Transcript CRYPTOGRAPHY - Brown University

CRYPTOGRAPHY
Lecture 4
Secure transmission
Steganography
cryptography
Transposition
Monoalphabetic
Substitution
Mono-alphabetic
Substitution Cipher
• Allow any permutation of the alphabet
• Each letter is replaced by a different letter
or symbol
• Roughly 288 possibilities: checking 1 billion
per second, would take 12 billion years
• Too many possibilities to break by brute
force! This is a major strength of the
substitution cipher.
Mono-alphabetic
Substitution Cipher
• The major weakness: frequency analysis can
help break this kind of cipher.
• But unlimited substitution ciphers require
exchange of a lot of information – the entire
alphabet!
• A good key would be something you can look
up in a book.
Frequency
Analysis
Problem # 4a: Monoalphabetic
Substitution cipher
SK BKGKC FBTKCHZWBT W ZXUBA HM SKOO,
WBT EWQK UZ MFC MSB, WH SXKB SK XWGK
TUHJMGKCKT UZ DMC MFCHKOGKH
Problem # 4b: Mono-alphabetic
Substitution cipher
CGXTOUNZL NQ UDOU HDNTD BCJONLQ
HDCL ZLC DOQ WZBMZUUCL CACBEUDNLM
DC KCOBLCG NL QTDZZK.
Problem # 4c: Mono-alphabetic
Substitution cipher
UWZEZ VTPUW ZBEIK WVRWT UPUZT UWPUV YZFZE PAIQB
SISVT RBFZE TZJPR UNIKW PUUWZ GAVFZ ETZVT YBEPA
SKWIV UVTWZ EZVUK VNNVA TUPAU NISVT PCCZP EPASQ
ZEZCN PRZSQ ITBOZ UWVAX ZFZAO BEZQV HPEEZ PASVA
ZJCNV RPQNZ UWZEZ VTPAB UWZEU WZBEI KWVRW TUPUZ
TUWPU UWVTW PTPNE ZPSIW PCCZA ZS
What can we do to improve the
substitution cipher?
In 1460 Battista Alberti wrote an essay on what he
believed to be a new form of cipher: use two or more
cipher alphabets alternately to encrypt a message.
ABCDEFGHIJKLMNOPQRSTUVWXYZ
GHIJKLMNOPQRSTUVWXYZABCDEF
RSTUVWXYZABCDEFGHIJKLMNOPQ
Let’s encrypt the statement
IT IS WAY TOO EARLY IN THE DAY TO BE DOING THIS
OK OJ CRE KUF KRXCE ZT KNV JRE KU SK UUZTX ZYOJ
12 34 567 890 12345 67 890 123 45 67 89012 3456
plain text
cipher1
cipher2
Ciphers
• Monoalphabetic ciphers: each letter in the
plaintext is encoded by only one letter from
the cipher alphabet, and each letter in the
cipher alphabet represents only one letter in
the plaintext.
• Polyalphabetic ciphers: each letter in the
plaintext can be encoded by any letter in the
cipher alphabet, and each letter in the cipher
alphabet may represent different letters from
the plaintext each time it appears.
What can we do to improve the
substitution cipher?
Alberti was followed by Johannes Trithemius (born
1462) and Giovanni Porta (born 1535) who developed
his ideas. Finally, Vigenere put all these ideas
together. Let’s take a whole table of Caesar shift
alphabets. The first row will have a Caesar shift of 1,
the second of 2, etc. Each letter in the plaintext
message can be enciphered by a different row.
Vigenere
cipher:
Start
with a
table of
Caesar
shift
alphabets.
