Homomorphic Cryptosystems and their Applications

Doerte K. Rappe

Abstract

In this thesis we consider homomorphic cryptosystems and their applications. Homomorphic cryptosystems allow for computations on encrypted data. We prove that the search for an algebraically homomorphic scheme can be reduced to the search of a homomorphic scheme on a special non-abelian group. Furthermore, we focus on a special application: computing with encrypted functions and data, respectively. For this application we develop an improved protocol that is efficient for functions that are computable by polynomial branching programs. Finally, we generalise the elliptic curve Paillier scheme by S. Galbraith in order to construct a threshold version of it. For this threshold scheme we develop several Sigma-protocols. Using these protocols we apply our threshold scheme on multiparty computations, electronic voting and commitment schemes.

Available format(s)
Category
Public-key cryptography
Publication info
Published elsewhere. Ph.D thesis
Keywords
Homomorphic cryptosystemsencrypted computationbranching programselliptic curve Paillier scheme
Contact author(s)
doerte rappe @ gmx de
History
Short URL
https://ia.cr/2006/001

CC BY

BibTeX

@misc{cryptoeprint:2006/001,
author = {Doerte K.  Rappe},
title = {Homomorphic Cryptosystems and their Applications},
howpublished = {Cryptology ePrint Archive, Paper 2006/001},
year = {2006},
note = {\url{https://eprint.iacr.org/2006/001}},
url = {https://eprint.iacr.org/2006/001}
}

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