# Re: Do non-positional number systems present security issues?

From: SS (sisrivas@blueyonder.co.uk)
Date: Mon Apr 12 2010 - 12:57:25 CDT

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1/
I think all numbering system based their arithmetic without the use of place
holder 0, prior to the introduction of placeholder 0.

2/
yes, all modern arithmetic and mathematics use positional 0.

3/
there is a need to allow ancient numbering systems to operate on limited and
special situations.
ie, do not allow these methods to replace contemporary mathematics.

4/
There is also a rumoured view that these archaic methods without place
holder 0 may reach areas of mathematics where the contemporary numbering
system might not reach. this is a rumour and I'm not an expert on this
theory.

Note: I'm not commenting on any security issue that the ancient system might
cause, if mixed with contemporary system.

Sinnathurai

----- Original Message -----
From: "karl williamson" <public@khwilliamson.com>
Cc: <unicode@unicode.org>
Sent: 12 April 2010 18:09
Subject: Re: Do non-positional number systems present security issues?

> Shriramana Sharma wrote:
>> On 2010-Apr-05 01:58, karl williamson wrote:
>>> Tamil's digits are not positional according to Richard Gillam. They
>>> have General category of Nd. Could this be used to cause a naive program
>>> to calculate an incorrect value of an input number, such that mention of
>>> this possibility would be warranted in TR36?
>>
>> Have you read: http://www.unicode.org/notes/tn21/ ? It is hinted (though
>> not perhaps very explicitly said) that today the positional system is
>> indeed used. Therefore I (a native Tamil speaker and writer) do not think
>> that today we would expect applications to *commonly* support the old
>> numeral system.
>>
>> In any case, non-positional evaluation of numbers should only be
>> performed by an application if it encounters the characters ௰ ௱ and ௲. A
>> number which does not use these characters can safely be processed as
>> positional. A number which uses them, on the other hand, will have to be
>> checked for being properly formatted, i.e. properly composed, since in
>> the non-positional system digits like ௧ ௨ etc would never be seen
>> adjacent to each other without being punctuated by one of the three
>> characters ௰ ௱ and ௲. Therefore any number containing one of ௰ ௱ and ௲
>> but also containing any two normal digits ௧ ௨ etc adjacent to each other
>> is badly formatted and hence has no (defined) value.
>>
>> Therefore there is a clear distinction between the two systems, and while
>> the same numerical value can be represented by two different strings of
>> characters, one for each system, the same string cannot represent two
>> different numbers. These systems are self-exclusive. I mean to say that
>> they both naturally exclude the simultaneous use of the other system in
>> the same number. Therefore I think that there is little scope for
>> security problems here.
>>
>