<s>
The	O
Vigenère	B-Algorithm
cipher	I-Algorithm
(	O
)	O
is	O
a	O
method	O
of	O
encrypting	O
alphabetic	O
text	O
by	O
using	O
a	O
series	O
of	O
interwoven	O
Caesar	O
ciphers	O
,	O
based	O
on	O
the	O
letters	O
of	O
a	O
keyword	O
.	O
</s>
<s>
It	O
employs	O
a	O
form	O
of	O
polyalphabetic	B-Algorithm
substitution	I-Algorithm
.	O
</s>
<s>
Many	O
people	O
have	O
tried	O
to	O
implement	O
encryption	O
schemes	O
that	O
are	O
essentially	O
Vigenère	B-Algorithm
ciphers	I-Algorithm
.	O
</s>
<s>
In	O
1863	O
,	O
Friedrich	O
Kasiski	O
was	O
the	O
first	O
to	O
publish	O
a	O
general	O
method	O
of	O
deciphering	O
Vigenère	B-Algorithm
ciphers	I-Algorithm
.	O
</s>
<s>
The	O
very	O
first	O
well-documented	O
description	O
of	O
a	O
polyalphabetic	B-Algorithm
cipher	I-Algorithm
was	O
by	O
Leon	O
Battista	O
Alberti	O
around	O
1467	O
and	O
used	O
a	O
metal	O
cipher	O
disk	O
to	O
switch	O
between	O
cipher	O
alphabets	O
.	O
</s>
<s>
Later	O
,	O
Johannes	O
Trithemius	O
,	O
in	O
his	O
work	O
Polygraphiae	O
(	O
which	O
was	O
completed	O
in	O
manuscript	O
form	O
in	O
1508	O
but	O
first	O
published	O
in	O
1518	O
)	O
,	O
invented	O
the	O
tabula	B-Algorithm
recta	I-Algorithm
,	O
a	O
critical	O
component	O
of	O
the	O
Vigenère	B-Algorithm
cipher	I-Algorithm
.	O
</s>
<s>
In	O
1586	O
Blaise	O
de	O
Vigenère	O
published	O
a	O
type	O
of	O
polyalphabetic	B-Algorithm
cipher	I-Algorithm
called	O
an	O
autokey	B-Algorithm
cipher	I-Algorithm
–	O
because	O
its	O
key	O
is	O
based	O
on	O
the	O
original	O
plaintext	O
–	O
before	O
the	O
court	O
of	O
Henry	O
III	O
of	O
France	O
.	O
</s>
<s>
The	O
cipher	O
now	O
known	O
as	O
the	O
Vigenère	B-Algorithm
cipher	I-Algorithm
,	O
however	O
,	O
is	O
that	O
originally	O
described	O
by	O
Giovan	O
Battista	O
Bellaso	O
in	O
his	O
1553	O
book	O
La	O
cifra	O
del	O
Sig	O
.	O
</s>
<s>
He	O
built	O
upon	O
the	O
tabula	B-Algorithm
recta	I-Algorithm
of	O
Trithemius	O
but	O
added	O
a	O
repeating	O
"	O
countersign	O
"	O
(	O
a	O
key	O
)	O
to	O
switch	O
cipher	O
alphabets	O
every	O
letter	O
.	O
</s>
<s>
In	O
the	O
19th	O
century	O
,	O
the	O
invention	O
of	O
Bellaso	B-Algorithm
's	I-Algorithm
cipher	I-Algorithm
was	O
misattributed	O
to	O
Vigenère	O
.	O
</s>
<s>
The	O
Vigenère	B-Algorithm
cipher	I-Algorithm
gained	O
a	O
reputation	O
for	O
being	O
exceptionally	O
strong	O
.	O
</s>
<s>
Noted	O
author	O
and	O
mathematician	O
Charles	O
Lutwidge	O
Dodgson	O
(	O
Lewis	O
Carroll	O
)	O
called	O
the	O
Vigenère	B-Algorithm
cipher	I-Algorithm
unbreakable	O
in	O
his	O
1868	O
piece	O
"	O
The	B-Algorithm
