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Number-Theoretic Transform specification#2088

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atrieu wants to merge 11 commits into
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atrieu:isomorphisms
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Number-Theoretic Transform specification#2088
atrieu wants to merge 11 commits into
mit-plv:masterfrom
atrieu:isomorphisms

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@atrieu atrieu commented May 14, 2025

This is a new version of #1997 using the suggestions given there for specifying the NTT.

Specifically, this provides

  • a theory of univariate polynomials (src/NTT/Polynomial.v)
  • the algebraic form of the Chinese Remainder Theorem for polynomials (src/NTT/PolynomialCRT.v)
  • explicit formulas for computing the CRT when the polynomial modulus has the form X^2 - a^2 (src/NTT/PolynomialCRT.v)
  • the NTT as recursive applications of the CRT, also proved a ring isomorphism (src/NTT/NTT.v)
  • lower level Gallina code implementing the NTT that is proved correct and should be more amenable to code generation (src/NTT/GallinaNTT.v)

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