#1.
n = 1739
since E = 385
, by factoring,
1739 = 37 X 47
, D can be determined as 985.
47 ==> 47
48 ==> 48
888 ==> 37
1006 ==> 33
1247 ==> 100
749 ==> 123
#2. If nA ,
Theorem :
Given
nB
and nC
are relatively prime to each other, then by Chinese Remainder
xi mod ni where ni are numbers relatively prime to each other ,
then there is an unique x mod n
where n =  i ni such that x = x i mod n i
David can compute c = m3 mod n = nA X nB X nC
Since m < nA , nB , nC , so
.
m3 < n and m can be computed as c
1/3
.
#3 ( 7.2)
Weakness
Types of attack
remedy
Sender is unauthenticated.
Masquerading, denial of
Service
End-to-end authentication
with digital signatures
Message contents not
Authenticated.
Tampering, masquerading.
End-to-end authentication with
Digital signatures (e.g. using PGP)
Message contents in the clear
Eavesdropping.
End-to-end encryption
Delivery and deletion from
POP/IMAP server is
authenticated only by a login
With password.
Masquerading.
Kerberos or SSL authentication of
clients.
Sender's clock is not guaranteed.
False dating of messages.
Include time certificates from a
trusted service