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Add some special case handling for ec_twin_mult
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Previously we were computing incorrect answers for `ec_twin_mult j S k T` in the following 4 special cases: `S == 0`, `T == 0`, `S+T == 0` and `S-T == 0`. In these cases, we must be more careful about performing normalization in the twin multiply procedure.
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@ -67,6 +67,15 @@ ec_is_nonsingular b = (fromInteger 4) * a^^3 + (fromInteger 27) * b^^2 != 0
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ec_is_identity : {p} (prime p, p > 3) => ProjectivePoint p -> Bit
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ec_is_identity S = S.z == 0 /\ ~(S.x == 0 /\ S.y == 0)
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/**
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* Test two projective points for equality, up to the equivalence relation
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* on projective points.
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*/
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ec_equal : {p} (prime p, p > 3) => ProjectivePoint p -> ProjectivePoint p -> Bit
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ec_equal S T =
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(S.z == 0 /\ T.z == 0) \/
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(S.z != 0 /\ T.z != 0 /\ ec_affinify S == ec_affinify T)
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/**
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* Compute a projective representative for the given affine point.
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*/
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@ -263,6 +263,11 @@ ec_sub p s t = ec_add p s u
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where u = t{ py = Integer.minusBigNat (primeMod p) (py t) }
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{-# INLINE ec_sub #-}
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ec_negate :: PrimeModulus -> ProjectivePoint -> ProjectivePoint
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ec_negate p s = s{ py = Integer.minusBigNat (primeMod p) (py s) }
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{-# INLINE ec_negate #-}
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-- | Compute the elliptic curve group addition operation
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-- for values known not to be the identity.
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-- In other words, if @S@ and @T@ are projective points on a curve,
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@ -381,10 +386,41 @@ ec_mult p d s
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-- and normalize all four values. This can be done jointly
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-- in a more efficient way than computing the necessary
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-- field inverses separately.
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-- When given points S and T, the returned tuple contains
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-- normalized representations for (S, T, S+T, S-T).
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--
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-- Note there are some special cases that must be handled separately.
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normalizeForTwinMult ::
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PrimeModulus -> ProjectivePoint -> ProjectivePoint ->
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(ProjectivePoint, ProjectivePoint, ProjectivePoint, ProjectivePoint)
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normalizeForTwinMult p s t = (s',t',spt',smt')
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normalizeForTwinMult p s t
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-- S == 0 && T == 0
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| Integer.isZeroBigNat a && Integer.isZeroBigNat b =
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(zro, zro, zro, zro)
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-- S == 0 && T != 0
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| Integer.isZeroBigNat a =
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let tnorm = ec_normalize p t
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in (zro, tnorm, tnorm, ec_negate p tnorm)
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-- T == 0 && S != 0
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| Integer.isZeroBigNat b =
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let snorm = ec_normalize p s
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in (snorm, zro, snorm, snorm)
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-- S+T == 0, both != 0
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| Integer.isZeroBigNat c =
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let snorm = ec_normalize p s
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in (snorm, ec_negate p snorm, zro, ec_double p snorm)
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-- S-T == 0, both != 0
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| Integer.isZeroBigNat d =
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let snorm = ec_normalize p s
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in (snorm, snorm, ec_double p snorm, zro)
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-- S, T, S+T and S-T all != 0
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| otherwise = (s',t',spt',smt')
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where
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spt = ec_add p s t
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smt = ec_sub p s t
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19
tests/regression/twinmult.cry
Normal file
19
tests/regression/twinmult.cry
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@ -0,0 +1,19 @@
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import PrimeEC
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zro : ProjectivePoint 7
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zro = { x = 1, y = 1, z = 0 }
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property twin_mult_zro j k =
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ec_equal`{7} (ec_twin_mult j zro k zro) zro
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property twin_mult_zro1 j k S =
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ec_equal`{7} (ec_twin_mult j zro k S) (ec_mult k S)
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property twin_mult_zro2 j k S =
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ec_equal`{7} (ec_twin_mult j S k zro) (ec_mult j S)
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property twin_mult_same j k S =
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ec_equal`{7} (ec_twin_mult j S k S) (ec_add (ec_mult j S) (ec_mult k S))
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property twin_mult_neg j k S =
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ec_equal`{7} (ec_twin_mult j S k (ec_negate S)) (ec_sub (ec_mult j S) (ec_mult k S))
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3
tests/regression/twinmult.icry
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3
tests/regression/twinmult.icry
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@ -0,0 +1,3 @@
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:l twinmult.cry
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:exhaust
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