Cryptography: 500 BC to Quantum Computing

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Cryptography: 500 BC - Quantum Computing

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About me I’m not a crypto engineer I’m a web developer  who got into  Security Engineering I’ve always been scared  and fascinated by crypto

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About this talk 2700 years in 40 minutes Don’t take notes Slides are already up at:  speakerdeck.com/groovecoder

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2 “stories” of cryptography

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technology

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code-makers   vs.  code-breakers

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Thru-out this talk, I’m going to track this with a timeline …

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“Ages” “Code-making” “Code-breaking”

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“Ages” of technology Ancient: 7m Renaissance: 5m Industrial: 7m Computing: 12m Quantum: 5m

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Ancient Code-making

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T ranspositional/Permutation  Ciphers Anagrams: move letters around

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Permutation Cipher For example, consider this short sentence 35 letters 50,000,000,000,000,000,000,000,000,000,000  (50 trillion trillion) permutations

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“Strength” of encryption systems: How “easy” or “hard” are they?

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Time Complexity

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Permutation Cipher EXPERIMENTATIONS FRESH CHORD LOSS 50,000,000,000,000,000,000,000,000,000,000  (50 trillion trillion) permutations 1 check/second =  1,500,000,000,000,000,000,000,000 years  (1 trillion billion years)

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Drawbacks of random permutation cipher Impossible for intended recipient too False positives: which anagram is right? Do Not Attack at Midnight Attack at Mind: do T onight

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We need a  deterministic way to encrypt & decrypt

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Algorithms & Keys

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Rail fence cipher http://crypto.interactive-maths.com/rail-fence-cipher.html

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Rail fence cipher key = 4 http://crypto.interactive-maths.com/rail-fence-cipher.html they are attacking from the north

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Rail fence cipher; k=4 http://crypto.interactive-maths.com/rail-fence-cipher.html they are attacking from the north

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Rail fence cipher; k=4 http://crypto.interactive-maths.com/rail-fence-cipher.html they are attacking from the north TEKOOHRACIRMNREATANFTETYTGHH

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Rail fence cipher; k=4 http://crypto.interactive-maths.com/rail-fence-cipher.html they are attacking from the north TEKOOHRACIRMNREATANFTETYTGHH they are attacking from the north

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Machines for cryptography

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Scytale, ~700 BCE - 120 AD Algorithm Wrap message around a cylinder Key Diameter of cylinder

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Ancient Scytale ~700 BC

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Cryptanalysis Breaking encrypted messages

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Breaking rail fence cipher http://crypto.interactive-maths.com/rail-fence-cipher.html “Naive Brute Force”   key search:  T ry a bunch of numbers of rows by hand

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Breaking rail fence cipher DELEHELFTAAEDSWNT 2 rows: daealeedhsewlnftt 3 rows: deslefwtlanaeetdh 4 rows: detwaheeanellfdts 5 rows: defend the east wall

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So, the ﬁrst cryptanalysis is simply “naive brute force”   key searching

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“Key space” How many possible keys are there?

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Breaking a Scytale “Naive Brute Force”  key search:  T ry a bunch of cylinders

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Ancient Scytale ~700 BC Brute Force Key Search

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Substitutional Cipher Change letters into other letters

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Caesar Cipher, 49 - 44 BC Algorithm Replace each letter with another letter Key K positions down the alphabet

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Caesar (Shift) Cipher Plain alphabet: abcdefghijklmnopqrstuvwxyz Cipher alphabet: DEFGHIJKLMNOPQRSTUVWXZYABC

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Ancient Steganography,  Scytale ~700 BC Brute Force Key Search Caesar Cipher ~50 BC

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Breaking a Caesar Cipher “Naive Brute Force”   key search:  26 possible shifts

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Can we give ourselves a really large key space?    So it would take an attacker a long time to search them all?

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Non-shifted Random Substitution Algorithm Replace each letter with another letter Key Any Cipher Alphabet (An anagram of the alphabet! such meta!)

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Non-shifted Substitutional Cipher 26 letters to re-arrange Key space: 403,291,461,000,000,000,000,000,000  (403 trillion trillion or ~288)  possible re-arrangements (English) 120,000,000,000,000,000,000  (120 billion billion)  years at 1 check/s

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Most crypto-systems don’t try to offer “perfect” encryption …

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… most crypto systems try to force attackers into   key searches that take too long to complete

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Key: XZAVOIDBYGERSPCFHJKLMNQTUW

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Can we create a  “pseudo-random” key that is easy to memorize?

