International Association for Cryptologic Research

International Association
for Cryptologic Research


Paper: Additive Homomorphic Encryption with t-Operand Multiplications

Carlos Aguilar Melchor
Philippe Gaborit
Javier Herranz
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Abstract: Homomorphic encryption schemes are an essential ingredient to design protocols where different users interact in order to obtain some information from the others, at the same time that each user keeps private some of his information. When the algebraic structure underlying these protocols is complicated, then standard homomorphic encryption schemes are not enough, because they do not allow to crypto-compute at the same time additions and products of plaintexts. In this work we define a theoretical object, $t$-chained encryption schemes, which can be used to design crypto-computers for the addition and product of $t$ integer values. Previous solutions in the literature worked for the case $t=2$. Our solution is not only theoretical: we show that some existing (pseudo-)homomorphic encryption schemes (some of them based on lattices) can be used to implement in practice the concept of $t$-chained encryption scheme.
  title={Additive Homomorphic Encryption with t-Operand Multiplications},
  booktitle={IACR Eprint archive},
  keywords={public-key cryptography / homomorphic encryption, lattices},
  note={ 14140 received 5 Sep 2008, last revised 18 Sep 2008},
  author={Carlos Aguilar Melchor and Philippe Gaborit and Javier Herranz},