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From: Mok-Kong Shen on 20 Jan 2010 16:52
Greg Rose wrote:
> In reply to Bob:
>
> In article<hj7an5$pj6$02$1(a)news.t-online.com>,
> Mok-Kong Shen<mok-kong.shen(a)t-online.de> wrote:
>> me13013 wrote:
>>> Mok-Kong Shen wrote:
>>>> Sorry, I am confused. If I don't err, you have not mentioned a wiki page
>>>> before. Which wiki page is it?
>>>
>>> Haha. You even quoted some text from the paragraph where I mentioned
>>> the wiki page. Now you don't think I mentioned a wiki page. I've
>>> been wondering if you've just been pulling my leg. Now, if I don't
>>> err, I am sure.
>>
>> Apology. I posted at a time of very weak concentration yesterday.
>>
>> As far as I can see, the algorithm you detailed in a previous post
>> could also function with composite M. For there exists a certain t
>> such that P^t is identity and hence the inverse of P is always
>> computable.
>
> Yes, M-K was pulling, and continues to pull, our
> collective legs. That's what he does.

This is a typical "unnecessary" waste of bandwidth of the group in my
humble view. Without such the atmosphere of the group would have
been better.

M. K. Shen
From: me13013 on 20 Jan 2010 19:13
On Jan 20, 11:24 am, Mok-Kong Shen <mok-kong.s...(a)t-online.de> wrote:
> As far as I can see, the algorithm you detailed in a previous post
> could also function with composite M. For there exists a certain t
> such that P^t is identity and hence the inverse of P is always
> computable.

The existence of such t is obviously true, but there are some
computational details that are messier with composites. I will leave
those details for you to discover, as you will learn more by hands-on
discovery.

I now bow humbly from this thread (I am finished with it).

Bob H

From: Mok-Kong Shen on 22 Jan 2010 05:00
wizzi fig wrote:

> Yes, you have erred. Everything necessary is computable, given
> invertible P(x) mod M (with M prime)
> - compute the cycles of P(x)
> - find the GCD g of the cycle lengths
> - determine P'(x) = inverse of P by composing P(x) with itself g-1
> times, reducing exponents using the rule x^M=x and reducing
> coefficients modulo M
> - determine H(x) = P(P'(x)+1), using the same reduction rules.

It's very unfortunate that wizzi fig (me13013) has left the thread
and couldn't confirm/refute himself. On re-reading the above, I
found a mistake: 'GCD' should be replaced by 'LCM'.

M. K. Shen


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