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[Gcl-devel] Re: revision & simplification & gmp_powm
From: |
Camm Maguire |
Subject: |
[Gcl-devel] Re: revision & simplification & gmp_powm |
Date: |
01 Nov 2005 12:31:09 -0500 |
User-agent: |
Gnus/5.09 (Gnus v5.9.0) Emacs/21.2 |
Greetings
Robert Boyer <address@hidden> writes:
> Here is a simple correction to the description I sent you of the RSA
> decryption algorithm. I must have been asleep. All I have done here is to
> set the constant d to 1.
>
> Now, the RSA decryption computation simply consists of computing
>
> m(i) = (( input(i) ) ^ e) mod (p * q)
>
> for successive i, where p, q, and e are fixed positive integers (with some
> other properties not especially relevant to the computation) and each
> input(i) in a nonnegative integer less than p*q. We imagine an input
> "file"
> which we read by asking for successive chunks, input(0), input(1),
> input(2),
> ..., input(n). We wish to assemble as our answer m(0), m(1), m(2), ...,
> m(n). As soon as we have read any input(i), we can fork off a job to
> compute
> m(i). We don't want to fork off too many jobs, of course, and we do want
> to
> assemble answers in a timely orderly fashion, maximizing use of available
> hardware, writing the output to an output file as and when we can.
>
> To simplify the example further, one might want to replace (p * q) with just
> single constant, say r.
>
> m(i) = (( input(i) ) ^ e) mod r
>
> for successive i, where r and e are fixed positive integers (with some ...
>
> It is also the case that one can assume that e is less than r.
>
> For all I know, GMP already has a function to do exactly this job very
> efficiently. I suspect it might be called gmp_powm. That's what they
> seem to call it in PHP, cf.
>
> http://aspn.activestate.com/ASPN/docs/PHP/function.gmp-powm.html
>
> So you'd be doing the GCL community a favor by making available directly in
> Lisp access to that gmp_powm function (if it does what I think). (And maybe
> a host of other gmp functions?)
Pushing forward the rest of gmp has been on my todo list for some
time. Thus far, I've taken an on-demand approach. Usually, I've
tried to integrate these functions into existing common lisp
functions, but here I can see no CL function which contains this one
(please correct me if wrong). Do we need a gmp package? What are the
other functions you would find useful?
Take care,
>
> Bob
>
>
>
--
Camm Maguire address@hidden
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