CRYPTOGRAPHY

Lecture 2

Tuesday, June 27th

Caesar shiftPlain : 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

Caesar shift

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

ABCDEFGHIJKLMNOPQRSTUVWXYZ

UVWXYZABCDEFGHIJKLMNOPQRST

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 let’s 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.

Caesar shift example

CAESAR'S WIFE MUST BE ABOVE SUSPICION

BZDRZQ'R VHED LTRS AD ZANUD RTROHBHNM

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

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.

www.simonsingh.net

http://starbase.trincoll.edu/~crypto/http://edeca.net/site/programs:rotutil

HELPFUL FACTS (for English)

Order Of Frequency Of Single LettersE T A O I N S H R D L U   

Order Of Frequency Of Digraphsth 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 Trigraphsthe and tha ent ion tio for nde has nce

edt tis oft sth men  

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

1. PMFBP PBKA PBZOBQ JBPPXDBP.

2. QEB XOJV FP LK QEB JLSB

3. QELJXP GBCCBOPLK ABPFDKBA X PRYPQFQRQFLK ZFMEBO

HW #2b: Caesar shift problems

1. MAX YTNEM, WXTK UKNMNL, EBXL GHM BG HNK LMTKL UNM BG HNKLXEOXL.

2. UHWXUA WR URPH 3. VJGEC GUCTU JKHVE KRJGT KUXGT APKEG

DWVQP EGAQW JCXGV JGUJK HVHKI WTGFQ WVVJG YJQNG OGUUC IG DG EQOGU QDXKQ WU.

HW #2c: Caesar shift problems(different shift, and hard:

why?).

1. KENKMOC PYBDEXK TEFKD

2. MHILYLZAZBHLXBPZXBLMVYABUHLHWWPBZJSHBKPBZJHLJBZKPJABTHYJHUBTLZA

HW #2d: Analysis

1. What makes a Caesar shift cipher easier or harder to break?

2. What techniques did you take advantage of?

3. How would you design a better cipher?

Reading

1. Read the code book p 14-442. Look online at sites that help

decipher Caesar shift ciphers3. Look around www.simonsingh.net4. Start thinking about what you’d like

to do for your final project.

Secure transmission

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

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.

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.

Tips for a more secure code

No spacesNo punctuationForeign languageMaybe 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.

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?

How many possibilities?!

• If my alphabet has 3 letters, I have the following ways of arranging it:

ABCACBBCABAC

CBACAB

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.

How many possibilities?!

• If my alphabet has 4 letters, I have the following ways of arranging it:

ABCD BCDA CDBA DABCABDC BCAD CDAB DACBACBD BACD CADB DBACACDB BADC CABD DBCAADBC BDAC CBAD DCABADCD BDCA CBDA DCBA

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,

there’s only one way to pick the last letter.– So there are 4*3*2*1 possibilities.– This is called 4! = 4*3*2*1=24

How many possibilities?!

• If my alphabet has 5 letters, how many possibilities do we have?– 5! = 5*4*3*2*1 = 120– let’s not write them out . . .

• If my alphabet has 26 letters, we have– 26! = 26*25*24*23* . . . *3*2*1 possibilities.

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

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.

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

. . .

Frequency Analysis

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

Example 1

E E E T E T TH EKGGLHQNL KZEL AKGB PL ARHAT EARL CKSGB CHV XNGG KX UHB E T TE TTEVLENSTAF VFVALPV CSTAALZ UF E E E E OLKOGL CRK SLHB HOOGTLB TESFOAKQSHORF. E E E E ET E - USNEL VERZLTLS, VLESLAV HZB GTLV

L occurs 18 times, A occurs 10 times. Example 1

E E E T E TH TH EKGGLHQNL KZEL AKGB PL ARHATHEARL CKSGB CHV XNGG KX UHB E T TE TTEVLENSTAF VFVALPV CSTAALZ UF E E H E E OLKOGL CRK SLHB HOOGTLB T HESFOAKQSHORF. E H E E E ET E - USNEL VERZLTLS, VLESLAV HZB GTLV

Example 1

A EA E E T E THATH EKGGLHQNL KZEL AKGB PL ARHATHE A AARL CKSGB CHV XNGG KX UHB E T TE TTEVLENSTAF VFVALPV CSTAALZ UF E E H EA A E OLKOGL CRK SLHB HOOGTLB T A HESFOAKQSHORF. E H E E E ET A E - USNEL VERZLTLS, VLESLAV HZB GTLV

Example 1

A OLLEA E O E TOL E THATH EKGGLHQNL KZEL AKGB PL ARHATHE O L A LL O AARL CKSGB CHV XNGG KX UHBSE T S STE S TTEVLENSTAF VFVALPV CSTAALZ UF PEOPLE HO EA APPL E OLKOGL CRK SLHB HOOGTLB PTO APHESFOAKQSHORF. E S H E E SE ETS A L ES - USNEL VERZLTLS, VLESLAV HZB GTLV

Example 1

A COLLEAGUE ONCE TOLD ME THATH EKGGLHQNL KZEL AKGB PL ARHATHE WORLD WAS FULL OF BADARL CKSGB CHV XNGG KX UHBSECURITY SYSTEMS WRITTEN BYVLENSTAF VFVALPV CSTAALZ UF PEOPLE WHO READ APPLIEDOLKOGL CRK SLHB HOOGTLBCRYPTOGRAPHY.ESFOAKQSHORF. BRUCE SCHNEIER, SECRETS AND LIES - USNEL VERZLTLS, VLESLAV HZB GTLV

Example 1

A harder example

• Shorter = less information

• R occurs 10 times, A occurs 9 times– (all others occur 4 or fewer times)

• Telegraph style; fewer short words

YIRLAZ MRACIRB CR PKORI CRP:

MRPPVAMQAY MRLACZRGA, VAYQAVW RA

Example 2

A harder example

E E E E E EYIRLAZ MRACIRB CR PKORI CRP: E E E EMRPPVAMQAY MRLACZRGA, VAYQAVW RA

E doesn’t begin any common 2-letter words

Example 2

A harder example

O O O O O OYIRLAZ MRACIRB CR PKORI CRP: O O O OMRPPVAMQAY MRLACZRGA, VAYQAVW RA

A occurs 9 times. What could it be?

Example 2

A harder example

O N ON O O O OYIRLAZ MRACIRB CR PKORI CRP: O N N O N O N N N ONMRPPVAMQAY MRLACZRGA, VAYQAVW RA

Example 2

A harder example

O N ONT O TO O TOYIRLAZ MRACIRB CR PKORI CRP: O N N O NT O N N N ONMRPPVAMQAY MRLACZRGA, VAYQAVW RA

Example 2

A harder example

G O N ONT O TO O TOYIRLAZ MRACIRB CR PKORI CRP: O N ING O NT O N NGIN ONMRPPVAMQAY MRLACZRGA, VAYQAVW RA

Example 2

A harder example

GROUND CONTROL TO MAJOR TOM:YIRLAZ MRACIRB CR PKORI CRP:COMMENCING COUNTDOWN, ENGINES ONMRPPVAMQAY MRLACZRGA, VAYQAVW RA

Example 2

Not a good candidate for frequency analysis:

FROM ZANIBAR TO ZAMBIA AND ZAIRE

OZONE ZONES MAKE ZEBRAS

RUN MANY ZIGZAGS

Example 3

The letter Z is the most common here!

HW # 3a: Substitution cipherHint: use www.simonsingh.net/The_Black_Chamber/frequencypuzzle.htm

Example 3

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