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 \(\mathbf {R_q}=\mathbb {Z}_q[X]/\mathbf (X^n -1)\) 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 \(2^{n/2}\) times.
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Laaji, E.H., Azizi, A., Ezzouak, S. (2020). Two Quantum Attack Algorithms Against NTRU When the Private Key and Plaintext Are Codified in Ternary Polynomials. In: Serrhini, M., Silva, C., Aljahdali, S. (eds) Innovation in Information Systems and Technologies to Support Learning Research. EMENA-ISTL 2019. Learning and Analytics in Intelligent Systems, vol 7. Springer, Cham. https://doi.org/10.1007/978-3-030-36778-7_61
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DOI: https://doi.org/10.1007/978-3-030-36778-7_61
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