CRYPTOGRAPHY

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CRYPTOGRAPHY

• Lecture 2
• Tuesday, June 27th

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Caesar shift

• Plain abcdefghijklmnopqrstuvwxyz
• ROT 0 ABCDEFGHIJKLMNOPQRSTUVWXYZ
• ROT 1 BCDEFGHIJKLMNOPQRSTUVWXYZA
• ROT 2 CDEFGHIJKLMNOPQRSTUVWXYZAB
• ROT 3 DEFGHIJKLMNOPQRSTUVWXYZABC
• ROT 4 EFGHIJKLMNOPQRSTUVWXYZABCD
• ROT 5 FGHIJKLMNOPQRSTUVWXYZABCDE
• ROT 6 GHIJKLMNOPQRSTUVWXYZABCDEF
• ROT 7 HIJKLMNOPQRSTUVWXYZABCDEFG
• ROT 8 IJKLMNOPQRSTUVWXYZABCDEFGH
• ROT 9 JKLMNOPQRSTUVWXYZABCDEFGHI
• ROT 10 KLMNOPQRSTUVWXYZABCDEFGHIJ
• ROT 11 LMNOPQRSTUVWXYZABCDEFGHIJK
• ROT 12 MNOPQRSTUVWXYZABCDEFGHIJKL
• ROT 13 NOPQRSTUVWXYZABCDEFGHIJKLM
• ROT 14 OPQRSTUVWXYZABCDEFGHIJKLMN
• ROT 15 PQRSTUVWXYZABCDEFGHIJKLMNO

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Caesar shift

• A Caesar shift of 20 (or 6, depending which way
  you are looking at it) gives
• ABCDEFGHIJKLMNOPQRSTUVWXYZ
• UVWXYZABCDEFGHIJKLMNOPQRST

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Caesar shift example

• BZDRZQ'R VHED LTRS AD ZANUD RTROHBHNM

• First clue the apostrophe. The only things
  that can work are a T or an S. But S would be
  more common. So lets assume that R in the
  cipher text means S. This means that every
  letter is the cipher is shifted over by one.
  Once the rule is clear, the whole message is
  easily deciphered.

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Caesar shift example

• CAESAR'S WIFE MUST BE ABOVE SUSPICION
• BZDRZQ'R VHED LTRS AD ZANUD RTROHBHNM

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Caesar shift clues

• To find what the shift is, we sometimes have
  clues
• Apostrophes tell us a lot
• Words with one letter can only be A or I
• The most common words with two letters are
• OF TO IN IS IT BE BY HE AS ON AT OR AN SO IF NO

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Caesar shift problems

• LWW RLFW TD OTGTOPO TYEZ ESCPP ALCED ZYP ZQ
  HSTNS ESP MPWRLP TYSLMTE ESP LBFTELYT LYZESPC
  ESZDP HSZ TY ESPTC ZHY WLYRFLRP LCP NLWWPO NPWED
  TY ZFC RLFWD ESP ESTCO LWW ESPDP OTQQPC QCZX PLNS
  ZESPC TY WLYRFLRP NFDEZXD LYO WLHD
• How many double letter combinations can we have?
  Notice the LWW in the beginning of this text.

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• www.simonsingh.net
• http//starbase.trincoll.edu/crypto/
• http//edeca.net/site/programsrotutil

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HELPFUL FACTS (for English)

• Order Of Frequency Of Single Letters
• E T A O I N S H R D L U   
• Order Of Frequency Of Digraphs
• th er on an re he in ed nd ha at en es of or nt
  ea ti to it st io le is ou ar as de rt ve  
• Order Of Frequency Of Trigraphs
• the and tha ent ion tio for nde has nce edt
  tis oft sth men  

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HW 2a Caesar shift problems3 messages all with
the same shift

• PMFBP PBKA PBZOBQ JBPPXDBP.
• QEB XOJV FP LK QEB JLSB
• QELJXP GBCCBOPLK ABPFDKBA X PRYPQFQRQFLK ZFMEBO

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HW 2b Caesar shift problems

• MAX YTNEM, WXTK UKNMNL, EBXL GHM BG HNK LMTKL UNM
  BG HNKLXEOXL.
• UHWXUA WR URPH
• VJGEC GUCTU JKHVE KRJGT KUXGT APKEG DWVQP EGAQW
  JCXGV JGUJK HVHKI WTGFQ WVVJG YJQNG OGUUC IG DG
  EQOGU QDXKQ WU.

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HW 2c Caesar shift problems(different shift,
and hard why?).

• 1. KENKMOC PYBDEXK TEFKD
• 2. MHILYLZAZBHLXBPZXBLMVYABUHLHWWPBZJSHBKPBZJHLJBZ
  KPJABTHYJHUBTLZA

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HW 2d Analysis

• What makes a Caesar shift cipher easier or harder
  to break?
• What techniques did you take advantage of?
• How would you design a better cipher?

