🚀 go-pugleaf

In article <1993Jan4.145637.5551@newstand.syr.edu>, greeny@top.cis.syr.edu (J. S. Greenfield) writes:
> This sounds far too broad.  I would guess it's far more specific--somewhere
> along the lines of use of modular exponentiation with a modulus
> consisting of the product of two primes for cryptographic purposes.
> 
> Modular arithmetic was not at all new to cryptography when RSA was
> developed, so the patent would *have* to be much narrower than just that.

You're right.  Here's Claim 1 of the RSA patent:

1. A cryptographic communications system comprising:
  A. a communications channel,
  B. an encoding means coupled to said channel and adapted for
    transforming a transmit message word signal M to a ciphertext word
    signal C and for transmitting C on said channel,
    where M corresponds to a number representative of a message and

        0 <= M <= n-1

    where n is a composite number of the form

        n = p.q

    where p and q are prime numbers, and
    where C corresponds to a number representative of an enciphered
      form of said message and corresponds to

        C == M^e (mod n)

    where e is a number relatively prime to lcm(p-1, q-1), and
  C. a decoding means coupled to said channel and adapted for receiving
    C from said channel and for transforming C to a receive message
    word signal M'
    where M' corresponds to a number representative of a deciphered
      form of C and corresponds to

        M' == C^d (mod n)

    where d is a multiplicative inverse of e (mod lcm(p-1, q-1)).

It's very specific -- to infringe this claim, you'd have to use a device
with all three parts.  (N.B. -- before you start picking this apart,
and looking for the obvious ways around it, note two things.  First,
the RSA patent has about 40 claims, each covering a different variation.
Second, variations that are ``obvious to one skilled in the art'' also
infringe.)

Note, too, that RSA did *not* patent the equations themselves, nor did
they patent an algorithm.  They patented a ``cryptographic communications
system'' whose behavior is described by certain equations.  One way to
look at it -- in fact, the way I look at it -- is to regard this as
equivalent to patenting an electronic circuit whose behavior is described
by certain other equations -- as, of course, is generally the case.