Elliptic Curve Diffie–Hellman
ECDH
⎯ implementation of the
Diffie–Hellman key exchange
protocol on an
Elliptic Curve
.
Alice
Bob
1
General algorithm parameters. These numbers can be unique or generally accepted.
The initial values correspond to the Elliptic Curve parameters for Bitcoin.
Elliptic Curve Y
2
= X
3
+ a × X + b (mod M
EC
)
Y
2
= X
3
+
× X +
( mod
)
Base point G(x,y)
x
y
G
Order
2
Choose large numbers (random). Personal secrets. Large numbers <G
Order
a -- secret key
b -- secret key
3
The public key is derived from the private key.
A =
(x,y)
B =
(x,y)
4
Exchange of public parts of the future secret key.
5
The keys of the opposite parties to the correspondence.
B (x,y)
A (x,y)
6
Calculating a shared key for encryption and decryption
K=a×B=b×A=a×b×G
K =
K =
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