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CHAPTER 10
SymmetricKey Cryptography
(Solution to OddNumbered Problems)
Review Questions
1.
Symmetrickey cryptography is based on sharing secrecy; asymmetrickey cryp
tography is based on personal secrecy.
3.
In cryptography, a trapdoor is a secret with which Bob can use a feasible algorithm
to decrypt the ciphertext. If Eve does not know the trapdoor, she needs to use an
algorithm which is normally infeasible.
5.
RSA uses two exponents,
e
and
d
, where
e
is public and
d
is private. Alice calcu
lates C = P
e
mod
n
to create ciphertext C from plaintext P; Bob uses P = C
d
mod
n
to retrieve the plaintext sent by Alice.
a.
The oneway function is the C
=
P
e
mod
n.
Given P and
e
, it is easy to calculate
C; given C and
e
, it difficult to calculate P if
n
is very large.
b.
The trapdoor in this system is the value of
d
, which enables Bob to use P
=
C
d
mod
n.
c.
The public key is the tuple (
e
,
n
). The private key is
d.
d.
The security of RSA mainly depend on the factorization of
n
. If
n
is very large,
and the value of
e
and
d
are chosen properly, the system is secure.
7.
ElGamal is based on discrete logarithm problem. The plaintext is masked with
e
1
rd
to create the ciphertext. Part of the mask is created by Bob and become public; the
other part is created by Alice.
a.
The oneway function is C = mask (P). Given P and the mask, it is easy to cal
culate the C; given C is difficult to unmask P.
b.
The trapdoor is the value of
d
that enables Bob to unmask C.
c.
The public key is (
e
1
,
e
2
and
n
). The private key is
d
.
d.
The security of ElGamal depends on two points;
p
should be very large and
Alice needs to select a new
r
for each encryption.
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9.
An elliptic curve is an equation in two variables similar to the equations used to
calculate the length of a curve in the circumference of an ellipse. Elliptic curves
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 Spring '12
 YoungheLiu
 Cryptography, a. Alice

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