From: SS (firstname.lastname@example.org)
Date: Mon Apr 12 2010 - 12:57:25 CDT
I think all numbering system based their arithmetic without the use of place
holder 0, prior to the introduction of placeholder 0.
yes, all modern arithmetic and mathematics use positional 0.
there is a need to allow ancient numbering systems to operate on limited and
ie, do not allow these methods to replace contemporary mathematics.
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
Note: I'm not commenting on any security issue that the ancient system might
cause, if mixed with contemporary system.
----- Original Message -----
From: "karl williamson" <email@example.com>
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.
> Thanks for your response.
> Can anyone tell me: Are there other scripts where Gc=Nd characters can
> behave with other than the positional meanings of the digits 0-9? The
> only technical note that has "number" in the title is the one that
> Shriramana mentioned, so I'm assuming not.
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