* Encounter: an open-source library providing an implementation of Paillier cryptosystem and a cryptographic counters construction based on the same.

* Paillier cryptosystem

Paillier cryptosystem •

The Paillier cryptosystem, named after and invented by Pascal Paillier in 1999, is a probabilistic asymmetric algorithm for public key cryptography.

A notable feature of the Paillier cryptosystem is its homomorphic properties.

Paillier cryptosystem exploits the fact that certain discrete logarithms can be computed easily.

* The Okamoto – Uchiyama cryptosystem as a historical antecedent of Paillier.

* The Damgård – Jurik cryptosystem is a generalization of Paillier.

* The Paillier cryptosystem interactive simulator demonstrates a voting application.

* An interactive demo of the Paillier cryptosystem.

* The Homomorphic Encryption Project implements the Paillier cryptosystem along with its homomorphic operations.

# REDIRECT Paillier cryptosystem

# REDIRECT Paillier cryptosystem

More efficient probabilistic encryption algorithms include Elgamal, Paillier, and various constructions under the random oracle model, including Optimal Asymmetric Encryption Padding ( OAEP ).

In the Paillier, ElGamal, and RSA cryptosystems, it is also possible to combine several ciphertexts together in a useful way to produce a related ciphertext.

In Paillier, given only the public-key and an encryption of and, one can compute a valid encryption of their sum.

However, given the Paillier encryptions of two messages there is no known way to compute an encryption of the product of these messages without knowing the private key.

Semantically secure encryption algorithms include Goldwasser-Micali, El Gamal and Paillier.

The first provably-secure PAKE protocols were given in work by M. Bellare, D. Pointcheval, and P. Rogaway ( Eurocrypt 2000 ) and V. Boyko, P. MacKenzie, and S. Patel ( Eurocrypt 2000 ).

A considerable number of alternative, secure PAKE protocols were given in work by M. Bellare, D. Pointcheval, and P. Rogaway, variations, and security proofs have been proposed in this growing class of password-authenticated key agreement methods.

* T. Okamoto and D. Pointcheval ( 2000 ).

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