Note 4/20/17: Due to circumstances I have had to move my web pages here.

Choose one of the two following elliptic curves:
 Curve over GF(p) Given a prime p, the elliptic curves modulo p that we use are of the form: y2 = x3 + ax + b. The curve and key information used for this page is: Curve over GF(2m) Given a field GF(2m) and a irreducable polynomial, the curve is of the form: y2 + xy = x3 + ax2 + b. The curve and key information used for this page is:
A common use of elliptic curve cryptography is to generate a shared secret key for use in secret key systems. The Diffie-Hellman protocol can be applied to elliptic curves as follows:
• Alice generates a secret key rA
• Alice calculates PA = rA*e1 and sends it to Bob.
• Bob generates a secret key rB
• Bob calculates PB = rB*e1 and sends it to Alice.
• Alice receives PB and calculates P = rA*PB
• Bob receives PA and calculates P = rB*PA
• Alice and Bob can use P to generate a shared secret key suitable for AES or some other system. Some protocols use the x coordinate of P as the shared key, or a hash can be applied to P to generate the key.

Note that if Alice already has published an elliptic curve public key, then Bob and Alice can agree to use Q in place of PA.

A's random value:
B's random value:

Details:

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