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Reading

• Read the code book p 14-44
• Look online at sites that help decipher Caesar
  shift ciphers
• Look around www.simonsingh.net
• 4. Start thinking about what youd like to do
  for your final project.

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(No Transcript)
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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
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Weakness of Caesar shift

• If you figured out the shift, the whole message
  quickly unravels.
• If there are spaces, or punctuation, you can get
  a handle on the message.
• If the message is long enough, or if you have
  enough messages with the same shift, you can
  solve by frequency analysis
• If all else fails, try all 26 possibilities.
  This may take a while by hand, but it is not
  inherently difficult.

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What makes the Caesar cipher so convenient?

• The key is easy everyone can decrypt it just by
  knowing one small bit of information.
• How do you transmit the key? Maybe you can agree
  on something in advance, e.g. that every day of
  the month you shift over by that number of days
  (this has to be modified a little to work), or
  that the name of the month is the letter that A
  shifts to . . . Some agreed upon way of shifting.
• The problem of the key will recur in many of the
  ciphers we see.

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Tips for a more secure code

• No spaces
• No punctuation
• Foreign language
• Maybe we can change letters in a way that does
  not have a chain reaction solution? It will
  still be a mono-alphabetic cipher but each
  letter can be independently determined.

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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?

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How many possibilities?!

• If my alphabet has 3 letters, I have the
  following ways of arranging it
• ABC
• ACB
• BCA
• BAC
• CBA
• CAB

There are 3 ways of choosing the first letter
either A B or C. Once the first letter is chosen,
there are only 2 letters left, they can only be
arranged in 2 different ways.
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How many possibilities?!

• If my alphabet has 4 letters, I have the
  following ways of arranging it
• ABCD BCDA CDBA DABC
• ABDC BCAD CDAB DACB
• ACBD BACD CADB DBAC
• ACDB BADC CABD DBCA
• ADBC BDAC CBAD DCAB
• ADCD BDCA CBDA DCBA

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How many possibilities?!

• If my alphabet has 4 letters,
• there are 4 ways of arranging the first letter
• For each of those choices there are only 3 ways
  to arrange the remaining 3 letters
• For any given arrangement of the first 2 letters,
  there are 2 ways of arranging the next 2 letters
• For any given arrangement of the first 3 letters,
  theres only one way to pick the last letter.
• So there are 4321 possibilities.
• This is called 4! 432124

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How many possibilities?!

• If my alphabet has 5 letters, how many
  possibilities do we have?
• 5! 54321 120
• lets not write them out . . .
• If my alphabet has 26 letters, we have
• 26! 26252423 . . . 321 possibilities.

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Mono-alphabeticSubstitution Cipher

• 26! 403,291,461,126,605,635,584,000,000
• For encryption, one of these is not good (the
  abcdefg one) so we have one less possibility.
  Even if 26 of this are bad (the ones that
  correspond to the Caesar ciphers) that still
  leaves lots of good possibilities.
• Roughly 288 checking 1 billion per second,
  would take 12 billion years

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Mono-alphabeticSubstitution Cipher

• Too many possibilities to break by brute force!
  This is a major strength of the substitution
  cipher.
• But how will the recipient break it?
• You need to exchange a key, and it needs to be a
  key that one can remember.

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Mono-alphabetic Substitution Cipher

• Is there a better way to break it?
• al-Kindi, ninth century frequency analysis
• Not a recipe, but a good set of guidelines.
• This only works for longer messages . . .

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Frequency Analysis
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Example 1
H EKGGLHQNL KZEL AKGB PL ARHA ARL CKSGB CHV
XNGG KX UHB VLENSTAF VFVALPV CSTAALZ UF OLKOGL
CRK SLHB HOOGTLB ESFOAKQSHORF. - USNEL
VERZLTLS, VLESLAV HZB GTLV
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E E E T E T T H EKGGLHQNL KZEL
AKGB PL ARHA T E ARL CKSGB CHV XNGG KX UHB E
T TE TTE VLENSTAF VFVALPV CSTAALZ UF E
E E E OLKOGL CRK SLHB HOOGTLB
T ESFOAKQSHORF. E E E E ET
E - USNEL VERZLTLS, VLESLAV HZB GTLV
L occurs 18 times, A occurs 10 times.
Example 1
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E E E T E TH T H EKGGLHQNL KZEL
AKGB PL ARHA THE ARL CKSGB CHV XNGG KX UHB E
T TE TTE VLENSTAF VFVALPV CSTAALZ UF E
E H E E OLKOGL CRK SLHB HOOGTLB
T H ESFOAKQSHORF. E H E E E ET
E - USNEL VERZLTLS, VLESLAV HZB GTLV
Example 1
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A EA E E T E THAT H EKGGLHQNL KZEL
AKGB PL ARHA THE A A ARL CKSGB
CHV XNGG KX UHB E T TE TTE VLENSTAF
VFVALPV CSTAALZ UF E E H EA A E
OLKOGL CRK SLHB HOOGTLB T A
H ESFOAKQSHORF. E H E E E ET A
E - USNEL VERZLTLS, VLESLAV HZB GTLV
Example 1
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A OLLEA E O E TOL E THAT H EKGGLHQNL KZEL
AKGB PL ARHA THE O L A LL O A ARL CKSGB
CHV XNGG KX UHB SE T S STE S TTE VLENSTAF
VFVALPV CSTAALZ UF PEOPLE HO EA APPL E
OLKOGL CRK SLHB HOOGTLB PTO
APH ESFOAKQSHORF. E S H E E SE ETS A
L ES - USNEL VERZLTLS, VLESLAV HZB GTLV
Example 1
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A COLLEAGUE ONCE TOLD ME THAT H EKGGLHQNL KZEL
AKGB PL ARHA THE WORLD WAS FULL OF BAD ARL CKSGB
CHV XNGG KX UHB SECURITY SYSTEMS WRITTEN
BY VLENSTAF VFVALPV CSTAALZ UF PEOPLE WHO READ
APPLIED OLKOGL CRK SLHB HOOGTLB CRYPTOGRAPHY. ESFO
AKQSHORF. BRUCE SCHNEIER, SECRETS AND LIES -
USNEL VERZLTLS, VLESLAV HZB GTLV
Example 1
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A harder example
YIRLAZ MRACIRB CR PKORI CRP MRPPVAMQAY
MRLACZRGA, VAYQAVW RA