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Easy to memorize key JULIUS CAESAR  JULISCAER

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Easy to memorize key Cipher alphabet: JULISCAERTVWXYZBDFGHKMNOPQ JULIUS CAESAR  JULISCAER

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Easy to memorize key Plain alphabet: abcdefghijklmnopqrstuvwxyz Cipher alphabet: JULISCAERTVWXYZBDFGHKMNOPQ JULIUS CAESAR  JULISCAER Note: smaller key space

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“key derivation function” Cipher alphabet: JULISCAERTVWXYZBDFGHKMNOPQ JULIUS CAESAR

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Plain alphabet: abcdefghijklmnopqrstuvwxyz Cipher alphabet: JULISCAERTVWXYZBDFGHKMNOPQ Defend the East wall ISCSYI HES SJGH NJWW

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Ancient Steganography,  Scytale ~700 BC Brute Force Key Search Caesar Cipher ~50 BC Non-shifted  Substitution  Cipher

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So, we’ve got a simple crypto- system that would take decades for hundreds of thousands of computers to break!

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npm install keyed-substitution-cipher git commit -m  “lulz crypto”

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Non-shifted Substitution Cipher considered un-breakable for ~800 years, until …

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ةامعملا بتكلا جارختسا يف ةلاسر (On Decrypting Encrypted Correspondence) يدنكلا حاّبصلا قاحسإ نب بوقعي فسوي وبأ  (Abu Yūsuf Yaʻqūb ibn ʼIsḥāq aṣ-Ṣabbāḥ al-Kindī)  Al-Kindi 801-873 AD

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Frequency Analysis Attack

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“PCQ VMJYPD LBYK LYSO KBXBJXWXV BXV ZCJPO EYPD KBXBJYUXJ LBJOO KCPK. CP LBO LBCMKXPV XPV IYJKL PYDBL, QBOP KBO BXV OPVOV LBO LXRO CI SX’XJMI, KBO JCKO XPV EYKKOV LBO DJCMPV ZOICJO BYS, KXUYPD: “DJOXL EYPD, ICJ X LBCMKXPV XPV CPO PYDBLK Y BXNO ZOOP JOACMPLYPD LC UCM LBO IXZROK CI FXKL XDOK XPV LBO RODOPVK CI XPAYOPL EYPDK. SXU Y SXEO KC ZCRV XK LC AJXNO X IXNCMJ CI UCMJ SXGOKLU?” –OFYRCDMO, LXROK IJCS LBO LBCMKXPV XPV CPO PYDBLK

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Plain alphabet: abcdefghijklmnopqrstuvwxyz Cipher alphabet: ??????????????????????????

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Likeliest plaintext letters O = e X = t P = a

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English frequency rules Vowels appear before and after most other letters Consonants avoid many letters E.g., ‘e’ appears before/after virtually every other letter; while ’t’ is rarely seen before or after ‘b’, ‘d’, ‘g’, ‘j’, ‘k’, ‘m’, ‘q’, ‘v’ “ee” occurs more than “oo” occurs more than other double-vowels “a” occurs on its own often - more than “I” on its own ‘h’ frequently goes before ‘e’ but rarely after ‘e’

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Cipher O = e X = a Y = i B = h P = t ?

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“PCQ VMJiPD LhiK LiSe KhahJaWaV haV ZCJPe EiPD KhahJiUaJ LhJee KCPK. CP Lhe LhCMKaPV aPV IiJKL PiDhL, QheP Khe haV ePVeV Lhe LaRe CI Sa’aJMI, Khe JCKe aPV EiKKeV Lhe DJCMPV ZeICJe hiS, KaUiPD: “DJeaL EiPD, ICJ a LhCMKaPV aPV CPe PiDhLK i haNe ZeeP JeACMPLiPD LC UCM Lhe IaZReK CI FaKL aDeK aPV Lhe ReDePVK CI aPAiePL EiPDK. SaU i SaEe KC ZCRV aK LC AJaNe a IaNCMJ CI UCMJ SaGeKLU?” –eFiRCDMe, LaReK IJCS Lhe LhCMKaPV aPV CPe PiDhLK

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“Lhe” Plain alphabet: abcdefghijklmnopqrstuvwxyz Cipher alphabet: X???O??BY??????????L?????? “the”

