Post-Quantum Cryptography and NTT as a Polynomial Multiplication Method

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Aslı_Ebru_Kaya_Term_Project.pdf

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2023-1

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Kaya, Aslı Ebru

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Cryptology has been a crucial element in the rapidly evolving technology. Without a successful encryption, no one and no system can be secure. The advancements in another aspect of technology, namely the quantum computers, have turned out to be the destructive game changer for the schemes used in crypto-systems, which have been deemed to be safe until now in the era of classical computers. The widely used state of the art public-key crypto-schemes are not resistant to predicted quantum attacks. The threat posed by quantum computers gave a way for new research area, which is called post-quantum cryptology. Lattice based schemes seem to be the most promising crypto-systems among possible post-quantum cryptographic schemes. Polynomial multiplications are the bottleneck of the lattice based schemes since they are fundamentally used in these schemes and take considerable amount of time and power. There are different methods for polynomial multiplications with various levels of complexity. Simple and straightforward schoolbook method has a quadratic complexity which makes it unfeasible to be utilized in the crypto-schemes. Number Theoretic Transform, which is a specific case of Fast Fourier Transform, seems to be the most favorable polynomial multiplication method over finite fields with its almost linear complexity of O(nlogn). Since post-quantum cryptographic lattice based schemes deal with polynomials that have coefficients of integers, Number Theoretic Transform, in which all procedure is applied in the ring of integers, suits well to avoid any round-off error and accelerate the computations while reducing computational complexity considerably.

Subject Keywords

Post-quantum cryptography, Lattice based schemes, Number theoretic transform, Discrete fourier transform, Polynomial multiplication

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https://hdl.handle.net/11511/102002

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Graduate School of Applied Mathematics, Term Project

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Citation Formats

A. E. Kaya, “Post-Quantum Cryptography and NTT as a Polynomial Multiplication Method,” M.S. - Master Of Science Without Thesis, Middle East Technical University, 2023.