Cryptography



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CRYPTOGRAPHY

  • lecture 3
  • Wednesday
  • Steganography
  • cryptography
  • Transposition
  • Substitution
  • Monoalphabetic
  • 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.
  • 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.
  • ABCDEFGHIJKLMNOPQRSTUVWXYZ plain text
  • GHIJKLMNOPQRSTUVWXYZABCDEF cipher1
  • RSTUVWXYZABCDEFGHIJKLMNOPQ cipher2
  • 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.
  • 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 plain text
  • 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.


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