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“PCQ VMJiPD thiK tiSe KhahJaWaV haV ZCJPe EiPD KhahJiUaJ thJee KCPK. CP the thCMKaPV aPV IiJKt PiDht, QheP Khe haV ePVeV the taRe CI Sa’aJMI, Khe JCKe aPV EiKKeV the DJCMPV ZeICJe hiS, KaUiPD: “DJeat EiPD, ICJ a thCMKaPV aPV CPe PiDhtK i haNe ZeeP JeACMPtiPD tC UCM the IaZReK CI FaKt aDeK aPV the ReDePVK CI aPAiePt EiPDK. SaU i SaEe KC ZCRV aK tC AJaNe a IaNCMJ CI UCMJ SaGeKtU?” –eFiRCDMe, taReK IJCS the thCMKaPV aPV CPe PiDhtK “aPV” 5 times

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“aPV” Plain alphabet: abcdefghijklmnopqrstuvwxyz Cipher alphabet: X??VO??BY????P?????L?????? “and”

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“now during this time shahra[qxzj]ad had borne king shahriyar three sons. on the thousand and ﬁrst night, when she had ended the tale of ma’aruf, she rose and kissed the ground before him, saying: “great king, for a thousand and one nights i have been recounting to you the fables of past ages and the legends of ancient kings. may i make so bold as to crave a favour of your ma[qxzj]esty?” –epilogue, tales from the thousand and one nights Plain alphabet: abcdefghijklmnopqrstuvwxyz Cipher alphabet: XZAVOIDBY?ERSPCF?JKLMNQ?U?

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Frequency Analysis: An analytical attack faster than naive brute force key search

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Ancient Steganography,  Scytale ~700 BC Brute Force Key Search Caesar Cipher ~50 BC Non-shifted  Substitution  Cipher Frequency  Analysis  ~800 AD

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Frequency Analysis considered indefensible for ~800 years

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Code-makers needed a  crypto-system that wasn’t vulnerable to  Frequency Analysis

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Leon Battista Alberti 1404-1472 “poly-alphabetic” cipher

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D M B X K I V A S Z N P L Y F C J O R T E Q H WG U Z J D P A I Q H T WL F B G O X N H U K R C Y V S E 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 Poly-alphabetic Substitution Cipher

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D M B X K I V A S Z N P L Y F C J O R T E Q H WG U Z J D P A I Q H T WL F B G O X N H U K R C Y V S E 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 “secret” “R?????” Poly-alphabetic Substitution Cipher

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D M B X K I V A S Z N P L Y F C J O R T E Q H WG U Z J D P A I Q H T WL F B G O X N H U K R C Y V S E 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 “secret” “RA????” Poly-alphabetic Substitution Cipher

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D M B X K I V A S Z N P L Y F C J O R T E Q H WG U Z J D P A I Q H T WL F B G O X N H U K R C Y V S E 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 “secret” “RAB???” Poly-alphabetic Substitution Cipher

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D M B X K I V A S Z N P L Y F C J O R T E Q H WG U Z J D P A I Q H T WL F B G O X N H U K R C Y V S E “RABH??” 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 “secret” Poly-alphabetic Substitution Cipher

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D M B X K I V A S Z N P L Y F C J O R T E Q H WG U Z J D P A I Q H T WL F B G O X N H U K R C Y V S E “RABHK?” 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 “secret” Poly-alphabetic Substitution Cipher

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D M B X K I V A S Z N P L Y F C J O R T E Q H WG U Z J D P A I Q H T WL F B G O X N H U K R C Y V S E 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 “secret” “RABHKK” Poly-alphabetic Substitution Cipher

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False frequencies ‘e’ is enciphered as both ‘A’ and ‘K’ ‘K’ is deciphered as both ‘e’ and ‘t’ “secret” “RABHKK”

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Poly-alphabetic beats frequency analysis, but …

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Poly-alphabetic ciphers are complex D M B X K I V A S Z N P L Y F C J O R T E Q H WG U Z J D P A I Q H T WL F B G O X N H U K R C Y V S E 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 D M B X K I V A S Z N P L Y F C J O R T E Q H WG U Z J D P A I Q H T WL F B G O X N H U K R C Y V S E D M B X K I V A S Z N P L Y F C J O R T E Q H WG U Z J D P A I Q H T WL F B G O X N H U K R C Y V S E

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Keyword  SECRET D M B X K I V A S Z N P L Y F C J O R T E Q H WG U Z J D P A I Q H T WL F B G O X N H U K R C Y V S E 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

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Le Chiffre Indéchiffrable created by Blaise de Vigenère 1523 - 1596 Created new  poly-alphabetic cipher

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Vigenère Square

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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

