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Fix two misstatements of the Montgomery curve equation.

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I got it right in all the serious code (or else my Curve25519 key
exchange wouldn't have worked), but I wrote it down wrongly in the
comment in ecc.h, putting the coefficient b on the RHS x term rather
than the LHS y^2. Then I repeated the same error in the point
decompression function in eccref.py.
This commit is contained in:
Simon Tatham 2019-01-03 15:26:33 +00:00
parent 4eb1dedb66
commit 992f98d5d7
2 changed files with 3 additions and 3 deletions
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4
contrib/eccref.py
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@ -327,8 +327,8 @@ class MontgomeryCurve(CurveBase):
def cpoint(self, x, yparity=0):
if not hasattr(self, 'sqrtmodp'):
self.sqrtmodp = SqrtModP(self.p)
rhs = x**3 + self.a.n * x**2 + self.b.n * x
y = self.sqrtmodp.sqrt(rhs)
rhs = (x**3 + self.a.n * x**2 + x) / self.b
y = self.sqrtmodp.sqrt(int(rhs))
if (y - yparity) % 2:
y = -y
return self.point(x, y)

2
ecc.h
View File

@ -108,7 +108,7 @@ void ecc_weierstrass_get_affine(WeierstrassPoint *wp, mp_int **x, mp_int **y);
* Montgomery curves.
*
* A curve in this form is defined by two parameters a,b, and the
* curve equation is y^2 = x^3 + ax^2 + bx.
* curve equation is by^2 = x^3 + ax^2 + x.
*
* As with Weierstrass curves, there's an additional point at infinity
* that is the identity element, and the inverse of (x,y) is (x,-y).