Cryptography Reference
In-Depth Information
861278948248755535786849730970552604439202492188238906165904170011537676
301364684925762947826221081654474326701021369172596479894491876959432609
670712659248448276687
n
=
pq
is public:
n
=
646340121426220146014297533773399039208882053394309680642606908550493102
777357817863944028230458269273774359218437960389882391183009818421901763
047728965662412617547346019921835003955007793042135921152767681351365535
844372852395123236761886769523409411632917040726100857751517830821316172
151047982478607716803918058340827477683169176315227971638380003141234015
213715286981934574126958310812212353843734392842382104560615275941849712
736764525520559801471208444488841303619868703237828364738114662819239227
238184943188233259835607113670605755573747578481214665113626049865412769
43834825366579731809108470421496863793133.
Here is the bogus plaintext message that the adversary creates:
m
=
327562836508236509237590237590823750923875098275908237590827359082375908
723095873209875093285790328750932875093248750983275098327509832759082375
098370957309287509328750923858723658972365892365930275094327590342857326
589726598235698236598235689265892365095780936723985689236598236598236598
236598236598256982569823569826539823659826985273209568923658923793286598
2365982365987263986598236589726895698236598236598723658972.
The adversary computes the ciphertext by squaring the plaintext modulo
n
, and submits
this to the decryption machine:
C
=
633117525812174963141726511411569613510692954921413433904834216758854296
633124876624725803389226024659872532640785232933916621224271521661591779
805056806132874825319189837524810853175640040181499810175228697753511769
733199644184786773309701377090720855844334771741032864292654831554262834
830106099159752454122074338825214233151941406426968586422774039868803500
958440877983431882318911204475101540253926424708618519209984525553968321
269537413569633044293116969006410634311794364957784418800457585030758560
064753995190942293115578955198138212298271399040518748965782046565242764
02217687340373577434217196605168494458628.
The decryption machine calculates and returns four roots to the adversary (knowing
p
and
q
you should be able to do this yourself and verify these calculations):
x 1 =
136581210291743377386869067901142217233939214683424267658172999911458881
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