Cryptography Reference
In-Depth Information
589726598235698236598235689265892365095780936723985689236598236598236598
236598236598256982569823569826539823659826985273209568923658923793286598
2365982365987263986598236589726895698236598236598723658972.
Note that nowhere did the eavesdropper have to use any private information of either of
the intended recipients! You will be asked to program this attack in Java.
A similar situation to the repeated message problem occurs if the message
P
is small
2
is still less than
when compared to a modulus
n
. For, in this case, it may turn out that
P
n
.
2
, and one can derive the plaintext
Thus, the ciphertext
C
=
P
P
by simply taking the posi-
tive square root of
C
.
E
XAMPLE
.
Suppose we want to send the message
P
=
239018479210648921764876589475621934521754012450100521345271645216354721
645782153478215784521784587216547821547264765686587157161289768792648947
56345234
to someone using Rabin. Their public modulus is
n
=
646340121426220146014297533773399039208882053394309680642606908550493102
777357817863944028230458269273774359218437960389882391183009818421901763
047728965662412617547346019921835003955007793042135921152767681351365535
844372852395123236761886769523409411632917040726100857751517830821316172
151047982478607716803918058340827477683169176315227971638380003141234015
213715286981934574126958310812212353843734392842382104560615275941849712
736764525520559801471208444488841303619868703237828364738114662819239227
238184943188233259835607113670605755573747578481214665113626049865412769
43834825366579731809108470421496863793133.
By applying the enciphering transformation, we obtain the ciphertext
2
=
571298334041714108108345643190462228642901026856795346055535425667278441
850934824793736487150968102492632521428140126182308141623561315311127797
093705545511982088097169004995193640628781309718698309201990365156015487
814518004431530143866988010770332236034011312080519927953939004687628572
888504994514756.
C
=
P
The ciphertext is still smaller than the modulus; thus, all one needs to do is take the
square root of the ciphertext message to derive
P
:
P
=
239018479210648921764876589475621934521754012450100521345271645216354721
=
√
C
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