Re: Cryptographie asymétrique

On Thu, 31 May 2007 16:59:30 +0200, Stefan Tillich pisal:
[snip]
Eve:

Knows x, y, z
x = a+b
y = (x+c)*d + f = (a+b+c)*d + f = ad + bd + cd + f
z = y%a + cle = (ad + bd + cd + f)%a + cle = bd + cd + f + cle (a >
(b+c)*d + f)

Does
k = y - z = (ad + bd + cd + f) - (bd + cd + f + cle) = ad - cle
m = y % x = (a+b)*d + cd + f) % (a+b) = cd + f (because a > (b+c)*d +
f => (a+b) > (b+c)*d + f + b > cd + f)
n = z - m = (bd + cd + f + cle) - (cd + f) = bd + cle
p = k + n = (ad - cle) + (bd + cle) = ad + bd = (a+b)*d
=> p / x = ((a+b)*d) / (a+b) = d
=> m % d = (cd + f) % d = f (because d > f + cle => d > f)
=> z % d - f = (bd + cd + f + cle) % d - f = (f + cle) - f = cle
(because d > f + cle)

Nice job.

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