[Cryptography] Need a list of Solinas/pseudo Mersene Primes.
Viktor Dukhovni
cryptography at dukhovni.org
Fri Aug 31 13:41:01 EDT 2018
> On Aug 31, 2018, at 12:05 PM, Phillip Hallam-Baker <phill at hallambaker.com> wrote:
>
> The way that I drafted the spec, it requires the number of bits to be a multiple of 8 and the prime to be the largest prime that is smaller than the next power of two. Thus, folk can apply the spec to secrets of any length without re-writing the spec.
>
> I am considering changing this to require the number of bits to be a multiple of 32 and giving the primes for use with up to 512 bits.
For $2^{32k+1}-n$ prime with $n$ minimal, the values are:
• 2^33 - 9
• 2^65 - 49
• 2^97 - 141
• 2^129 - 25
• 2^161 - 159
• 2^193 - 31
• 2^225 - 49
• 2^257 - 93
• 2^289 - 493
• 2^321 - 9
• 2^353 - 139
• 2^385 - 265
• 2^418 - 29
• 2^449 - 241
• 2^481 - 273
• 2^513 - 445
[ via "x=33;x=x+32;x<=513;x*1000 + (1 SHL x) - B(1 SHL x)" plugged into
https://www.alpertron.com.ar/ECM.HTM ]
--
Viktor.
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