The Impact of Quantum Search Algorithms on NTRU Cryptosystem

Lattice-based cryptosystems rely on certain lattice problems for their socurity, such as the shortest vector and the closest vector probtems. NTRU is a kind of lattice based public key cryptosysytem gaining much attention because of its high efficiency. Its encryption and decryption use a mixing system suggested by polynomial algebra combined with a clustering principle based on elementary probability theory. With the availability of quantum computers, the security of cryptosystems based on classical mathematic problems needs to be reevaluated. Since lattice reduction is the main threat to lattice-based cryptosystems, lattice reduction using quantum search algorithms are analyzed to evaluate the security of NTRU in this paper. According to our results, original security paratneters proposed for NTRU should be increased in the event that Grover's quantum search algorithm is used for lattice reduction.