Re: MODP group modulus derivation [was: Re: I can has SHA-1 hashes for RFC 2409/3526 MODP groups?]

On 03/12/2014 05:24 PM, Niels Möller wrote:
> [email protected] (Niels Möller) writes:
> 
>> 3. The 8192-bit prime definitely seems a bit expensive to generate.
> 
> I've now ran the updated version of the program on a more high-end pc.
> For 8192 bits, it completed in about 52 minutes. Output:
> 
> p = 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!
>  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!
>  8e4475677e9aa9e3050e2765694dfc81f56e880b96e7160c980dd98edd3dff!
>  fffffffffffffff
> k = 4743157
> elapsed time 3133.28s
> 
> Which after a cursory look appears to agree with
> https://www.rfc-editor.org/rfc/rfc3526.txt (I guess the 47473157 vs
> 4743158 is an off-by-one error in my code. Does the spec's brackets in
> in "[2^8062 pi]" denote floor or round-to-nearest?

i was using floor for my calculations, not round-to-nearest.

	--dkg

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