A Generalisation, a Simplification and some Applications of Paillier’s Probabilistic Public-Key System

Damgård, Ivan; Jurik, Mads J.

doi:10.7146/brics.v7i45.20212

Cited by 317 publications

(627 citation statements)

References 8 publications

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“…The probabilistic encryption function of Paillier [Pai99], enhanced by threshold decryption [FPS00,DJ01], satisfies all required properties. This scheme has M = Z N for an RSA modulus N .…”

Section: Homomorphic Encryption Schemementioning

confidence: 99%

Upper Bounds on the Communication Complexity of Optimally Resilient Cryptographic Multiparty Computation

Hirt

Nielsen

2005

Lecture Notes in Computer Science

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Abstract. We give improved upper bounds on the communication complexity of optimally-resilient secure multiparty computation in the cryptographic model. We consider evaluating an n-party randomized function and show that if f can be computed by a circuit of size c, then O(cn 2 κ) is an upper bound for active security with optimal resilience t < n/2 and security parameter κ. This improves on the communication complexity of previous protocols by a factor of at least n. This improvement comes from the fact that in the new protocol, only O(n) messages (of size O(κ) each) are broadcast during the whole protocol execution, in contrast to previous protocols which require at least O(n) broadcasts per gate.Furthermore, we improve the upper bound on the communication complexity of passive secure multiparty computation with resilience t < n from O(cn 2 κ) to O(cnκ). This improvement is mainly due to a simple observation.

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“…The probabilistic encryption function of Paillier [Pai99], enhanced by threshold decryption [FPS00,DJ01], satisfies all required properties. This scheme has M = Z N for an RSA modulus N .…”

Section: Homomorphic Encryption Schemementioning

confidence: 99%

Upper Bounds on the Communication Complexity of Optimally Resilient Cryptographic Multiparty Computation

Hirt

Nielsen

2005

Lecture Notes in Computer Science

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“…On the other hand, schemes using mix-nets [1, 9-12, 14, 19, 22] and/or homomorphic encryption [3,6,7] may provide it.…”

Section: Universal Verifiability Of the Tallymentioning

confidence: 99%

“…In voting schemes based on homomorphic encryption [3,6,7] privacy relies on computational assumptions, and is thus not unconditional. When mix-nets are used, this is the same, since the latter applies on asymmetric encryptions of the votes.…”

Section: Unconditional Privacymentioning

confidence: 99%

On Some Incompatible Properties of Voting Schemes

Chevallier-Mames¹,

Fouque

Pointcheval

et al. 2010

Towards Trustworthy Elections

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Abstract. In this paper, we study the problem of simultaneously achieving several security properties, for voting schemes, without non-standard assumptions. More specifically, we focus on the universal verifiability of the computation of the tally, on the unconditional privacy/anonymity of the votes, and on the receipt-freeness properties, for the most classical election processes. Under usual assumptions and efficiency requirements, we show that a voting system that wants to publish the final list of the voters who actually voted, and to compute the number of times each candidate has been chosen, we cannot achieve:-universal verifiability of the tally (UV) and unconditional privacy of the votes (UP) simultaneously, unless all the registered voters actually vote;

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“…It is based on the Paillier's cryptosystem [35,19]. Another version to share Paillier cryptosystem appears in [15].…”

Section: Examplesmentioning

confidence: 99%

“…For example, in voting scheme, such as [15,1], the authority can check the universally checkable proofs of validity of ciphertext and compute the tally. However, the result will no longer be a ciphertext that withstands CCA.…”

Section: Ind-ccamentioning

confidence: 99%

Threshold Cryptosystems Secure against Chosen-Ciphertext Attacks

Fouque

Pointcheval

2001

Advances in Cryptology — ASIACRYPT 2001

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Abstract. Semantic security against chosen-ciphertext attacks (IND-CCA) is widely believed as the correct security level for public-key encryption scheme. On the other hand, it is often dangerous to give to only one people the power of decryption. Therefore, threshold cryptosystems aimed at distributing the decryption ability. However, only two efficient such schemes have been proposed so far for achieving IND-CCA. Both are El Gamal-like schemes and thus are based on the same intractability assumption, namely the Decisional Diffie-Hellman problem. In this article we rehabilitate the twin-encryption paradigm proposed by Naor and Yung to present generic conversions from a large family of (threshold) IND-CPA scheme into a (threshold) IND-CCA one in the random oracle model. An efficient instantiation is also proposed, which is based on the Paillier cryptosystem. This new construction provides the first example of threshold cryptosystem secure against chosen-ciphertext attacks based on the factorization problem. Moreover, this construction provides a scheme where the "homomorphic properties" of the original scheme still hold. This is rather cumbersome because homomorphic cryptosystems are known to be malleable and therefore not to be CCA secure. However, we do not build a "homomorphic cryptosystem", but just keep the homomorphic properties.

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A Generalisation, a Simplification and some Applications of Paillier’s Probabilistic Public-Key System

Cited by 317 publications

References 8 publications

Upper Bounds on the Communication Complexity of Optimally Resilient Cryptographic Multiparty Computation

Upper Bounds on the Communication Complexity of Optimally Resilient Cryptographic Multiparty Computation

On Some Incompatible Properties of Voting Schemes

Threshold Cryptosystems Secure against Chosen-Ciphertext Attacks

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