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Repeat keyword for all of text Plaintext: AttackFromTheSouthAtDawn Ciphertext: ???????????????????????? Keyword: SECRETSECRETSECRETSECRET

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Plaintext: AttackFromTheSouthAtDawn Ciphertext: SXVRGDXVQDXAWWQLXASXFRAG Keyword: SECRETSECRETSECRETSECRET

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Industrial Revolution ~1760 - 1840

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“Black Chambers” • 1700s • “Assembly-line” Cryptanalysis • Each European power had one • Breaking all mono-alphabetic ciphers • Encouraged adoption of Vigenère Square for  poly-alphabetic ciphers

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Ancient Steganography,  Scytale Brute Force Key Search Caesar Shift Non-shifted  Substitution Frequency  Analysis Homophonic Substitution Renaissance Poly-alphabetic Substitution Le Chiffre Indéchiffrable ~1550 AD Assembly-line Frequency Analysis ~1700’s Industrial

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Charles Babbage • 1791 - 1871 • 1854: Broke Vigenère Cipher • Without machinery

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REPEATING KEYWORD Plaintext: AttackFromTheSouthAtDawn Ciphertext: SXVRGDXVQDXAWWQLXASXFRAG Keyword: SECRETSECRETSECRETSECRET

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False SYMBOL frequencies • ‘e’ is enciphered as both ‘A’ and ‘K’ • ‘K’ is deciphered as both ‘e’ and ‘t’ “secret” “RABHKK”

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Word frequencies

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Plaintext: thesunandthemaninthemoon Ciphertext: DPRYEVNTNBUKWIAOXBUKWWBT Keyword: KINGKINGKINGKINGKINGKING

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Plaintext: thesunandthemaninthemoon Ciphertext: DPRYEVNTNBUKWIAOXBUKWWBT Keyword: KINGKINGKINGKINGKINGKING

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Breaking Vigenère • Look for repeated sequences of letters • Measure spacing between repetitions • Identify most likely length of key: L

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Cipher text WUBEFIQLZURMVOFEHMYMWTIXCQTMPIFKRZUPMVOIRQMM WOZMPULMBNYVQQQMVMVJLEYMHFEFNZPSDLPPSDLPEVQM WCXYMDAVQEEFIQCAYTQOWCXYMWMSEMEFCFWYEYQETRLI QYCGMTWCWFBSMYFPLRXTQYEEXMRULUKSGWFPTLRQAERL UVPMVYQYCXTWFQLMTELSFJPQEHMOZCIWCIWFPZSLMAEZ IQVLQMZVPPXAWCSMZMORVGVVQSZETRLQZPBJAZVQIYXE WWOICCGDWHQMMVOWSGNTJPFPPAYBIYBJUTWRLQKLLLMD PYVACDCFQNZPIFPPKSDVPTIDGXMQQVEBMQALKEZMGCVK UZKIZBZLIUAMMVZ

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REPETITIONS EFIQ, PSDLP, WCXYM, ETRL WUBEFIQLZURMVOFEHMYMWTIXCQTMPIFKRZUPMVOIRQMM WOZMPULMBNYVQQQMVMVJLEYMHFEFNZPSDLPPSDLPEVQM WCXYMDAVQEEFIQCAYTQOWCXYMWMSEMEFCFWYEYQETRLI QYCGMTWCWFBSMYFPLRXTQYEEXMRULUKSGWFPTLRQAERL UVPMVYQYCXTWFQLMTELSFJPQEHMOZCIWCIWFPZSLMAEZ IQVLQMZVPPXAWCSMZMORVGVVQSZETRLQZPBJAZVQIYXE WWOICCGDWHQMMVOWSGNTJPFPPAYBIYBJUTWRLQKLLLMD PYVACDCFQNZPIFPPKSDVPTIDGXMQQVEBMQALKEZMGCVK UZKIZBZLIUAMMVZ

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spacing between repetitions Repetition Spacing Possible Length of Key 2 3 4 5 6 7 8 9 10 11 121314 15 1617181920 EFIQ 95 ✓ ✓ PSDLP 5 ✓ WCXYM 20 ✓ ✓ ✓ ✓ ✓ ETRL 120 ✓ ✓ ✓ ✓ ✓ ✓ ✓ ✓ ✓ ✓

