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CRYPTOGRAPHY. lecture 3 Wednesday. The difference between substitution and transposition is that in: Subtitution: each letter retains its position but changes its identity, Transposition: each letter retains its identity but changes its position. Example 3. HW #2: Caesar shift problems.

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CRYPTOGRAPHY

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CRYPTOGRAPHY

lecture 3

Wednesday

The difference between substitution and transposition is that in:

Subtitution: each letter retains its position but changes its identity,

Transposition: each letter retains its identity but changes its position.

Example 3

HW #2: Caesar shift problems

2. KENKMOC PYBDEXK TEFKD

3.MHILYLZAZBHLXBPZXBLMVYABUHLHWWPBZJSHBKPBZJHLJBZKPJABTHYJHUBTLZAULBAYVU

• QK MEJXNEJJ ZMEVTJ Q YVNGEZ VNHKE KVMMHY JXMEEXJ HB FHWWNEJXHKE WEKEVXP XPE PVNH HB V JXMEEX NVTI Q XRMK TA FHNNVM XH XPE FHNZ VKZ ZVTI YPEK TA EAEJ YEME JXVWWEZ WA XPE BNVJP HB V KEHK NQDPX XPVX JINQX XPE KQDPX VKZ XHRFPEZ XPE JHRKZ HB JQNEKFE

new ciphers

• MPV DIZ DFF EPUQH D WZIM QUSZ NPY EZSUBJZIUQH GZTTDHZT UT UC KVQ

• HGJUBQPU V HY H CVP AHT BA DHQG ZVYBT V KB GVZJRT JB BJURW YQZVE JBB CQJ ZVTER VJ VZ YBZJGS EGHZZVEHG VJ KBRZ TBJ VTZDVWR HTS EVDURWR

new ciphers

• HGJUBQPU V HY H CVP AHT BA DHQG ZVYBT V KB GVZJRT JB BJURW YQZVE JBB CQJ ZVTER VJ VZ YBZJGS EGHZZVEHG VJ KBRZ TBJ VTZDVWR HTS EVDURWR

Mono-alphabetic Substitution Cipher

• Allow any permutation of the alphabet

• Each letter is replaced by a different letter or symbol

• Key = permutation (still need to decide on a key and exchange this information in a secure way).

• 26! Possibilities

• What does this mean?

Frequency Analysis

HW # 3: Reading

• Review: The Code Book chapter 1 & read chapter 2 p. 45-51

• Find websites on substitution ciphers and frequency analysis

• Begin research for a 5-7 page essay on “Why are substitution and transposition ciphers obsolete, and when did they become so.” Due on Monday in class.

(in class): Substitution cipher

SK BKGKC FBTKCHZWBT W ZXUBA HM SKOO,

WBT EWQK UZ MFC MSB, WH SXKB SK XWGK

TUHJMGKCKT UZ DMC MFCHKOGKH

(in class): Substitution cipher

CGXTOUNZL NQ UDOU HDNTD BCJONLQ

HDCL ZLC DOQ WZBMZUUCL CACBEUDNLM

DC KCOBLCG NL QTDZZK.

HW # 3: 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

HW # 3: Substitution cipher

VBIPA PMBIE DQFJI DTBQR WPIUI PMJAM HIEDR IJPIE IJJWF YTDFD PIGID GLIMD NAJJD LUIMB IGDLA MAEWL HWPNJ VBAEB BWUIE DPPIE MINMB IRVAM BWPDM BIFWP NMDWJ JQRIW RDPKM BIGDV IFJDT MBIIW FMBMB IJIGW FWMIW PNISQ WLJMW MADPM DVBAE BMBIL WVJDT PWMQF IWPND TPWMQ FIJKD NIPMA MLIMB IRWNI EIPMF IJGIE MMDMB IDGAP ADPJD TRWPO APNFI SQAFI JMBWM MBIYJ BDQLN NIELW FIMBI EWQJI JVBAE BARGI LMBIR MDMBI JIGWF WMADP

HW # 3: Substitution cipher

NBSQF VKLUV GZSGN BGVZQ SZMCR GZUVG RHABI FHSVW XGZMT

VLMVE LQSGV LSGVQ TRUVM RGLKC GRHCV ZQZMC NRMVG VXZMM

LSNRH HSGVQ VMVUV QDZHZ AZQTZ RMAVS SVQCQ RUVMG RHGVZ

QSRMN VPVVO HNVZM CGRNR MLMVN BGVZQ SRMGR NGRHS GLFTG

SHZMC HVMHV HTFRC VHGVK LUVHN BGVZQ SELQL MXVRS DZHGR

HLDMR XGVQR HGGRH AVXZF HVRMN VRSAR CVHGR HGVZQ SGRHD

LFMCQ VXVRU VCEQL NNBHR TGSNB GVZQS DZHDL FMCVC DRSGG

RHDLF MCVCG VZQSE LQZHE QLNNV LMGRN GRHGF QSCRC KRTGS

HLHSR KKNVS GLFTG SRMNV GRHGF QSCRC HNZQS ALSGV JFZKG

FQSRM SGRHX GZMTV HLFTG SLFQA KRHHN BSQFV KLUVG ZSGNB

GVZQS ZMCRG ZUVGR H

HW # 3: 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

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.

ABCDEFGHIJKLMNOPQRSTUVWXYZplain text

GHIJKLMNOPQRSTUVWXYZABCDEFcipher1

RSTUVWXYZABCDEFGHIJKLMNOPQcipher2

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

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.

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

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

CRYPTOGRAMCR keyword

URTTFSVCEMUV 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

• Frequency analysis does not apply.

• Enormous number of possible keys

• The Vigenere cipher is a polyalphabetic cipher.

• 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.

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.