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CompPoly/Fields/Montgomery Expand file tree Collapse file tree Original file line number Diff line number Diff line change @@ -7,16 +7,10 @@ Authors: Valerii Huhnin, Georgios Raikos
77import CompPoly.Fields.Montgomery.Basic
88
99/-!
10- # Montgomery Reduction — native `UInt32 × UInt64`, radix `R = 2^32`
10+ # Native 32-bit Montgomery Reduction
1111
12- The word-level bridge specialising `Montgomery.Basic` to 32-bit-word prime fields: the
13- Montgomery product fits in a `UInt64`, the radix is `R = UInt32.size = 2^32`, and the
14- high word is extracted with `>>> 32`. These lemmas relate the native-word computation to
15- the `Nat` formula proved generically in `Montgomery.Basic`, parameterized by the prime
16- `p`, the `UInt32` negated inverse `negInv`, and the `UInt64` modulus `modN`.
17-
18- A future 64-bit family would add a parallel `Native64` bridge (`>>> 64`,
19- `UInt64 × UInt128`) over the same `Montgomery.Basic` core.
12+ Native `UInt32` Montgomery reduction with radix `2 ^ 32`, connected to the generic
13+ natural-number specification in `Montgomery.Basic`.
2014-/
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2216namespace Montgomery
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