• Shorter less information
• R occurs 10 times, A occurs 9 times
• (all others occur 4 or fewer times)
• Telegraph style fewer short words

Example 2
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A harder example
E E E E E E YIRLAZ MRACIRB CR
PKORI CRP E E E
E MRPPVAMQAY MRLACZRGA, VAYQAVW RA
E doesnt begin any common 2-letter words
Example 2
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A harder example
O O O O O O YIRLAZ MRACIRB CR
PKORI CRP O O O
O MRPPVAMQAY MRLACZRGA, VAYQAVW RA
A occurs 9 times. What could it be?
Example 2
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A harder example
O N ON O O O O YIRLAZ MRACIRB CR
PKORI CRP O N N O N O N N N
ON MRPPVAMQAY MRLACZRGA, VAYQAVW RA
Example 2
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A harder example
O N ONT O TO O TO YIRLAZ MRACIRB CR
PKORI CRP O N N O NT O N N N
ON MRPPVAMQAY MRLACZRGA, VAYQAVW RA
Example 2
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A harder example
G O N ONT O TO O TO YIRLAZ MRACIRB CR
PKORI CRP O N ING O NT O N NGIN
ON MRPPVAMQAY MRLACZRGA, VAYQAVW RA
Example 2
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A harder example
GROUND CONTROL TO MAJOR TOM YIRLAZ MRACIRB CR
PKORI CRP COMMENCING COUNTDOWN, ENGINES
ON MRPPVAMQAY MRLACZRGA, VAYQAVW RA
Example 2
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Not a good candidate for frequency analysis
FROM ZANIBAR TO ZAMBIA AND ZAIRE OZONE ZONES
MAKE ZEBRAS RUN MANY ZIGZAGS
The letter Z is the most common here!
Example 3
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HW 3a Substitution cipher Hint use
www.simonsingh.net/The_Black_Chamber/frequencypuzz
le.htm
AVWJM VIPMY DPIYI WFJVB IPAVF DMIMB AJJDP KARMV
IPMYM VDPDV HQMAV DPMHI TDFLD PKMAR IBQFF AIJDP
WPNMB ILIWU IJMBW MWFIK FIIPM QFPMD HFDVP WPNMB
IYVAM BIFVA MBMBI VAPNW PNMBI YEFQR HLIAP YDQFB
WPNDP EIRYB IWFMV WJTAL LINVA MBMBI LDUID TWKAF
LABIL NBIFE LDJIH QMJBI TWNIN APMBI PAKBM LAOIW
GDIRA RIWPM MDVFA MIWPN MBILI WUIJM BWMWF IKFII
PMQFP MDHFD VPWPN MBIYV AMBIF VAMBM BIVAP NWPNM
BIYEF QRHLI APYDQ FBWPN AMBFI VWGIH HLIAP WHFDD
OWPNV WMEBI NMBIF AGGLI JFQPW VWYWP NMBIY PIUIF
RWNIW JDQPN WPNMB ILIWU IJMBW MWFIK FIIPM QFPIN
MDHFD VPWPN MBIYV AMBIF VAMBM BIVAP NWPNM BIYEF
QRHLI APYDQ FBWPN BILLD BILLD BILLD BILLD KDDNH
YIKDD NHYIK DDNHY IKDDN HYIMB WMJWL LMBIF IAJWP
NMBIL IWUIJ MBWMW FIKFI IPMQF PINMD HFDVP WPNMB
IYVAM BIFVA MBMBI VAPNW PNMBI YEFQR HLIAP YDQFB
WPN
Example 3