[Cryptography] Need a list of Solinas/pseudo Mersene Primes.

[Viktor Dukhovni]

> 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.