Efficient FPGA Implementation of Modular Multiplication and Exponentiation

The NTRUencrypt authors submitted four versions to National Institute of Standardization (NIST) competition since 2016 and it is still in process for the second round. The NTRU_pke release is one of them, it is defined in the ring Rq = Zq[X] / (Xn−1); and the private keys and the plaintext are codified in trinary polynomial, that means all their coefficients are in {-1,0,1}. Our two quantum attacks algorithms KA_NTRU and PA_NTRU on NTRU_pke implementation, inspired from Grover’s Algorithm, targeted respectively to find Private Keys and Plaintext. For testing the implementation attacks, we create a NTRU_pke test version named NTRU Attacks. In the general case, the quantum algorithms can break a system of dimension n in 2n/2 time.