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Tip revision: 492973e7cf3e9b0c13a36aa776d984d1deae0516 authored by Jonathan Protzenko on 09 March 2018, 21:57:53 UTC
Makefile fixes + support for -fnostruct-passing
Makefile fixes + support for -fnostruct-passing
Tip revision: 492973e
Hacl.Spec.Bignum.Field.fst
module Hacl.Spec.Bignum.Field
module ST = FStar.HyperStack.ST
open FStar.HyperStack.All
open FStar.Mul
open Hacl.Bignum.Constants
(** Type of elements of the commutative field Z/pZ where p is prime **)
type elem = e:int{e >= 0 /\ e < prime}
val zero: elem
let zero = 0
val one:elem
let one = 1
let addition (a:elem) (b:elem) : Tot elem = (a + b) % prime
let multiplication (a:elem) (b:elem) : Tot elem = (a * b) % prime
let opposite (a:elem) : Tot elem = (prime - a - 1)
let rec scalarmult (a:elem) (b:nat) : Tot elem =
if b = 0 then 0 else addition a (scalarmult a (b-1))
let rec exp (a:elem) (b:nat) : Tot elem =
if b = 0 then 1 else multiplication a (exp a (b-1))
let inverse (a:elem) : Tot elem = exp a (prime - 2)
val lemma_addition_is_commutative: a:elem -> b:elem -> Lemma (addition a b = addition b a)
let lemma_addition_is_commutative a b = ()
val lemma_multiplication_is_commutative: a:elem -> b:elem -> Lemma (multiplication a b = multiplication b a)
let lemma_multiplication_is_commutative a b = ()
assume val lemma_addition_associativity: a:elem -> b:elem -> c:elem ->
Lemma (addition (addition a b) c = addition a (addition b c))
assume val lemma_multiplication_associativity: a:elem -> b:elem -> c:elem ->
Lemma (multiplication (multiplication a b) c = multiplication a (multiplication b c))
val lemma_addition_neutral_element: a:elem ->
Lemma (addition a zero = a)
let lemma_addition_neutral_element a = ()
val lemma_multiplication_neutral_element: a:elem ->
Lemma (multiplication a one = a)
let lemma_multiplication_neutral_element a = ()
assume val lemma_addition_symmetry: a:elem ->
Lemma (addition (opposite a) a = zero)
assume val lemma_multiplication_symmetry: a:elem ->
Lemma (multiplication (inverse a) a = one)
inline_for_extraction let op_At_Plus a b = addition a b
inline_for_extraction let op_At_Star a b = multiplication a b
inline_for_extraction let op_At_Plus_Plus a b = scalarmult b a
inline_for_extraction let op_At_Star_Star a b = exp b a