anthony zanontian - my professors crytography presentation from ucsd

8/14/2019 Anthony Zanontian - My Professors Crytography Presentation from UCSD

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04/03/29 1

CryptographyCryptography

Kevin O’[email protected]/~kobryant

Math 187MWF 4:00 – 4:50 pmwww.math.ucsd.edu/~crypto

mailto:[email protected]

http://www.math.ucsd.edu/~kobryant

http://www.math.ucsd.edu/~kobryant

mailto:[email protected]



04/03/2904/03/29 22

DefinitionsDefinitions

PlaintextPlaintext• The message that Alice wants Bob to readThe message that Alice wants Bob to read

CiphertextCiphertext

• The message that Alice sends BobThe message that Alice sends Bob CryptosystemCryptosystem

• The algorithm that Alice uses to turn plaintextThe algorithm that Alice uses to turn plaintextinto ciphertext.into ciphertext.

KeyKey• Something Bob and Alice agree on beforehandSomething Bob and Alice agree on beforehand

that customizes the cryptosystemthat customizes the cryptosystem



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CryptosystemsCryptosystems

Two basic types:Two basic types:• Substitution (replace letters)Substitution (replace letters)

• Transposition (rearrange letters)Transposition (rearrange letters) Caeser CipherCaeser Cipher

• Shift each letter by the same amountShift each letter by the same amount• Key: how much to shiftKey: how much to shift

Monoalphabetic SubstitutionMonoalphabetic Substitution• Replace each letter with some other letter in a one-to-Replace each letter with some other letter in a one-to-

one mannerone manner

• Key: the bottom line of Key: the bottom line of

Plaintext: abcdefghijklmnopqrstuvwxyzPlaintext: abcdefghijklmnopqrstuvwxyz

Ciphertext: QWERTYUIOPASDFGHJKLZXCVBNMCiphertext: QWERTYUIOPASDFGHJKLZXCVBNM



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Caeser Cipher Caeser Cipher

GZO PN OCZMZAJMZ WMVXZ JPMNZGQZN OJ JPMGZO PN OCZMZAJMZ WMVXZ JPMNZGQZN OJ JPM

YPOT, VIY NJ WZVM JPMNZGQZN, OCVO DA OCZYPOT, VIY NJ WZVM JPMNZGQZN, OCVO DA OCZ

WMDODNC ZHKDMZ VIY DON XJHHJIRZVGOC GVNOWMDODNC ZHKDMZ VIY DON XJHHJIRZVGOC GVNO

AJM V OCJPNVIY TZVMN, HZI RDGG NODGG NVT,AJM V OCJPNVIY TZVMN, HZI RDGG NODGG NVT,

'OCDN RVN OCZDM ADIZNO CJPM.‘'OCDN RVN OCZDM ADIZNO CJPM.‘

Caeser CipherCaeser Cipher• StrengthsStrengths

Very FastVery Fast Easy to rememberEasy to remember



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Cipher WheelsCipher Wheels



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Caeser Cipher Caeser Cipher

GZO PN OCZMZAJMZ WMVXZ JPMNZGQZN OJ JPM YPOT, VIY NJ WZVMGZO PN OCZMZAJMZ WMVXZ JPMNZGQZN OJ JPM YPOT, VIY NJ WZVM

JPMNZGQZN, OCVO DA OCZ WMDODNC ZHKDMZ VIY DON XJHHJIRZVGOC GVNOJPMNZGQZN, OCVO DA OCZ WMDODNC ZHKDMZ VIY DON XJHHJIRZVGOC GVNO

AJM V OCJPNVIY TZVMN, HZI RDGG NODGG NVT, 'OCDN RVN OCZDMAJM V OCJPNVIY TZVMN, HZI RDGG NODGG NVT, 'OCDN RVN OCZDM

ADIZNO CJPM.‘ADIZNO CJPM.‘

Caeser CipherCaeser Cipher• StrengthsStrengths

Very FastVery Fast Easy to rememberEasy to remember

• WeaknessesWeaknesses Formatting gives away the houseFormatting gives away the house Small number of keys: 26 (and one is weak)Small number of keys: 26 (and one is weak) Frequency analysisFrequency analysis



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Strengthening Caeser Strengthening Caeser

Fixing the Formatting WeaknessFixing the Formatting Weakness

• Strip out punctuation, and put letters inStrip out punctuation, and put letters inblocks of the same length.blocks of the same length.GZO PN OCZMZAJMZ WMVXZ JPMNZGQZN OJ JPM YPOT, VIY NJGZO PN OCZMZAJMZ WMVXZ JPMNZGQZN OJ JPM YPOT, VIY NJ

