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Re: string-stack.4th

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lehs <skydda.barnen@gmail.com> writes:
> GForth Android runs on 1.6 GHz Rockchip RK3066
> The others on 1.6 GHz Celeron both dual core. 

Pretty good.  On the original IBM PC, with a C implementation, this
calculation apparently would have taken minutes.

> I've no idea how to code public-key cryptography or why I would need it.

Basically say I want to send you a secret message.  You pick two random
primes p and q and compute the product N=pq and send me N.  Other people
(including me) can't find p and q from N, under the assumption that
factoring numbers of this size is computationally intractable.  Now you
figure out the totient phi(N)=(p-1)*(q-1), which is the size of Z*(N),
the group of numbers coprime to N.  Since you can find p and q from
phi(N), that means finding phi(N) is as hard as factoring, so N won't
leak info about phi(N) more than it does about the factors.

Now use the extended Euclidean algorithm to find a number d such that
d*3 == 1 (mod phi(N)) and keep d secret.  I take my message M and send
you M**3 mod N.  You use d to find M**(3*d) mod N, but since 3*d-1 is
a multiple of phi(N),  that means that M**(3*d) mod N is just M.

So without telling me anything secret, on a channel where anyone can be
listening, you've sent me info that lets me send you an encrypted
message.  This is public-key cryptography and the above algorithm is
called "RSA" after its inventors Rivest, Shamir, and Adelman.

Obviously there are a lot of practical details glossed over above, but
basically it's all about how fast you can do modular exponentials in a
group of size around 2**1000.  That's why I wanted that timing.

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Re: string-stack.4th lehs <skydda.barnen@gmail.com> - 2017-04-16 08:23 -0700
  Re: string-stack.4th lehs <skydda.barnen@gmail.com> - 2017-04-16 08:33 -0700
    Re: string-stack.4th "Rudy Velthuis" <newsgroups@rvelthuis.de> - 2017-04-16 22:34 +0000
      Re: string-stack.4th lehs <skydda.barnen@gmail.com> - 2017-04-16 17:11 -0700
        Re: string-stack.4th "Rudy Velthuis" <newsgroups@rvelthuis.de> - 2017-04-17 23:22 +0000
          Re: string-stack.4th lehs <skydda.barnen@gmail.com> - 2017-04-17 18:14 -0700
            Re: string-stack.4th hughaguilar96@gmail.com - 2017-04-17 18:44 -0700
            Re: string-stack.4th "Rudy Velthuis" <newsgroups@rvelthuis.de> - 2017-04-19 23:09 +0000
  Re: string-stack.4th lehs <skydda.barnen@gmail.com> - 2017-04-16 09:02 -0700
    Re: string-stack.4th lehs <skydda.barnen@gmail.com> - 2017-04-16 15:29 -0700
    Re: string-stack.4th hughaguilar96@gmail.com - 2017-04-16 19:43 -0700
      Re: string-stack.4th hughaguilar96@gmail.com - 2017-04-16 22:42 -0700
        Re: string-stack.4th hughaguilar96@gmail.com - 2017-04-16 23:09 -0700
          Re: string-stack.4th lehs <skydda.barnen@gmail.com> - 2017-04-16 23:34 -0700
            Re: string-stack.4th lehs <skydda.barnen@gmail.com> - 2017-04-17 00:15 -0700
            Re: string-stack.4th Paul Rubin <no.email@nospam.invalid> - 2017-04-17 01:19 -0700
              Re: string-stack.4th lehs <skydda.barnen@gmail.com> - 2017-04-17 02:06 -0700
                Re: string-stack.4th lehs <skydda.barnen@gmail.com> - 2017-04-17 02:50 -0700
                Re: string-stack.4th Paul Rubin <no.email@nospam.invalid> - 2017-04-17 13:14 -0700
                Re: string-stack.4th lehs <skydda.barnen@gmail.com> - 2017-04-17 15:58 -0700
                Re: string-stack.4th Paul Rubin <no.email@nospam.invalid> - 2017-04-17 16:57 -0700
                Re: string-stack.4th "Elizabeth D. Rather" <erather@forth.com> - 2017-04-17 15:07 -1000
                Re: string-stack.4th lehs <skydda.barnen@gmail.com> - 2017-05-17 05:32 -0700
                Re: string-stack.4th hughaguilar96@gmail.com - 2017-04-17 19:49 -0700
              Re: string-stack.4th "David N. Williams" <williams@umich.edu> - 2017-04-17 20:11 -0500
                Re: string-stack.4th Paul Rubin <no.email@nospam.invalid> - 2017-04-17 18:15 -0700
                Re: string-stack.4th lehs <skydda.barnen@gmail.com> - 2017-04-17 19:13 -0700
                Re: string-stack.4th Paul Rubin <no.email@nospam.invalid> - 2017-04-17 19:21 -0700
                Re: string-stack.4th lehs <skydda.barnen@gmail.com> - 2017-04-18 01:25 -0700
                Re: string-stack.4th Paul Rubin <no.email@nospam.invalid> - 2017-04-18 19:27 -0700
                Re: string-stack.4th "David N. Williams" <williams@umich.edu> - 2017-04-18 11:27 -0500
                Re: string-stack.4th mhx@iae.nl - 2017-04-18 11:53 -0700
                Re: string-stack.4th albert@cherry.spenarnc.xs4all.nl (Albert van der Horst) - 2017-04-20 20:48 +0200
                Re: string-stack.4th mhx@iae.nl - 2017-04-20 14:58 -0700
          Re: string-stack.4th lehs <skydda.barnen@gmail.com> - 2017-04-17 00:46 -0700
  Re: string-stack.4th hughaguilar96@gmail.com - 2017-04-16 19:31 -0700

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