A
B
C
D
E
F
G
H
I
J
K
L
M
N
O
P
Q
R
S
T
U
V
W
X
Y
Z
B
C
D
E
F
G
H
I
J
K
L
M
N
O
P
Q
R
S
T
U
V
W
X
Y
Z
A
C
D
E
F
G
H
I
J
K
L
M
N
O
P
Q
R
S
T
U
V
W
X
Y
Z
A
B
D
E
F
G
H
I
J
K
L
M
N
O
P
Q
R
S
T
U
V
W
X
Y
Z
A
B
C
E
F
G
H
I
J
K
L
M
N
O
P
Q
R
S
T
U
V
W
X
Y
Z
A
B
C
D
F
G
H
I
J
K
L
M
N
O
P
Q
R
S
T
U
V
W
X
Y
Z
A
B
C
D
E
G
H
I
J
K
L
M
N
O
P
Q
R
S
T
U
V
W
X
Y
Z
A
B
C
D
E
F
H
I
J
K
L
M
N
O
P
Q
R
S
T
U
V
W
X
Y
Z
A
B
C
D
E
F
G
I
J
K
L
M
N
O
P
Q
R
S
T
U
V
W
X
Y
Z
A
B
C
D
E
F
G
H
J
K
L
M
N
O
P
Q
R
S
T
U
V
W
X
Y
Z
A
B
C
D
E
F
G
H
I
K
L
M
N
O
P
Q
R
S
T
U
V
W
X
Y
Z
A
B
C
D
E
F
G
H
I
J
L
M
N
O
P
Q
R
S
T
U
V
W
X
Y
Z
A
B
C
D
E
F
G
H
I
J
K
M
N
O
P
Q
R
S
T
U
V
W
X
Y
Z
A
B
C
D
E
F
G
H
I
J
K
L
N
O
P
Q
R
S
T
U
V
W
X
Y
Z
A
B
C
D
E
F
G
H
I
J
K
L
M
O
P
Q
R
S
T
U
V
W
X
Y
Z
A
B
C
D
E
F
G
H
I
J
K
L
M
N
P
Q
R
S
T
U
V
W
X
Y
Z
A
B
C
D
E
F
G
H
I
J
K
L
M
N
O
Q
R
S
T
U
V
W
X
Y
Z
A
B
C
D
E
F
G
H
I
J
K
L
M
N
O
P
R
S
T
U
V
W
X
Y
Z
A
B
C
D
E
F
G
H
I
J
K
L
M
N
O
P
Q
S
T
U
V
W
X
Y
Z
A
B
C
D
E
F
G
H
I
J
K
L
M
N
O
P
Q
R
T
U
V
W
X
Y
Z
A
B
C
D
E
F
G
H
I
J
K
L
M
N
O
P
Q
R
S
U
V
W
X
Y
Z
A
B
C
D
E
F
G
H
I
J
K
L
M
N
O
P
Q
R
S
T
V
W
X
Y
Z
A
B
C
D
E
F
G
H
I
J
K
L
M
N
O
P
Q
R
S
T
U
W
X
Y
Z
A
B
C
D
E
F
G
H
I
J
K
L
M
N
O
P
Q
R
S
T
U
V
X
Y
Z
A
B
C
D
E
F
G
H
I
J
K
L
M
N
O
P
Q
R
S
T
U
V
W
Y
Z
A
B
C
D
E
F
G
H
I
J
K
L
M
N
O
P
Q
R
S
T
U
V
W
X
Z
A
B
C
D
E
F
G
H
I
J
K
L
M
N
O
P
Q
R
S
T
U
V
W
X
Y
A
B
C
D
E
F
G
H
I
J
K
L
M
N
O
P
Q
R
S
T
U
V
W
X
Y
Z
B
C
D
E
F
G
H
I
J
K
L
M
N
O
P
Q
R
S
T
U
V
W
X
Y
Z
A
C
D
E
F
G
H
I
J
K
L
M
N
O
P
Q
R
S
T
U
V
W
X
Y
Z
A
B
D
E
F
G
H
I
J
K
L
M
N
O
P
Q
R
S
T
U
V
W
X
Y
Z
A
B
C
E
F
G
H
I
J
K
L
M
N
O
P
Q
R
S
T
U
V
W
X
Y
Z
A
B
C
D
F
G
H
I
J
K
L
M
N
O
P
Q
R
S
T
U
V
W
X
Y
Z
A
B
C
D
E
G
H
I
J
K
L
M
N
O
P
Q
R
S
T
U
V
W
X
Y
Z
A
B
C
D
E
F
H
I
J
K
L
M
N
O
P
Q
R
S
T
U
V
W
X
Y
Z
A
B
C
D
E
F
G
I
J
K
L
M
N
O
P
Q
R
S
T
U
V
W
X
Y
Z
A
B
C
D
E
F
G
H
J
K
L
M
N
O
P
Q
R
S
T
U
V
W
X
Y
Z
A
B
C
D
E
F
G
H
I
K
L
M
N
O
P
Q
R
S
T
U
V
W
X
Y
Z
A
B
C
D
E
F
G
H
I
J
L
M
N
O
P
Q
R
S
T
U
V
W
X
Y
Z
A
B
C
D
E
F
G
H
I
J
K
M
N
O
P
Q
R
S
T
U
V
W
X
Y
Z
A
B
C
D
E
F
G
H
I
J
K
L
N
O
P
Q
R
S
T
U
V
W
X
Y
Z
A
B
C
D
E
F
G
H
I
J
K
L
M
O
P
Q
R
S
T
U
V
W
X
Y
Z
A
B
C
D
E
F
G
H
I
J
K
L
M
N
P
Q
R
S
T
U
V
W
X
Y
Z
A
B
C
D
E
F
G
H
I
J
K
L
M
N
O
Q
R
S
T
U
V
W
X
Y
Z
A
B
C
D
E
F
G
H
I
J
K
L
M
N
O
P
R
S
T
U
V
W
X
Y
Z
A
B
C
D
E
F
G
H
I
J
K
L
M
N
O
P
Q
S
T
U
V
W
X
Y
Z
A
B
C
D
E
F
G
H
I
J
K
L
M
N
O
P
Q
R
T
U
V
W
X
Y
Z
A
B
C
D
E
F
G
H
I
J
K
L
M
N
O
P
Q
R
S
U
V
W
X
Y
Z
A
B
C
D
E
F
G
H
I
J
K
L
M
N
O
P
Q
R
S
T
V
W
X
Y
Z
A
B
C
D
E
F
G
H
I
J
K
L
M
N
O
P
Q
R
S
T
U
W
X
Y
Z
A
B
C
D
E
F
G
H
I
J
K
L
M
N
O
P
Q
R
S
T
U
V
X
Y
Z
A
B
C
D
E
F
G
H
I
J
K
L
M
N
O
P
Q
R
S
T
U
V
W
Y
Z
A
B
C
D
E
F
G
H
I
J
K
L
M
N
O
P
Q
R
S
T
U
V
W
X
Z
A
B
C
D
E
F
G
H
I
J
K
L
M
N
O
P
Q
R
S
T
U
V
W
X
Y
SAVEMEPLEASE
CRYPTOGRAMCR
URTTFSVCEMUV
plain text
keyword
enciphered
The first letter, S is encrypted using
the row beginning with C
The second letter, A is encryted
using the row beginning with R
The third letter, V is encrypted using
the row beginning with Y
The fourth letter, E, is encrypted
using the row beginning with P.