Alphabet	I-Algorithm
Cipher	I-Algorithm
"	O
in	O
a	O
children	O
's	O
magazine	O
.	O
</s>
<s>
In	O
1917	O
,	O
Scientific	O
American	O
described	O
the	O
Vigenère	B-Algorithm
cipher	I-Algorithm
as	O
"	O
impossible	O
of	O
translation	O
"	O
.	O
</s>
<s>
The	O
Vigenère	B-Algorithm
cipher	I-Algorithm
is	O
simple	O
enough	O
to	O
be	O
a	O
field	O
cipher	O
if	O
it	O
is	O
used	O
in	O
conjunction	O
with	O
cipher	O
disks	O
.	O
</s>
<s>
The	O
Confederate	O
States	O
of	O
America	O
,	O
for	O
example	O
,	O
used	O
a	O
brass	O
cipher	O
disk	O
to	O
implement	O
the	O
Vigenère	B-Algorithm
cipher	I-Algorithm
during	O
the	O
American	O
Civil	O
War	O
.	O
</s>
<s>
A	O
Vigenère	B-Algorithm
cipher	I-Algorithm
with	O
a	O
completely	O
random	O
(	O
and	O
non-reusable	O
)	O
key	O
which	O
is	O
as	O
long	O
as	O
the	O
message	O
becomes	O
a	O
one-time	B-Algorithm
pad	I-Algorithm
,	O
a	O
theoretically	O
unbreakable	O
cipher	O
.	O
</s>
<s>
Gilbert	O
Vernam	O
tried	O
to	O
repair	O
the	O
broken	O
cipher	O
(	O
creating	O
the	O
Vernam	O
–	O
Vigenère	B-Algorithm
cipher	I-Algorithm
in	O
1918	O
)	O
,	O
but	O
the	O
technology	O
he	O
used	O
was	O
so	O
cumbersome	O
as	O
to	O
be	O
impracticable	O
.	O
</s>
<s>
The	O
Vigenère	B-Algorithm
cipher	I-Algorithm
has	O
several	O
Caesar	O
ciphers	O
in	O
sequence	O
with	O
different	O
shift	O
values	O
.	O
</s>
<s>
To	O
encrypt	O
,	O
a	O
table	O
of	O
alphabets	O
can	O
be	O
used	O
,	O
termed	O
a	O
tabula	B-Algorithm
recta	I-Algorithm
,	O
Vigenère	B-Algorithm
square	I-Algorithm
or	O
Vigenère	B-Algorithm
table	I-Algorithm
.	O
</s>
<s>
Therefore	O
,	O
row	O
A	O
and	O
column	O
L	O
of	O
the	O
Vigenère	B-Algorithm
square	I-Algorithm
are	O
used	O
,	O
namely	O
L	O
.	O
Similarly	O
,	O
for	O
the	O
second	O
letter	O
of	O
the	O
plaintext	O
,	O
the	O
second	O
letter	O
of	O
the	O
key	O
is	O
used	O
.	O
</s>
<s>
The	O
idea	O
behind	O
the	O
Vigenère	B-Algorithm
cipher	I-Algorithm
,	O
like	O
all	O
other	O
polyalphabetic	B-Algorithm
ciphers	I-Algorithm
,	O
is	O
to	O
disguise	O
the	O
plaintext	O
letter	O
frequency	O
to	O
interfere	O
with	O
a	O
straightforward	O
application	O
of	O
frequency	O
analysis	O
.	O
</s>
<s>
However	O
,	O
by	O
using	O
the	O
Vigenère	B-Algorithm
cipher	I-Algorithm
,	O
e	O
can	O
be	O
enciphered	O
as	O
different	O
ciphertext	O
letters	O
at	O
different	O
points	O
in	O
the	O
message	O
,	O
which	O
defeats	O
simple	O
frequency	O
analysis	O
.	O
</s>
<s>
The	O
primary	O
weakness	O
of	O
the	O
Vigenère	B-Algorithm
cipher	I-Algorithm
is	O
the	O
repeating	O
nature	O
of	O
its	O
key	O
