✨ Update Primes

This issue has been created since 2021-03-01.

Issue

This was request by @benaloh and is an update to the primes. The following are the values that should change.

p

The large prime p should be the following.

Decimal:

1044388881413152506691752710716624382579964249047383780384233483283953907971553643537729993126875883902173634017777416360502926082946377942955704498542097614841825246773580689398386320439747911160897731551074903967243883427132918813748016269754522343505285898816777211761912392772914485521155521641049273446207578961939840619466145806859275053476560973295158703823395710210329314709715239251736552384080845836048778667318931418338422443891025911884723433084701207771901944593286624979917391350564662632723703007964229849154756196890615252286533089643184902706926081744149289517418249153634178342075381874131646013444796894582106870531535803666254579602632453103741452569793905551901541856173251385047414840392753585581909950158046256810542678368121278509960520957624737942914600310646609792665012858397381435755902851312071248102599442308951327039250818892493767423329663783709190716162023529669217300939783171415808233146823000766917789286154006042281423733706462905243774854543127239500245873582012663666430583862778167369547603016344242729592244544608279405999759391099769165589722584216017468464576217318557948461765770700913220460557598574717173408252913596242281190298966500668625620138188265530628036538314433100326660047110143

Hex:

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

FWIW, the prior prime was the 4,278,778th value larger than (2^256 - 1)2^3840 + 2**256(gamma) + (2^256 – 1) with gamma = floor(euler_constant*2^3584) that is one greater than a multiple of q. But it turned out that the 3,793,825th such value also met all of the conditions. Evidently the prior generation code attempted to optimize a bit too much and effectively tested only every second possible value. It therefore missed the new value which was found with an odd number of iterations.

q

The small prime q remains unchanged at 2^256-189.

r

The new value of r (which is (p-1)/q) is as follows.

Decimal:

9019518416950528558373478086511232658951474842525520401496114928154304263969655687927867442562559311457926593510757267649063628681241064260953609180947464800958467390949485096429653122916928704841547265126247408167856620024815508684472819746384115369148322548696439327979752948311712506113890045287907335656308945630141969472484100558565879585476547782717283106837945923693806973017510492730838409381014701258202694245760602718602550739205297257940969992371799325870179746191672464736721424617639973324090288952006260483222894269928179970153634220390287255837625331668555933039199194619824375869291271098935000699785346405055160394688637074599519052655517388596327473273906029869030988064607361165803129718773877185415445291671089029845994683414682274353665003204293107284473196033588697845087556526514092678744031772226855409523354476737660407619436531080189837076164818131039104397776628128325247709678431023369197272126578394856752060591013812807437681624251867074769638052097737959472027002770963255207757153746376691827309573603635608169799503216990026029763868313819255248026666854405409059422844776556067163611304891154793770115766608153679099327786

Hex:

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

As required by the spec … and the thing that makes the search for p challenging, this value r is twice a prime. (r will always be even, so r being twice a prime is the best that we can do.)

g

Finally, the new value of g (which is 2^r mod p) is as follows.

Decimal:

119359756198641231858139651428439585561105914902686985078252796680474637856752833978884422594516170665312423393830118608408063594508087813277769835084746883589963798527237870817233369094387978405585759195339509768803496494994109693743279157584139079471178850751266233150727771094796709619646350222242437970473900636242584673413224137139139346254912172628651028694427789523683070264102332413084663100402635889283790741342401259356660761075766365672754329863241692760862540151023800163269173550320623249398630247531924855997863109776955214403044727497968354022277828136634059011708099779241302941071701051050378539485717425482151777277387633806111112178267035315726401285294598397677116389893642725498831127977915200359151833767358091365292230363248410124916825814514852703770457024102738694375502049388804979035628232209959549199366986471874840784466132903083308458356458177839111623113116525230200791649979270165318729763550486200224695556789081331596212761936863634467236301450039399776963661755684863012396788149479256016157814129329192490798309248914535389650594573156725696657302152874510063002532052622638033113978672254680147128450265983503193865576932419282003012093526302631221491418211528781074474515924597472841036553107847

Hex:

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
More Details About Repo
Owner Name microsoft
Repo Name electionguard-cpp
Full Name microsoft/electionguard-cpp
Language C++
Created Date 2020-05-05
Updated Date 2022-03-31
Star Count 16
Watcher Count 12
Fork Count 18
Issue Count 49

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