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Photo by Isaac Smith on Unsplash

What has a point x=9, and protects your security?

Well, that will be Curve 25519, and takes a base point at x=9, and then uses:

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Type:  Curve25519_Montgomery
a= 486662
b= 1
p= 57896044618658097711785492504343953926634992332820282019728792003956564819949
x-point= 9
Z= 39420360
Y= 14781619447589544791020593568409986887264606134616475288964881837755586237401
s= 0

P=( 9 , 14781619447589544791020593568409986887264606134616475288964881837755586237401 )
2P=( 14847277145635483483963372537557091634710985132825781088887140890597596352251 , 48981431527428949880507557032295310859754924433568441600873610210018059225738 )

=== Just checking for (x2, y2).
These have to be the same, to prove that 2P is on the elliptic curve:

x^3+ax^2+x (mod p)= 33907837233136750156209621146237833792591564891953031467287095746800606444521
y^2 (mod p)= 33907837233136750156209621146237833792591564891953031467287095746800606444521
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2P=( 14847277145635483483963372537557091634710985132825781088887140890597596352251 , 48981431527428949880507557032295310859754924433568441600873610210018059225738 )

Conclusions

Elliptic Curve Cryptography (ECC) is just beautiful in its formation, and Curve 25519 is especially special.

Professor of Cryptography. Serial innovator. Believer in fairness, justice & freedom. EU Citizen. Auld Reekie native. Old World Breaker. New World Creator.

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