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

  • El Hassane LaajiEmail author
  • Abdelmalek Azizi
  • Siham Ezzouak
Conference paper
Part of the Learning and Analytics in Intelligent Systems book series (LAIS, volume 7)


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.


NTRU NewHope Lattice- based-cryptography Post quantum cryptography Grover’s algorithm 


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Copyright information

© Springer Nature Switzerland AG 2020

Authors and Affiliations

  • El Hassane Laaji
    • 1
    Email author
  • Abdelmalek Azizi
    • 1
  • Siham Ezzouak
    • 2
  1. 1.Mohammed First UniversityOujdaMorocco
  2. 2.Sidi Mahammed Ben Abdellah University FesFesMorocco

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