Implementação do esquema totalmente homomórfico sobre inteiros de chave reduzida.

Guilherme Rodrigues BilarLuan Cardoso dos SantosFabio Dacêncio Pereira

In this paper we implemented the fully homomorphic scheme with shoter key (DGHV with shorter key) proposed by Jean-Sébastian Coron, Avradip Mandal , David Naccache and Mehdi Tibouchi , which was published in the conference CRYPTO 2011, this same scheme can be compared with the Gentry's fully homomorphic scheme, being it a fully homomorphic scheme with a simpler construction, however this simplicity comes at the cost of the public key having an estimated size of O (?10), which according to Coron et al, makes it impossible to use in practical systems. The DGHV scheme over integers with shorter public key decreases the size of the generated public key to O (?7), encrypting the information of the public key in a quadratic manner, instead of encrypting them in a linear way. To do so, the python programming language was used, with the library of mathematics and number theory GMPY2.

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