.	O
</s>
<s>
In	O
1863	O
,	O
Friedrich	O
Kasiski	O
was	O
the	O
first	O
to	O
publish	O
a	O
successful	O
general	O
attack	O
on	O
the	O
Vigenère	B-Algorithm
cipher	I-Algorithm
.	O
</s>
<s>
In	O
1854	O
,	O
Charles	O
Babbage	O
was	O
goaded	O
into	O
breaking	O
the	O
Vigenère	B-Algorithm
cipher	I-Algorithm
when	O
John	O
Hall	O
Brock	O
Thwaites	O
submitted	O
a	O
"	O
new	O
"	O
cipher	O
to	O
the	O
Journal	O
of	O
the	O
Society	O
of	O
the	O
Arts	O
.	O
</s>
<s>
When	O
Babbage	O
showed	O
that	O
Thwaites	O
 '	O
cipher	O
was	O
essentially	O
just	O
another	O
recreation	O
of	O
the	O
Vigenère	B-Algorithm
cipher	I-Algorithm
,	O
Thwaites	O
presented	O
a	O
challenge	O
to	O
Babbage	O
:	O
given	O
an	O
original	O
text	O
(	O
from	O
Shakespeare	O
's	O
The	O
Tempest	O
:	O
Act	O
1	O
,	O
Scene	O
2	O
)	O
and	O
its	O
enciphered	O
version	O
,	O
he	O
was	O
to	O
find	O
the	O
key	O
words	O
that	O
Thwaites	O
had	O
used	O
to	O
encipher	O
the	O
original	O
text	O
.	O
</s>
<s>
The	O
Friedman	O
test	O
(	O
sometimes	O
known	O
as	O
the	O
kappa	O
test	O
)	O
was	O
invented	O
during	O
the	O
1920s	O
by	O
William	O
F	O
.	O
Friedman	O
,	O
who	O
used	O
the	O
index	B-General_Concept
of	I-General_Concept
coincidence	I-General_Concept
,	O
which	O
measures	O
the	O
unevenness	O
of	O
the	O
cipher	O
letter	O
frequencies	O
to	O
break	O
the	O
cipher	O
.	O
</s>
<s>
A	O
better	O
approach	O
for	O
repeating-key	O
ciphers	O
is	O
to	O
copy	O
the	O
ciphertext	O
into	O
rows	O
of	O
a	O
matrix	O
with	O
as	O
many	O
columns	O
as	O
an	O
assumed	O
key	O
length	O
and	O
then	O
to	O
compute	O
the	O
average	O
index	B-General_Concept
of	I-General_Concept
coincidence	I-General_Concept
with	O
each	O
column	O
considered	O
separately	O
.	O
</s>
<s>
When	O
that	O
is	O
done	O
for	O
each	O
possible	O
key	O
length	O
,	O
the	O
highest	O
average	O
index	B-General_Concept
of	I-General_Concept
coincidence	I-General_Concept
then	O
corresponds	O
to	O
the	O
most-likely	O
key	O
length	O
.	O
</s>
<s>
Kerckhoffs	O
 '	O
method	O
is	O
not	O
applicable	O
if	O
the	O
Vigenère	B-Algorithm
table	I-Algorithm
has	O
been	O
scrambled	O
,	O
rather	O
than	O
using	O
normal	O
alphabetic	O
sequences	O
,	O
but	O
Kasiski	O
examination	O
and	O
coincidence	O
tests	O
can	O
still	O
be	O
used	O
to	O
determine	O
key	O
length	O
.	O
</s>
<s>
The	O
Vigenère	B-Algorithm
cipher	I-Algorithm
,	O
with	O
normal	O
alphabets	O
,	O
essentially	O
uses	O
modulo	O
arithmetic	O
,	O
which	O
is	O
commutative	O
.	O
</s>
<s>
The	O
running	B-Algorithm
key	I-Algorithm
variant	O
of	O
the	O
Vigenère	B-Algorithm
