Re: 'monotonic increasing'

Hi.

Tom.Petch wrote:
> The phrase 'monotonic increasing' seems to be a Humpty-Dumpty one, used with a
> different sense within RFC to that which I see defined elsewhere; and this
> could lead to a reduction in security.
>
> Elsewhere - dictionaries, encyclopaedia, text books -  I see it
> defined so that when applied to a sequence of numbers, then each number is not
> less than its predecessor, so that
> 1 1 1 1 1 1 1 1 1 1
> 1 1 2 3 5 8 13
> 1 2.71828 3.14159 4.18 42
> are all monotonic increasing sequences whereas
> 1 2 3 4 5 6 7 9 8 10
> is not.
>   
On the definition of monotonic increasing: I just checked my memory with 
my copy of Apostol (Mathematical Analysis, vintage 1968 or so) and 
monotonic increasing implies element (n+1) greater than or equal to 
element n for all n.  'Strictly monotonic increasing' implies greater 
than.  On line 
http://www-history.mcs.st-and.ac.uk/~john/analysis/Lectures/L8.html 
confirms this.
> Within RFC, mostly those related to security or network management, the context
> of its use implies, in addition, one or more of
> a) each number in the sequence is different (as in number used once)
> b) each number is an integer
> c) each number is one greater than its predecessor (as in message sequencing) .
>
> Most likely, an implementation that conforms to the rest of the world definition
> would interwork with one that conforms to the RFC one, but with some loss of
> security, since numbers that are intended to be used only once could be reused.
>
> Q1) Can anyone point me to an authoritative source that endorses the RFC usage?
>
> Q2) Even so, since the  rest of the world usage seems to be so widely defined,
> should we change our terminology, eg specifying seqences to be strictly
> increasing when that is what is needed?
>
>   
I just did a full text search of all the RFCs using the zvon repository 
which covers up to RFC3999.  the fragment 'monotonic' (including 
'monotonically') appears in RFCs 1323, 1379, 1644, 1889, 2326, 2681, 
3571 and 3550.  All these cases (either about timestamps or TCP sequence 
numbers)  appear to use monotonically increasing in line with the 
mathematical definition although it is possible that a couple of them 
(e.g., RFC3571, s4) ought to use strictly monotonic, although the usage 
is clear from the additional words.

In many cases the phraseology is explicitly used because the sequence 
(of tiimestamps used, for example)  does not have every possible integer 
represented.

Do you have a concrete example of your problem?

Regards,
Elwyn
>  Tom Petch
>
>
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