Cryptography Reference
In-Depth Information
Alice and Bob have access to an SKC, which we will call
S
. Also, Bob has
a public-private key pair (
e, d
). In order to send a message
m
to Bob, Alice
first generates a symmetric key, called a
session key
or
data encryption key
,
k
to be used only once. (The property of producing a new session key each time
a pair of users wants to communicate is called
key freshness
.) Alice enciphers
m
using
k
and
S
obtaining ciphertext
E
k
(
m
)=
c
. Using Bob's public key
e
,
Alice encrypts
k
to get
E
e
(
k
)=
k
. Both of these encryptions are fast since
S
is e8cient in the first enciphering, and the session key is small in the second
enciphering. Then Alice sends
c
and
k
to Bob, who deciphers
k
with his private
key
d
, via
D
d
(
k
)=
k
. Then Bob easily deduces the symmetric deciphering key
k
−
1
, which he uses to decipher,
D
k
−
1
(
c
)=
D
k
−
1
(
E
k
(
m
)) =
m
.
Hence, the PKC is used only for the sending of the session key, which provides
a digital envelope that is both secure and e8cient, a very nice and elegant
resolution of the above problems.
Diagram 4.1 (Digital Envelope — Hybrid Cryptosystem)
✞
Private Key
d
Bob
D
d
(
k
)=
k
D
k
−
1
(
c
)=
m
✝
✆
✞
Public Key
e
✝
✆
✞
✝
✆
✞
✝
✆
(
E
e
(
k
)
,
E
k
(
m
))
−−−−−−−−−−−−→
=(
k
,
c
)
S
−−−−→
k
Alice
Example 4.1
Suppose that the symmetric-key cryptosystem,
S
, that Alice and
Bob agree to use is a permutation cipher
(
see page 114
)
with parameters
r
=7
,
M
=
C
=
Z
/
26
Z
, and key
k
=
1234567
3476512
.
Alice wants to send
m
=
travels
to Bob.Alice converts
m
to numerical equivalents via Table 1.3 on page 11 to
get
m
= (19
,
17
,
0
,
21
,
4
,
11
,
18)
to which she applies
k
to get
c
=
E
k
(
m
)=(0
,
21
,
18
,
11
,
4
,
19
,
17)
.
She then proceeds to encipher
k
using Bob's public key as follows.
Since
m
has seven letters, then we may encipher the key
k
(
second row
)
as
a
7
-digit, base
10
integer:
10
6
+4
10
5
+7
10
4
+6
10
3
+5
10
2
+1
k
=3
·
·
·
·
·
·
10 + 2 = 3476512
.
(4.1)
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