Two Quantum Attack Algorithms Against NTRU When the Private Key and Plaintext Are Codified in Ternary Polynomials

Abstract

Our cryptanalysis is focused on the NTRU second round candidate submitted to National Institute of Standards and Technology (NIST) competition. The NTRU domain is the ring with the private keys and the plaintext are codified in ternary polynomials, that means all their coefficients are in {−1, 0, 1}. Our two quantum attack algorithms namely KA_NTRU and PA_NTRU, inspired from Grover’s Algorithm, targeted respectively to find Private Keys and Plaintext. To test the proposed algorithms, we create a test release named NTRU_Attacks that integrate the principal cryptographic functions and the two attacks functions. In the general case, the quantum algorithms can break a system of dimension n in times.