# A New Distribution Version of Boneh-Goh-Nissim Cryptosystem: Security and performance analysis

## TL;DR

This paper introduces two distributed variants of the Boneh-Goh-Nissim cryptosystem, proving their security and efficiency, with one version outperforming ElGamal on elliptic curves under certain assumptions.

## Contribution

It presents two new distributed versions of BGNC, with security proofs and efficiency comparisons to existing cryptosystems, enhancing practical cryptographic applications.

## Key findings

- First version is semantically secure against active non-adaptive adversaries.
- Second version is more efficient than EDECC and secure under SDP assumption.
- Provides formal security proofs for both variants.

## Abstract

The aim of this paper is to provide two distributed versions of the Boneh-Goh-Nissim Cryptosystem (BGNC). We give a proof of the semantic security for the first one. This guaranties that our algorithm is semantically secure in the contest of active non-adaptive adversaries. Furthermore, we prove that the second version of our distributed scheme is computationally more efficient than the ElGamal destributed elliptic curve cryptosystem (EDECC) and secure under the Subgroup Decision problem (SDP) assumption.