2026-09-18T19:18:58Zhttps://dspace.mit.edu/server/oai/requestoai:dspace.mit.edu:1721.1/1571892024-10-10T03:15:11Zcom_1721.1_7582com_1721.1_7581col_1721.1_131023
Athalye, Anish
Zeldovich, Nickolai
Ono, Rick R.
Massachusetts Institute of Technology. Department of Electrical Engineering and Computer Science
2024-10-09T18:27:11Z
2024-10-09T18:27:11Z
2024-09
2024-10-07T14:34:36.025Z
https://hdl.handle.net/1721.1/157189
As engineers continue to develop more sophisticated algorithms to optimize cryptographic algorithms, their often simple mathematical specifications become convoluted in the algorithms, from which a class of correctness bugs arise. Because cryptographic algorithms often secure sensitive information, their correctness, and in turn their security is a top priority. The Number Theoretic Transform (NTT) is an algorithm that enables efficient polynomial multiplication and has recently gained importance in post-quantum cryptography. This thesis presents a proof of correctness of the NTT in F⋆ , a proof-oriented programming language that extracts to OCaml, and shows that we can use the NTT to perform polynomial multiplications. We provide an implementation of the Cooley-Tukey fast NTT algorithm and a proof that it matches the original NTT specification. This thesis also presents a representation of polynomials in the F⋆ subset Low*, which extracts to performant C code.
M.Eng.
Massachusetts Institute of Technology
Attribution-NonCommercial-NoDerivatives 4.0 International (CC BY-NC-ND 4.0)
Copyright retained by author(s)
https://creativecommons.org/licenses/by-nc-nd/4.0/
Verifying Correctness of the Number Theoretic Transform and Fast Number Theoretic Transform in F⋆
Thesis
application/pdf
Master
Master of Engineering in Electrical Engineering and Computer Science
Publication
unknown
unknown
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<Abstract>As engineers continue to develop more sophisticated algorithms to optimize cryptographic algorithms, their often simple mathematical specifications become convoluted in the algorithms, from which a class of correctness bugs arise. Because cryptographic algorithms often secure sensitive information, their correctness, and in turn their security is a top priority. The Number Theoretic Transform (NTT) is an algorithm that enables efficient polynomial multiplication and has recently gained importance in post-quantum cryptography. This thesis presents a proof of correctness of the NTT in F⋆ , a proof-oriented programming language that extracts to OCaml, and shows that we can use the NTT to perform polynomial multiplications. We provide an implementation of the Cooley-Tukey fast NTT algorithm and a proof that it matches the original NTT specification. This thesis also presents a representation of polynomials in the F⋆ subset Low*, which extracts to performant C code.</Abstract>
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