A Meet-In-The-Middle Attack against NTRU with Trinary Parameters

Abstract

In this paper, we introduce a modified version of meet-in-the-middle attack on NTRUEncrypt private keys. In the original meet-in-the-middle attack, which was described by N. Howgrave-Graham et al., the attacker performs a combinatorial search and is capable of retrieving the private key efficiently due to a severe drop in security level of the system under meet-in-the-middle attack. Several changes have been made to the parameter set to enhance the security level of NTRUEncrypt, such as changing the private keys from binary to trinary polynomials, and therefore increase the searching space of meet-in-the-middle attack and consolidate the cryptosystem. As the searching space enlarges, the implementation also have a geometrical growth of complexity in both time and memory requirement. Under the circumstances, we designed an adapted meet-in-the-middle attack to break the NTRUEncrypt cryptosystem with the new parameter set. In order to cope with the corresponding larger searching space, our attack employs a more sophisticated combinatorial search over all possible private keys. Simulation results show that our method works for small degree.