cipher	I-Algorithm
was	O
also	O
considered	O
unbreakable	O
at	O
one	O
time	O
.	O
</s>
<s>
If	O
this	O
effective	O
key	O
length	O
is	O
longer	O
than	O
the	O
ciphertext	O
,	O
it	O
achieves	O
the	O
same	O
immunity	O
to	O
the	O
Friedman	O
and	O
Kasiski	O
tests	O
as	O
the	O
running	B-Algorithm
key	I-Algorithm
variant	O
.	O
</s>
<s>
If	O
one	O
uses	O
a	O
key	O
that	O
is	O
truly	O
random	O
,	O
is	O
at	O
least	O
as	O
long	O
as	O
the	O
encrypted	O
message	O
,	O
and	O
is	O
used	O
only	O
once	O
,	O
the	O
Vigenère	B-Algorithm
cipher	I-Algorithm
is	O
theoretically	O
unbreakable	O
.	O
</s>
<s>
However	O
,	O
in	O
that	O
case	O
,	O
the	O
key	O
,	O
not	O
the	O
cipher	O
,	O
provides	O
cryptographic	O
strength	O
,	O
and	O
such	O
systems	O
are	O
properly	O
referred	O
to	O
collectively	O
as	O
one-time	B-Algorithm
pad	I-Algorithm
systems	O
,	O
irrespective	O
of	O
the	O
ciphers	O
employed	O
.	O
</s>
<s>
It	O
is	O
different	O
from	O
the	O
Beaufort	B-Algorithm
cipher	I-Algorithm
,	O
created	O
by	O
Francis	O
Beaufort	O
,	O
which	O
is	O
similar	O
to	O
Vigenère	O
but	O
uses	O
a	O
slightly	O
modified	O
enciphering	O
mechanism	O
and	O
tableau	O
.	O
</s>
<s>
The	O
Beaufort	B-Algorithm
cipher	I-Algorithm
is	O
a	O
reciprocal	O
cipher	O
.	O
</s>
<s>
Despite	O
the	O
Vigenère	B-Algorithm
cipher	I-Algorithm
's	O
apparent	O
strength	O
,	O
it	O
never	O
became	O
widely	O
used	O
throughout	O
Europe	O
.	O
</s>
<s>
The	O
Gronsfeld	O
cipher	O
is	O
a	O
variant	O
created	O
by	O
Count	O
Gronsfeld	O
(	O
Josse	O
Maximilaan	O
van	O
Gronsveld	O
né	O
van	O
Bronckhorst	O
)	O
;	O
it	O
is	O
identical	O
to	O
the	O
Vigenère	B-Algorithm
cipher	I-Algorithm
except	O
that	O
it	O
uses	O
just	O
10	O
different	O
cipher	O
alphabets	O
,	O
corresponding	O
to	O
the	O
digits	O
0	O
to	O
9	O
)	O
.	O
</s>
<s>
Vigenère	O
actually	O
invented	O
a	O
stronger	O
cipher	O
,	O
an	O
autokey	B-Algorithm
cipher	I-Algorithm
.	O
</s>
<s>
The	O
name	O
"	O
Vigenère	B-Algorithm
cipher	I-Algorithm
"	O
became	O
associated	O
with	O
a	O
simpler	O
polyalphabetic	B-Algorithm
cipher	I-Algorithm
instead	O
.	O
</s>
<s>
In	O
fact	O
,	O
the	O
two	O
ciphers	O
were	O
often	O
confused	O
,	O
and	O
both	O
were	O
sometimes	O
called	O
le	B-Algorithm
chiffre	I-Algorithm
indéchiffrable	I-Algorithm
.	O
</s>
<s>
Babbage	O
actually	O
broke	O
the	O
much-stronger	O
autokey	B-Algorithm
cipher	I-Algorithm
,	O
but	O
Kasiski	O
is	O
generally	O
credited	O
with	O
the	O
first	O
published	O
solution	O
to	O
the	O
fixed-key	O
polyalphabetic	B-Algorithm
ciphers	I-Algorithm
.	O
</s>
