Towards a DL-Based Additively Homomorphic Encryption Scheme

ElGamal scheme has been the first encryption scheme based on discrete logarithm. One of its main advantage is that it is simple, natural and efficient, but also that its security is clearly understood. However, one of its — often forgotten — disadvantages is that this scheme requires the encoding of messages into group elements, in order to be semantically secure. Unfortunately, this need prevents the scheme to be fully practical. In this paper, we propose a new way to deal with the problem of message encoding, which offers several advantages though some disadvantages. Our scheme is based on a quite simple combination of the standard ElGamal scheme with a message encoding inspired by the Naccache-Stern cryptosystem. We consider our solution as a new step towards the open problem of designing a discrete-logarithm based encryption scheme with the property of being additively homomorphic. Unfortunately, our construction is still not a complete solution. We hope however that it might...

• Type: Conference
• Year: 2007
• Where: ISW
• Authors: Guilhem Castagnos, Benoît Chevallier-Mames
• Keywords: ElGamal Scheme, Encryption Scheme, ISW 2007, first Encryption Scheme