Re: Can someone please check these figures

From: Michael Amling (nospam_at_nospam.com)
Date: 07/29/04 

Date: Thu, 29 Jul 2004 17:34:48 GMT

Sebastian Gottschalk wrote:

> Michael Amling schrieb:
>
>
>> What are you using to do these calculations?
>> 88**7 mod 67591 is 59156, not 36487.
>>
>>
>>>Can you find d?
>>
>> Try 4791.
>
>
> What are you doing? e=7, 7*4791 mod 67072 != 1

   I agree. Nevertheless, d=4791 works for all messages.
>
>
>>59156**4791 mod 67591 is 88.
>
>
> Sure? AFAIK there's only one inverse for e in Zn when gcd(e,n)=1.
>
> So here's what I got:
>
> p=257
> q=263
> n=67591
> phi.n=67072
> e=7
> -> d=38327
>
> c=88
> -> C=59156
>
> C^d mod n =
> 59156^38327 mod 67591
> 59156*43493^19163 mod 67591
> 20493*39323^9581 mod 67591
> 26337*21861^2395 mod 67591
> 13019*34951^1197 mod 67591
> 4457*(-1027)^299 mod 67591
> 18849*40864^149 mod 67591
> 46091*26729^37 mod 67591
> 52773*53714^9 mod 67591
> 17564*34696 mod 67591
> 88
>
> And I did do this with calc.exe and notepad.exe to verify the results from
> MAPLE.

   That's fine. I agree that 38327 works just as well as 4791. What do
you get for 59156**4791 mod 67591?

--Mike Amling

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