WZVM JPMNZGQZN, OCVO DA OCZ WMDODNC ZHKDMZ VIY DONWZVM JPMNZGQZN, OCVO DA OCZ WMDODNC ZHKDMZ VIY DON

XJHHJIRZVGOC GVNO AJM V OCJPNVIY TZVMN, HZI RDGGXJHHJIRZVGOC GVNO AJM V OCJPNVIY TZVMN, HZI RDGG

NODGG NVT, 'OCDN RVN OCZDM ADIZNO CJPM.‘NODGG NVT, 'OCDN RVN OCZDM ADIZNO CJPM.‘

becomesbecomes

GZOP NOCZ MZAJ MZWM VXZJ PMNZ GQZN OJJP MYPO TVIYGZOP NOCZ MZAJ MZWM VXZJ PMNZ GQZN OJJP MYPO TVIYNJWZ VMJP MNZG QZNO CVOD AOCZ WMDO DNCZ HKDM ZVIYNJWZ VMJP MNZG QZNO CVOD AOCZ WMDO DNCZ HKDM ZVIY

DONX JHHJ IRZV GOCG VNOA JMVO CJPN VIYT ZVMN HZIRDONX JHHJ IRZV GOCG VNOA JMVO CJPN VIYT ZVMN HZIR

DGGN ODGG NVTO CDNR VNOC ZDMA DIZN OCJP MDGGN ODGG NVTO CDNR VNOC ZDMA DIZN OCJP M



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Key weakness is fixed by monoalphabeticKey weakness is fixed by monoalphabeticsubstitutionsubstitution• StrengthsStrengths

403,291,461,126,605,635,584,000,000 keys403,291,461,126,605,635,584,000,000 keys FastFast

• WeaknessesWeaknesses How many keys are easy to remember?How many keys are easy to remember?

Frequency analysisFrequency analysisWe saw the frequencies of individual letters, but it is also possible---We saw the frequencies of individual letters, but it is also possible---

and reasonable---to look at pairs of letters, and triples, etc. Moreand reasonable---to look at pairs of letters, and triples, etc. Moreon this in three weeks.on this in three weeks.



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Fixing Frequency analysisFixing Frequency analysis

• Many ways to make frequency analysisMany ways to make frequency analysisharder:harder: send “e” to 3 letters (do you really need zsend “e” to 3 letters (do you really need z

and x?)and x?) spell poorly (do you really need all thosespell poorly (do you really need all those

silent letters?)silent letters?) send short messagessend short messages use several different keys in one messageuse several different keys in one message



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VigenVigenèère’s Cryptosystemre’s Cryptosystem

StrengthsStrengths• Infinite number of keywordsInfinite number of keywords

• Scrambles frequenciesScrambles frequencies

• Easy to remember keyEasy to remember key• Considered unbreakable in Black chambers forConsidered unbreakable in Black chambers for

200 years200 years

WeaknessesWeaknesses• Can perform frequency analysis if we know-orCan perform frequency analysis if we know-or

guess-the length of the keywordguess-the length of the keyword



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HistoryHistory

• Idea of entertwining two keys cameIdea of entertwining two keys camefrom Leon Battista Alberti around 1465from Leon Battista Alberti around 1465

in Florencein Florence• Developed byDeveloped by

Johannes TrithemiusJohannes Trithemius

Giovanni PortaGiovanni PortaBlaise de VigenBlaise de Vigenèèrere



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HistoryHistory• Idea of entertwining two keys cameIdea of entertwining two keys came

from Leon Battista Alberti around 1465from Leon Battista Alberti around 1465

in Florencein Florence• Developed byDeveloped by

Johannes TrithemiusJohannes TrithemiusGiovanni PortaGiovanni Porta

Blaise de VigenBlaise de Vigenèèrere• Broken by Charles BabbageBroken by Charles Babbage

• Publicly broken by Friedrich KasiskiPublicly broken by Friedrich Kasiski



04/03/2904/03/29 1515

The Vision of SinThe Vision of Sin

Sit thee down, and have no shame,Sit thee down, and have no shame,Cheek by jowl, and knee by knee:Cheek by jowl, and knee by knee:What car I for any name?What car I for any name?What for order or degree?What for order or degree?

Let me screw thee up a peg:Let me screw thee up a peg:Let me loose thy tongue with wine:Let me loose thy tongue with wine:Callest thou that thing a leg?Callest thou that thing a leg?

Which is thinnest? Thine or mine?Which is thinnest? Thine or mine?

Thou shalt not be saved by works:Thou shalt not be saved by works:Thou has been a sinner too:Thou has been a sinner too:Ruined trunks on withered forks,Ruined trunks on withered forks,Empty scarecrows, I and you!Empty scarecrows, I and you!

