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patent on elliptic curve public-key cryptography
I received some requests for clarification on my note that there are
patents covering public-key cryptosystems based on elliptic curves.
The specific patent I had in mind is (U.S.) patent number 5,159,632,
issued 10/27/1992, assigned to NeXT, with Richard Crandall as the inventor.
It covers some special cases of elliptic curve cryptography, and in
particular those cases that can be implemented efficiently. The broadest
claim is where the elliptic curve is over a finite field F_pk, where
``p is one of a class of numbers such that mod p arithmetic is performed
in a processor using only shift and add operations''. The remaining
claims cover various specific instances that meet those criteria, such
as where p is 2^q-C where C is no more than 32 bits long.
I haven't tried to see if there's an obvious D-H analog; at a guess,
the answer is yes, but it would be considered ``obvious'' given this
patent and the D-H patent. (Btw, there's no doubt that the D-H patent
covers this scheme as well, since it's just a specific instance of a
public-key cryptosystem. When an invention is covered by two patents,
you need licenses from both patent-holders to practice the invention.)