RSA decryption is very slow

Question

I've implemented RSA in php, my private key is 640 digits long and I'm using the Chinese Reminder Theorem for faster results but it still take me more than three second for a single decryption for a 50 digit long(AES key)which I think is very very slow, considering it takes no more than milliseconds on most an https sites.

$dec = bcmod(  bcadd(   bcmul(bcmul($q,$cp),bcpowmod(bcmod($keyrsa,$p),$dp,$p)),  bcmul(bcmul($p,$cq),bcpowmod(bcmod($keyrsa,$p),$dp,$p))   )     ,   $n );

This is how I've implemented it if you're interested. Almost all of the variables are pre calculated.

In python it is very fast using same algorithm but still for some reason php is slower.

1. Is there a better implementation?

2. How do most HTTPS websites do it so much faster with so much traffic?

Answer 1

I think the problem is type conversion, everytime a bc function is called it needs to convert the string to internal representation then convert it back into a decimal string, which then gets passed to the next function

try using GMP integer math instead, man page here

<?php
$keyrsa = gmp_init("9832475748957245");
$p = gmp_init("8354079484936541914927899085066667840301483360503839666157604136172921017528434146469774903867827180301976075982694562560689572638988092925269813627463374625291252908846201647344151611753461104963119608859115640201075591792459197160119945258486367627500121879818096099203595248003716117545512480479865709921453");
$q = gmp_init("938412744368825581535702355433426163883459511114687878154024994897102350822189947166755477679382811899594449736937158715413660429942933801527664946168421987845759422078910224872347655774496994538836516350730448938820126252589141481797770481863822310785941175596494671215977389040699889153301120914503446716507973489992786954188813");
//$cq = "90158151585243433649068545530051893622966883012518795089220114585310968302320502026270948815940384941612296625138324093461024924511161402917200931834290201708637643850750136849813026570271943168694883902320057242885955055614162225328861522256625184296048689139146938390662090382632227663474386093495477914592794162872990148364116";
//$cp = "7551459988262214427840190779497680155475105762407164553046829825327340315927179742834418691277481624391481553210225801715295088793857458100116513396506530756291114733889990865992240204940649387943199598796499358274552099683283819575613245477264444414822005200002309824389674861969207905172310540069768226872734";
$dp = gmp_init("1965665761161539274100682137662745374188584320118550509684142149687746121771396269757594095027724042423994370819457544131926958267997198335357603206461970500068530096199106269963329791000814377638381084437438974164958962774696281684734104766702674735882381618780728493930257705412639086481297054230556637628577");
//$dq = "883211994700071135563013981584401095419726598696176826497905877550213977244414067921652214286477940611383011517117325849801092169358055342614272890511455988560714750191915505762209558375997171330669662447746304883595412943613309629927313394695362174857356400561406749379743424979482248614871643213650302792007504461169681839236529");
$qtcp = gmp_init("7086386291576524054360302742239998876673708944686465411626570038380444601875306630964988910095131487662281790536626963003506657704070876201964033331286024035984707744160238401059534677753482122942131531324658709164939274183600052634838272332743659199253932999987961039598035528397374750903876542815898982226118836076739179152436733287292195730452100700462917916533108208521409272086529455286245592495898895482186435700595327952372741822199742491182942283075691359064307215568687412510144120677674012937164826009435459181454662134489129797327892892707673596353503035243628926739960488503739316122718017371542430284689864394081681732757524742");
//$d = "9684180457578041703423518212984665367413021472235946617919642829863937153436059290504589391395592577209702599096169971796160405050131992497221547725184873244919981572828194571494694548428547986158684865534112722970807920768563560619443671077664354596805006314087514740257760893103656422610790000570529248962650590971772121591956305661910290201820155312347599369833629985907639681332639927293587022614471157370529051414542594064576484579816117675667970018652822901408587669420741843654459983059048798380989538136593189533517910165268761423288024908153885735118716648190934832866700250304833422760360615089471368245425769057619094702167123265";
$n = gmp_init("7839574656134605188485705220035205297429588810857671071649234671794615790876809901837048554939289229169759246887375691454034613612011612973941252920387754531601889844670443224543324158251681703080840129241900775738273078717408596691930590872394953721223100349499416694494377865845817104018258571890428439636432369199417038685736648639886105668941162211691589720601790029355870681555006383931825756229459276736474343941175285895314774582071354222952445036285378330268675333052497389891203339480294275218891997254728399246701139093936159885498019009817278067080240490608754607645219870614833288791258716931448852885321580818328787411561305289");
$ptcq = gmp_init("753188364558081134125402477795206420755879866171205660022664633414171189001503270872059644844157741507477456350748728450527955907940736771977219589101730495617182100510204823483789480498199580138708597917242066573333804533808544057092318539651294521969167349511455654896342337448442353114382029074529457410313533122677859533299915352593909938489061511228671804068681820834461409468476928645580163733560381254287908240579957942942032759871611731769502753209686971204368117483809977381059218802620262281727171245292940065246476959447030088170126117109604470726737455365125680905259382111093972668540699559906422600631716424247105678803780548");

$gmpPowm = gmp_powm(gmp_mod($keyrsa, $p), $dp, $p);
$gmpResult = gmp_mod(gmp_add(gmp_mul($qtcp, $gmpPowm), gmp_mul($ptcq, $gmpPowm)), $n);

$dec = gmp_strval($gmpResult);

echo $dec . "\n";