Lattice-Based Knowledge Assumption and IND-CCA1 Scheme

Abstract

This thesis introduces a lattice-based encryption scheme, Dual LWE ElGamal ($\mathcal{DLEG}$) that is IND-CCA1 secure and is relatively simple to construct. The scheme is an analog to Damgaard's ElGamal encryption scheme, which is also IND-CCA1 secure. The scheme is constructed using lattice trapdoors and its security relies on a lattice analog of the Knowledge of Exponent Assumption, called the Knowledge of LWE Secret Assumption (LWEK). This thesis motivates the construction of $\mathcal{DLEG}$ scheme and gives a proof of security. We also show that LWEK is a member of Subset Witness Assumptions (SWK) and discuss some possible future work.