Cryptology ePrint Archive: Report 2006/001

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.

Category / Keywords: public-key cryptography / Homomorphic cryptosystems; encrypted computation; branching programs; elliptic curve Paillier scheme

Publication Info: Ph.D thesis

Date: received 31 Dec 2005

Contact author: doerte rappe at gmx de

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Version: 20060103:084929 (All versions of this report)

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