specificnumber.STEP2:Clusteringofthenodesbyfuzzyc-meanslogicThenodeswiththeirrespectivedatapointsareclusteredbythefuzzyc-meanslogicaccordingtothemembershipvaluesandfuzzinesscoefficientsassignedtotheparticularnode.Bymeansofclusteringtheenergyconsumptionisreducedtoanefficientamount.STEP3:KeysharesusingCRTHeredifferentco-primenumbersaretakensoastofindtheuniquesolutionusingthemodulararithmeticusedinChineseRemaindertheorem.TheequationsobtainedbyCRTareintheform
x=n1modm1
x=n2modm2
:
x=nimodmi
Herexistheuniquesolution,(n1,n2……ni)aretheremaindersobtainedbydividingxbyco-primedivisors(m1,m2….mi).Forexample,herewetakethreeequationsandgettheuniquesolutionas29
29=4mod5………………..(4)
29=1mod7………………..(5)
29=7mod11………………(6)
Wefurtherconstructanotherlevelorratheralowerlevelofuniqueidentitieshavingtheirsolutionsas5,7,11respectivelyFromequation(4)wefurtherdivide5bytwoco-primenumbers2and3andobtaintheequations:
5=1mod2…………………(7)
5=2mod3…………………(8)
Fromequation(5)wefurtherdivide7bytwoco-primenumbers3and5andobtaintheequations:
7=2mod5…………………(9)
5=1mod3…………………(10)
Fromequation(6)wefurtherdivide11bytwoco-primenumbers5and7andobtaintheequations:
11=4mod7…………………(11)
11=1mod5…………………(12)
Eachoftheequationscanbedividedfurther,thoughweareconsideringonlytwolevelshereTheseequationsrepresentpointsintheform(x,y)wherex-coordinateistheremainderandycoordinateisthedivisor
bywhichtheuniquesolutionwasdivided.Thustheequation
29=4mod5representsapoint(4,5).Eachofthepointisauniqueidentityorakeyshareofthenodesclusteredtogether
inoneclusterandtheuniquesolutionofthesesharesgiven
byCRTistheidentityoftheclusterhead.