Practical lattice-based cryptography: NTRUEncrypt and NTRUSign

Abstract

We provide a brief history and overview of lattice based cryptography and cryptanalysis: shortest vector problems, closest vector problems, subset sum problem and knapsack systems, GGH, Ajtai-Dwork and NTRU. A detailed discussion of the algorithms NTRUEncrypt and NTRUSign follows. These algorithms have attractive operating speed and keysize and are based on hard problems that are seemingly intractable. We discuss the state of current knowledge about the security of both algorithms and identify areas for further research.