Fill the cup, and fill the can:Fill the cup, and fill the can:Have a rouse before the morn:Have a rouse before the morn:

Every moment dies a man,Every moment dies a man,Every moment one is born.Every moment one is born. Alfred Tennyson

Image taken fromhttp://charon.sfsu.edu/TENNYSON/tennyson.html



04/03/2904/03/29 1616

Babbage to TennysonBabbage to Tennyson

[suggested correction to “otherwise[suggested correction to “otherwisebeautiful” poem]beautiful” poem]

It must be manifest that if this were true,It must be manifest that if this were true,the population of the world would be at athe population of the world would be at astandstill . . . I would suggest that in thestandstill . . . I would suggest that in thenext edition of your poem you have it readnext edition of your poem you have it read– “Every moment dies a man, Every– “Every moment dies a man, Every

moment 1moment 111

/ /1616 is born.” The actual figure isis born.” The actual figure isso long I cannot get it onto a line, but Iso long I cannot get it onto a line, but Ibelieve the figure 1believe the figure 1 11 / /1616 will be sufficientlywill be sufficientlyaccurate for poetry.accurate for poetry.



04/03/2904/03/29 1717

TranspositionsTranspositions

Part of an actual telegram from Union Army General Halleck to General BuellPart of an actual telegram from Union Army General Halleck to General Buell(quoted from Battle Cry of Freedom: The Civil War Era)(quoted from Battle Cry of Freedom: The Civil War Era)

YOU MARCHED THE IS THE ELSEWHERE MOVE OF SURPRISING TWOYOU MARCHED THE IS THE ELSEWHERE MOVE OF SURPRISING TWOTIMES HALLECK AS SLOWLY ARMY IN HAS DISTANCE HAVE FOUR LASTTIMES HALLECK AS SLOWLY ARMY IN HAS DISTANCE HAVE FOUR LASTMOST IMMOBILITY YOU HERE TOO YOUR BRAGG MONTHS THEMOST IMMOBILITY YOU HERE TOO YOUR BRAGG MONTHS THE

HALLECKHAVEYOUDISTANCETHE

TIMESFOURMARCHEDHASMONTHSTWOLASTTHEINBRAGG

SURPRISINGMOSTISARMYYOUR

OFIMMOBILITYTHESLOWLYTOO

MOVEYOUELSEWHEREASHERE



04/03/2904/03/29 1818

From LincolnFrom Lincoln

1863 WOULD RELIEVED1863 WOULD RELIEVEDMEADE SINCE HAVE THEMEADE SINCE HAVE THEWITHOUT ME WAS WHO THEWITHOUT ME WAS WHO THESATURDAY HEVY A WARSATURDAY HEVY A WARFIGHTING CORPS KNOWFIGHTING CORPS KNOWPLEASE THE TO OF ANDPLEASE THE TO OF ANDIMPRESSION TO CAMERON 15IMPRESSION TO CAMERON 15

I BE THAT ALL GETTYSBURGI BE THAT ALL GETTYSBURGGET RIVER TELL WHOGET RIVER TELL WHOCOMMANDER IN ON LINCOLNCOMMANDER IN ON LINCOLNSIGNED OF FOR ONE YOUSIGNED OF FOR ONE YOUFIGHT OVER ONLY BATTLEFIGHT OVER ONLY BATTLESMITH THE MUCH SIMONSMITH THE MUCH SIMONWASHINGTON FOR GIVE OFWASHINGTON FOR GIVE OF

COUCH THE STRIVEN ENEMYCOUCH THE STRIVEN ENEMYANOTHER IF THE WASANOTHER IF THE WASCOUNCIL NIGHTCOUNCIL NIGHT

Image fromhttp://www.picturehistory.com/



04/03/2904/03/29 2020

Rectangular TranspositionRectangular Transposition

Step 2: Write the plaintext under theStep 2: Write the plaintext under thepermutation rowwisepermutation rowwise

rvuzx jqre

gnortsemsekamemyor

tsedtonse

odtahwraw

f oloohcss

ef ilf otuo

341798256



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Rectangular TranspositionRectangular Transposition

rvuzx jqre

gnortsems

ekamemyor

tsedtonse

odtahwraw

f oloohcss

ef ilf otuo

341798256

•Step 3: Write down the columns according to the numbers at the top:ILTEAOU TCRNYEQ EFOTEGR FODSKNV USASOMR

OSWERSE LOADMRZ OHWOMSJ FOHTETX



04/03/2904/03/29 2323

GradesGrades

6 out of 7 quizzes (60%)6 out of 7 quizzes (60%) Computer Homework (20%)Computer Homework (20%)

Final Exam (or project) (20%)Final Exam (or project) (20%)



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SummarySummary

Caeser SucksCaeser Sucks Monoalphabetic substitution is betterMonoalphabetic substitution is better

Vigenère is goodVigenère is good Transposition is a nice idea, andTransposition is a nice idea, and

deserves to be looked at moredeserves to be looked at more

The EndThe End

anthony zanontian - my professors crytography presentation from ucsd

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