Cryptography Reference
In-Depth Information
to reduce modulo
26
, namely, throw away all multiples of
26
until we are left
with a nonnegative numerical value less than
26
.
)
E
e
(
m
1
) = (12
,
4)
25
34
= (10
,
24) =
c
1
,
E
e
(
m
2
) = (18
,
18)
25
34
= (12
,
6) =
c
2
,
E
e
(
m
3
)=(0
,
6)
25
= (18
,
24) =
c
3
,
E
e
(
m
4
)=(4
,
1)
25
34
34
= (11
,
24) =
c
4
,
E
e
(
m
5
) = (24
,
12)
25
=(6
,
12) =
c
5
,
E
e
(
m
6
)=(0
,
19)
25
34
34
=(5
,
24) =
c
6
,
E
e
(
m
7
) = (17
,
8)
25
34
=(6
,
13) =
c
7
,
and
E
e
(
m
8
) = (23
,
25)
25
34
= (17
,
7) =
c
8
.
Now we use Table 1.3 to get the ciphertext letter equivalents and send
KYMGSYLYGMFYGNRH
.
as the cryptogram. Now we show how decryption works. Once the cryptogram
is received, we must calculate the inverse of
e
, which is
e
−
1
=
d
=
18 23
19 22
.
To see why this is the case, see Example A.12 on page 493 in Appendix A, and
note that the multiplicative inverse of
−
det(
e
)=
7
modulo
26
is given by
7)
−
1
−
≡
11(mod 26)
,
fromExampleA.5onpage478inAppendixA.Nowapplythedecipheringtrans-
formation to the numerical equivalents of the ciphertext as follows:
D
d
(
c
1
)=
D
e
−
1
(10
,
24) = (10
,
24)
18 23
19 22
(
= (12
,
4) =
m
1
,
D
d
(
c
2
)=
D
e
−
1
(12
,
6) = (12
,
6)
18 23
19 22
= (18
,
18) =
m
2
,
and so on until we achieve the original plaintext numerical equivalents. The
letter equivalents now give us back the original plaintext message via Table 1.3.
Search WWH ::
Custom Search