{"id":{"repo_id":"mit","oai_identifier":"oai:dspace.mit.edu:1721.1/157189"},"canonical_url":"https://search.dev.ndltd.org/etd/mit/oai:dspace.mit.edu:1721.1/157189","repository":{"repo_id":"mit","name":"MIT","base_url":"https://dspace.mit.edu/oai/request"},"display":{"title":"Verifying Correctness of the Number Theoretic Transform and Fast Number Theoretic Transform in F⋆","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_html":"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_has_math":false,"creators":["Ono, Rick R."],"institution":"Massachusetts Institute of Technology","degree_name":"Master","degree_level":null,"degree_discipline":null,"degree_department":"Massachusetts Institute of Technology. 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