Elliptic curve arithmetic: Difference between revisions
Added 11l
m (→{{header|Sage}}: updated to work with Python 3) |
Alextretyak (talk | contribs) (Added 11l) |
||
Line 42:
<br>for any point '''P''' and integer '''n''', the point '''P + P + ... + P''' ('''n''' times).
<br><br>
=={{header|11l}}==
{{trans|Python}}
<lang 11l>T Point
Float x, y
F (x = Float.infinity, y = Float.infinity)
.x = x
.y = y
F.const copy()
R Point(.x, .y)
F.const is_zero()
R .x > 1e20 | .x < -1e20
F neg()
R Point(.x, -.y)
F dbl()
I .is_zero()
R .copy()
I .y == 0
R Point()
V l = (3 * .x * .x) / (2 * .y)
V x = l * l - 2 * .x
R Point(x, l * (.x - x) - .y)
F add(q)
I .x == q.x & .y == q.y
R .dbl()
I .is_zero()
R q.copy()
I q.is_zero()
R .copy()
I q.x - .x == 0
R Point()
V l = (q.y - .y) / (q.x - .x)
V x = l * l - .x - q.x
R Point(x, l * (.x - x) - .y)
F mul(n)
V p = .copy()
V r = Point()
V i = 1
L i <= n
I i [&] n
r = r.add(p)
p = p.dbl()
i <<= 1
R r
F String()
R ‘(#.3, #.3)’.format(.x, .y)
V Point_b = 7
F show(s, p)
print(s‘ ’(I p.is_zero() {‘Zero’} E p))
F from_y(y)
V n = y * y - Point_b
V x = I n >= 0 {n ^ (1. / 3)} E -((-n) ^ (1. / 3))
R Point(x, y)
V a = from_y(1)
V b = from_y(2)
show(‘a =’, a)
show(‘b =’, b)
V c = a.add(b)
show(‘c = a + b =’, c)
V d = c.neg()
show(‘d = -c =’, d)
show(‘c + d =’, c.add(d))
show(‘a + b + d =’, a.add(b.add(d)))
show(‘a * 12345 =’, a.mul(12345))</lang>
{{out}}
<pre>
a = (-1.817, 1.000)
b = (-1.442, 2.000)
c = a + b = (10.375, -33.525)
d = -c = (10.375, 33.525)
c + d = Zero
a + b + d = Zero
a * 12345 = (10.759, 35.387)
</pre>
=={{header|C}}==
| |||