And so on . . .
You can use http://www.simonsingh.net/The_Black_Chamber/v_square.html
Vigenere cipher
• The Vigenere cipher is a polyalphabetic
cipher.
• Frequency analysis does not apply.
• Enormous number of possible keys
• It was then neglected for 2 centuries –
it is hard to break but also hard to
encrypt.
Vigenere cipher:
the unbreakable code
• At first glance the Vigenère Cipher appears
to be unbreakable, due to its use of up to 26
different cipher alphabets. Ciphers like this,
which use more than one cipher alphabet are
known as Polyalphabetic Ciphers. These can be
incredibly difficult to decipher, because of
their resistance to letter frequency analysis.
Indeed, over time, the Vigenère cipher
became known as 'Le Chiffre Undechiffrable',
or 'The Unbreakable Cipher'.
This slide and the next few copied directly from Simon Singh’s website.
Vigenere cipher:
the unbreakable code
• It wasn't until 1854, over two hundred years
later, that the Vigenère Cipher was finally
cracked by the British cryptographer Charles
Babbage. Babbage employed a mix of
cryptographic genius, intuition and sheer
cunning to break the Vigenère Cipher.
Amazingly, his work was never published in his
lifetime, and it was over a hundred years
later, in the 1970's, that his technique was
finally made public.
This slide and the next few copied directly from Simon Singh’s website.
Vigenere cipher:
the unbreakable code
The strength of the Vigenère Cipher is that the
same letter can be encrypted in different ways.
For example, if the keyword is KING, then every
plaintext letter can be encrypted in 4 ways,
because the keyword contains 4 letters. Each
letter of the keyword defines a different cipher
alphabet in the Vigenère Square. . . whole words
will be enciphered in different ways - the word
'the' could be enciphered as DPR, BUK, GNO
and ZRM depending on its position relative to
the keyword. Although this makes cryptanalysis
difficult, it is not impossible.
This slide and the next few copied directly from Simon Singh’s website.
Next time . . .
How Babbage cracked the
undecipherable cipher.
HW #4a: Vigenere
• 1. Encrypt the sentence “Simon Singh is a
singularly talented writer” using the
keyword “CODE”
• 2. Encrypt 1 message (at least 100 words
long) using a chosen keyword. Swap and
try to crack it.
HW # 4b: Monoalphabetic
Substitution cipher
NBSQF
VLMVE
LSNRH
QSRMN
SHZMC
HLDMR
LFMCQ
RHDLF
HLHSR
FQSRM
GVZQS
VKLUV
LQSGV
HSGVQ
VPVVO
HVMHV
XGVQR
VXVRU
MCVCG
KKNVS
SGRHX
ZMCRG
GZSGN
LSGVQ
VMVUV
HNVZM
HTFRC
HGGRH
VCEQL
VZQSE
GLFTG
GZMTV
ZUVGR
BGVZQ
TRUVM
QDZHZ
CGRNR
VHGVK
AVXZF
NNBHR
LQZHE
SRMNV
HLFTG
H
SZMCR
RGLKC
AZQTZ
MLMVN
LUVHN
HVRMN
TGSNB
QLNNV
GRHGF
SLFQA
GZUVG
GRHCV
RMAVS
BGVZQ
BGVZQ
VRSAR
GVZQS
LMGRN
QSCRC
KRHHN
RHABI
ZQZMC
SVQCQ
SRMGR
SELQL
CVHGR
DZHDL
GRHGF
HNZQS
BSQFV
FHSVW
NRMVG
RUVMG
NGRHS
MXVRS
HGVZQ
FMCVC
QSCRC
ALSGV
KLUVG
XGZMT
VXZMM
RHGVZ
GLFTG
DZHGR
SGRHD
DRSGG
KRTGS
JFZKG
ZSGNB
HW # 4c: Mono-alphabetic
Substitution cipher
826821526251162515231172625148114
14826232621111161411615142623722526
14826168262326172213262514826232621111
11221614231252212142221622161827182625
8262326116252026232671782152625148114
14826232621111161411615142623722526
252610711112512011
Websites which help
http://www.geocities.com/cryptogramcorner/
http://cs.colgate.edu/faculty/nevison/Core139Web/tools/substitution.html