Re: 'monotonic increasing'

[Elwyn Davies <[e-mail]>]

Hmm!  I don't think I see your problem with any of the usages in the 
RFCs mentioned.  In all cases monotonically is used to express that the 
sequence is non-decreasing which is in line both with the mathematical 
definition and the Merriam-Webster online dictionary #2 sense.  In some 
of the cases the sequence required is actually strictly monotonically 
increasing but the other words make this clear, and since strictly 
monotonic sequences are also monotonic, it is not wrong.  The only one 
where there could be (IMO) a soupçon of doubt is RFC2679 where it isn't 
absolutely clear whether or not T in the (n+1)-th pair needs to be 
strictly greater than T in the nth pair, and I suspect it doesn't  
matter in this case - it certainly wouldn't break interoperability.

Regards,
Elwyn

Tom.Petch wrote:
> Elwyn
>
> To be more concrete, I have some 1800 RFC readily available and find monotonic
> in 54 of them from RFC677 (1975) to RFC4303.
>
> Plucking a few at random, RFC3412 (SNMP) suggests that monotonic increasing
> would avoid reuse while RFC2406 (IPsec) suggests monotonic increasing can be
> used in the context of replay attacks.  (I accept that in the latter, as in many
> cases, understanding the context, the whole document or set of RFC, does imply
> that the sequence should be strictly increasing).  RFC2679 (IPPM) is more
> mathematical in its approach, where I would expect the term to be informed by
> its use in mathematical textbooks, but it appears not to be
>
> Tom Petch
>
> ----- Original Message -----
> From: "Elwyn Davies" <[e-mail]>
> To: "Tom.Petch" <[e-mail]>
> Cc: "ietf" <[e-mail]>
> Sent: Friday, February 17, 2006 8:19 PM
> Subject: 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
>>>
>>>
>>> _______________________________________________
>>> Ietf mailing list
>>> [e-mail]
>>> https://www1.ietf.org/mailman/listinfo/ietf
>>>
>>>       
>
>   

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