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无赋权的LEW嵌入的图
TheLEWEmbedding:AnOverviewanditsApplications
TheLEWembeddingisanimportanttechniqueincryptographythatisusedtogenerateaone-wayfunctionfromavarietyofinputdata.ThisapproachwasfirstintroducedbyLewko,WatersandWongin2010,andhassincebecomeapopularmethodfortransformingdatainareassuchassmartgridinfrastructure,cloudcomputing,andblockchaintechnology.
OverviewoftheLEWEmbedding
TheLEWembeddingisaconstructionthatmapsinputdataintoanellipticcurve,usingaparameterizedcurveequationoftheformE(a,b),whereaandbareintegersthatcanbechosenatrandom.ThiscurveisusuallyderivedfromafixedcurveusingtheWeierstrassequation.Then,theinputdataismappedtoapointonthecurveusingthemappingfunctionthattranslatesbytestringsinaparticularway.
Indetail,letE(a,b)beanellipticcurveoverafinitefieldF(q)oforderq,letPbeapointonE(a,b),andlethfbeahashfunctionthatmapsarbitrarylengthstringstoelementsofF(q).TheLEWembeddingproceedsasfollows:
1.Chooserandomintegersaandb,andconstructtheellipticcurveE(a,b).
2.ChooseapointPonE(a,b)andahashfunctionhf.
3.TakeanarbitrarylengthinputI.
4.Computeahashh=hf(I).
5.Computeanumbern=log2(q),wherenisthebitlengthofq.
6.Converthtoabinarystringoflengthn.
7.Interpretthebinarystringasanintegerh'intherange[0,q-1].
8.ComputeapointQonE(a,b)byQ=h'P.
9.ReturnthecoordinatesofQinaffineform,as(x,y).
ApplicationsoftheLEWEmbedding
TheLEWembeddinghasseveralapplicationsincryptographythatarecenteredarounditsabilitytoprovideaone-wayfunctionmapping.Thismeansthemappingfromtheoriginaldatatotheellipticcurveiseasytocompute,buttheinversemappingiscomputationallyinfeasible.
OneofthekeyapplicationsoftheLEWembeddingisinsmartgridinfrastructure,whereitcanbeusedtosecurethedatabeingsentoverthenetwork.ByusingtheLEWembedding,datacanbetransformedintoaformthatishardertoreverseengineer,providinganadditionallevelofsecuritytothesystem.
AnotherimportantareawheretheLEWembeddingisusedisincloudcomputing.Here,itcanbeusedtotransformuserdataintoaformthatmakesitdifficultforcloudproviderstoaccesstheinformation,whilestillallowingau