The public key cryptosystem NTRUEncrypt is analyzed with a main focus on lattice based attacks. We give a brief overview of NTRUEncrypt and the padding scheme NAEP. We propose NTRU-KEM, a key encapsulation method using NTRU, and prove it secure. We briefly cover some non-lattice based attacks but most attention is given to lattice attacks on NTRUEncrypt. Different lattice reduction techniques, alterations to the NTRUEncrypt lattice and breaking times for optimized lattices are studied.