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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 ..."
Abstract

Cited by 149 (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 Protocols based on Probabilistic Encryption using Composite Degree Residue Classes
, 2001
"... We study various applications and variants of Paillier's probabilistic encryption scheme. First, we propose a threshold variant of the scheme, and also zeroknowledge protocols for proving that a given ciphertext encodes a given plaintext, and for verifying multiplication of encrypted values. We the ..."
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Cited by 13 (0 self)
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We study various applications and variants of Paillier's probabilistic encryption scheme. First, we propose a threshold variant of the scheme, and also zeroknowledge protocols for proving that a given ciphertext encodes a given plaintext, and for verifying multiplication of encrypted values. 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. Finally, we propose a variant of the encryption scheme, that allows reducing the expansion factor of Paillier's scheme from 2 to almost 1.
The Theory and Implementation of an Electronic Voting System
 SECURE ELECTRONIC VOTING
, 2003
"... We describe the theory behind a practical voting scheme based on homomorphic encryption. We give an example of an ElGamalstyle encryption scheme, which can be used as the underlying cryptosystem. Then, we ..."
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Cited by 9 (1 self)
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We describe the theory behind a practical voting scheme based on homomorphic encryption. We give an example of an ElGamalstyle encryption scheme, which can be used as the underlying cryptosystem. Then, we