Example of Key Exchange

 

We give a simple example of the key exchange protocol (with small n so that the example is possible to demonstrate easily). Draw the corresponding diagrams as an exercise – solutions can be found on the next page.

 

·        Suppose A and B agreed upon n=4 and  (defined in the properties of braids page).

·        A chooses the braid  and sends B the braid  in its normal form. With the notation of the properties page, and , so A actually sends .

·        B chooses the braid  and computes_. Note that this is not in its normal form.

·        B sends A the braid  in its normal form. . With the notation of the properties page, and , so B actually sends .

·        A computes _.

 

To store K, it must be converted into normal form, but we do not show this computation here. The equalities shown in the computations above can be obtained by using the elementary isotopies on the braid introduction page.