliptic group of very reasonable size. Furthermore, it can be made distributed and proactive. 1
Proactive security: Longterm protection against breakins
 CryptoBytes
, 1997
"... Dalit Naor y Proactive security provides a method for maintaining the overall security of a system, even when individual components are repeatedly broken into and controlled by an attacker. In particular it provides for automated recovery of the security of individual components, avoiding the use of ..."
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Cited by 64 (9 self)
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Dalit Naor y Proactive security provides a method for maintaining the overall security of a system, even when individual components are repeatedly broken into and controlled by an attacker. In particular it provides for automated recovery of the security of individual components, avoiding the use of expensive and inconvenient manual processes (unless perhaps when an ongoing attack is detected). The technique calls for the distribution of trust among several components (servers), together with periodic refreshments of the sensitive data held by the servers. This way, the proactive approach guarantees uninterrupted security as long as not too many servers are broken into at the same time. We describe the proactive approach and review some algorithms, implementations, and applications. We elaborate on two of the most important results: proactive signatures and proactive secure communication. Proactive signatures provide a solution for longlived secret keys, such as the key of a certi cation authority. Proactive secure communication ensures secrecy and authenticity ofcommunication, with automated refresh of the secret keys. 1
Communication Preserving Protocols for Secure Function Evaluation
 In Proc. of 33rd STOC
, 2001
"... A secure function evaluation protocol allows two parties to jointly compute a function f(x; y) of their inputs in a manner not leaking more information than necessary. A major result in this field is: "any function f that can be computed using polynomial resources can be computed securely usin ..."
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Cited by 64 (5 self)
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A secure function evaluation protocol allows two parties to jointly compute a function f(x; y) of their inputs in a manner not leaking more information than necessary. A major result in this field is: "any function f that can be computed using polynomial resources can be computed securely using polynomial resources" (where `resources' refers to communication and computation). This result follows by a general transformation from any circuit for f to a secure protocol that evaluates f . Although the resources used by protocols resulting from this transformation are polynomial in the circuit size, they are much higher (in general) than those required for an insecure computation of f . We propose a new methodology for designing secure protocols, utilizing the communication complexity tree (or branching program) representation of f . We start with an efficient (insecure) protocol for f and transform it into a secure protocol. In other words, "any function f that can be computed using communication complexity c can be can be computed securely using communication complexity that is polynomial in c and a security parameter". We show several simple applications of this new methodology resulting in protocols efficient either in communication or in computation. In particular, we exemplify a protocol for the "millionaires problem ", where two participants want to compare their values but reveal no other information. Our protocol is more efficient than previously known ones in either communication or computation. 1.