From: Rick Busdiecker <rfb@lehman.com>
Date: Sun, 14 Jan 96 20:39:30 PST
To: Peter Wayner <pcw@access.digex.net>
Subject: Re: Bignum support added to XLISP 2.1h
In-Reply-To: <v02130502ad193fbd1b75@[199.125.128.5]>
Message-ID: <9601150438.AA22146@cfdevx1.lehman.com>
MIME-Version: 1.0
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    Date: Wed, 10 Jan 1996 11:26:49 -0500
    From: Peter Wayner <pcw@access.digex.net>
    
    Many cypherpunks might enjoy programming in XLISP 2.1h because the freely
    available implementation of LISP now offers support for BIGNUMS. That means
    it is quite easy to write cryptographic algorithms that use very large
    numbers without adding extra support. The downside is that the language is
    interpretted and thus much slower than something like C.

This is good to hear.  However it's also worth noting that a number of
other freely available lisps, e.g. CLISP, gcl (previously kcl and
akcl) and CMU Common Lisp, also support bignums.  CMU Common Lisp has
the disadvantage of not being as portable as the others, but has the
advantage of compiling to native code on supported architectures which
include Sparc, Pmax, and HP.
    
    It should also be possible to write RSA in a very short XLISP program. I
    don't know if you can do 4 lines, but it should be quite short.

Yup.  I've written some code that generates large numbers, tests for
primality and does RSA.  The basic RSA enclode is just (mod-expt m e
n) and decrypt is (mod-expt c d n) where mod-expt is just an optimized
version of (mod (expt x p) n), ala Schneier, page 200 (1st edition).
Even with CLISP (compiles to a byte code which is then interpreted),
I've generated RSA keys in the range that PGP deals with.

			Rick