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From: Richard Heathfield <rjh@cpax.org.uk>
Newsgroups: sci.crypt
Subject: Re: Seriation
Date: Mon, 3 Feb 2025 10:17:24 +0000
Organization: Fix this later
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On 03/02/2025 09:00, David Entwistle wrote:
> On Sun, 2 Feb 2025 10:06:03 -0000 (UTC), David Entwistle wrote:
> 
>> I did have a bit of trouble with SCOS, not because it was hard to
>> decrypt,
>> but my implementation wasn't... There's a word, but I'm not sure what it
>> is... When you perform an operation on a set, the result of that
>> operation is should be guaranteed to belong to the same original set,
>> but in my case it wasn't. So in this case, when encrypting and
>> decrypting occasionally, due to some odd punctuation mark, or an
>> accented character, the result would lie outside the reasonable bounds
>> of characters. The web, which I often use as a source of plain text, is
>> full of such characters. That was my problem, not a problem with SCOS,
>> but it did cause me some grief.
> 
> "Closure: In mathematics, a subset of a given set is closed under an
> operation of the larger set if performing that operation on members of the
> subset always produces a member of that subset".
> 
> So, should an encryption / decryption operation always be closed? Maybe
> SCOS was closed, but I think it would depend how you defined the full
> character set and that may have to be quite wide.

In a sense, SCOS's character set is defined by these four lines:

#define UPPER "ABCDEFGHIJKLMNOPQRSTUVWXYZ"
#define LOWER "abcdefghijklmnopqrstuvwxyz"
#define DIGIT "0123456789"
#define PUNCT "!\"$%^&*()_-+={}[]#~'@;:/?.>,<\\|"

which isn't particularly wide, but any encryption of any of those 
characters will *always* produce a character drawn from the same 
set. When faced with something *not* from that set, SCOS leaves 
it unchanged. So I think I'm right in saying that by the above 
definition SCOS /is/ closed.

-- 
Richard Heathfield
Email: rjh at cpax dot org dot uk
"Usenet is a strange place" - dmr 29 July 1999
Sig line 4 vacant - apply within