Diffie-Hellman

Another key exchange system.

Whitfield Diffie and Marty Hellman, 1976

Setup:

Alice and Bob agree on a prime p and a number s between 1 and p-1.

[Graphics:Images/index_gr_1.gif]
[Graphics:Images/index_gr_2.gif]
[Graphics:Images/index_gr_3.gif]
[Graphics:Images/index_gr_4.gif]
[Graphics:Images/index_gr_5.gif]
[Graphics:Images/index_gr_6.gif]

Alice chooses a secret number a between 1 and p-1:

[Graphics:Images/index_gr_7.gif]
[Graphics:Images/index_gr_8.gif]
[Graphics:Images/index_gr_9.gif]
[Graphics:Images/index_gr_10.gif]

Bob chooses a secret number b between 1 and p-1:

[Graphics:Images/index_gr_11.gif]
[Graphics:Images/index_gr_12.gif]
[Graphics:Images/index_gr_13.gif]
[Graphics:Images/index_gr_14.gif]

Alice computes [Graphics:Images/index_gr_15.gif]:

[Graphics:Images/index_gr_16.gif]
[Graphics:Images/index_gr_17.gif]
[Graphics:Images/index_gr_18.gif]
[Graphics:Images/index_gr_19.gif]
[Graphics:Images/index_gr_20.gif]
[Graphics:Images/index_gr_21.gif]
[Graphics:Images/index_gr_22.gif]
[Graphics:Images/index_gr_23.gif]

Bob computes [Graphics:Images/index_gr_24.gif]:

[Graphics:Images/index_gr_25.gif]
[Graphics:Images/index_gr_26.gif]
[Graphics:Images/index_gr_27.gif]
[Graphics:Images/index_gr_28.gif]

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Converted by Mathematica      March 17, 2001