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5 separate cipher texts WIREWQFPROLVVEESSV XVITXSCYLGWYXELWRL VXLSECWLQPSRQRBQCH OTPYWLCNPVGVAMZUZ WIREWQFPROLVVEESSV XVITXSCYLGWYXELWRL VXLSECWLQPSRQRBQCH OTPYWLCNPVGVAMZUZ WIREWQFPROLVVEESSV XVITXSCYLGWYXELWRL VXLSECWLQPSRQRBQCH OTPYWLCNPVGVAMZUZ WIREWQFPROLVVEESSV XVITXSCYLGWYXELWRL VXLSECWLQPSRQRBQCH OTPYWLCNPVGVAMZUZ WIREWQFPROLVVEESSV XVITXSCYLGWYXELWRL VXLSECWLQPSRQRBQCH OTPYWLCNPVGVAMZUZ Break each with frequency analysis

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Ancient Steganography,  Scytale Brute Force Key Search Caesar Shift Non-shifted  Substitution Frequency  Analysis  ~800 AD Homophonic Substitution Renaissance Poly-alphabetic Substitution Le Chiffre Indéchiffrable ~1550 AD Assembly-line Frequency Analysis ~1700’s Industrial Babbage Frequency Analysis ~1800’s

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Electric Telegraphs • Buried underground or suspended overhead • 1844  60km wire between Baltimore & Washington DC

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How can you represent letters and words as electrical signals?

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Morse Code: “Encoding” not “Encryption”

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I.e., this is still “plaintext”

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Radio, 1899-1901 • 3,000 km from Cornwall to to Newfoundland • Transatlantic communication • Instant military commands • All messages reach enemy too • Increases need for encryption

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Enigma: Electrical Encryption • Arthur Scherbius, 1918 • Mass Production in 1925 CC BY-SA 3.0, https://commons.wikimedia.org/w/index.php?curid=497329

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Input Keyboard Rotors Output Lampboard

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By User:RadioFan, CC BY-SA 3.0, https://commons.wikimedia.org/w/index.php?curid=30719651

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By MesserWoland - Own work based on Image:Enigma-action.pnj by Jeanot; original diagram by Matt Crypto, CC BY-SA 3.0, https://commons.wikimedia.org/w/index.php?curid=1794494

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3 rotors of 26 wirings 26 x 26 x 26 = 17,576 Cipher Alphabets

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17,576 orientations x 6 arrangements = 105,456 Cipher Alphabets

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105,456 possible keys • A new key was used every day • Assume 1 orientation check per minute • (Just type ciphertext and look at plaintext) • 96 enigma machines = .75 days to crack

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Plugboard By Bob Lord - German Enigma Machine, uploaded in english wikipedia on 16. Feb. 2005 by en:User:Matt Crypto, CC BY-SA 3.0, https://commons.wikimedia.org/w/index.php?curid=258976 Swap up to 6 of 26 letters

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100,391,791,500 Plugboard Settings

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10,586,916,711,696 (10 trillion) Total Possible Keys

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10,586,916,711,696 possible keys • At 1 check per minute: • 38,291,799 enigma machines = 1 day to crack

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Message Keys • Using day key, send a message rotor orientation ﬁrst.   E.g., A, S, D • Send it at the beginning, twice for integrity.   E.g., ‘asdasd’ = QWERTY • Receiver types QWERTY, sees ‘asdasd’ • Re-orients their rotors to A, S, D for the rest of the message • Minimizes amount of ciphertext created by day key

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Is cracking Enigma possible? • At 1 check per minute: • 38,291,799 enigma machines = 1 day to crack     A SINGLE MESSAGE!

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Ancient Steganography,  Scytale Brute Force Key Search Caesar Shift Non-shifted  Substitution Frequency  Analysis  ~800 AD Homophonic Substitution Renaissance Poly-alphabetic Substitution Le Chiffre Indéchiffrable Assembly-line Frequency Analysis Industrial Babbage Frequency Analysis One-Time Pad Enigma ~1925

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Cracking Enigma

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Polish Biuro Szyfrów • Established after WWI to protect Poland from Russian & Germany • Received photographs of Enigma instruction manual from French espionage • Deduced rotor wirings • Usage of codebook A. Jankowski "Warszawa" Publisher:Wydawnictwo Polskie, Poznań,   Public Domain, https://commons.wikimedia.org/w/index.php?curid=1514113

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Marian Rejewski By Unknown - Rejewski's daughter's private archive, CC BY-SA 2.5, https://commons.wikimedia.org/w/index.php?curid=216461

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Found “chain” cycles  in the first 6 letters 4th Letter: FQHPLWOGBMVRXUYCZITNJEASDK 1st Letter: ABCDEFGHIJKLMNOPQRSTUVWXYZ 3 links: A-F-W-A

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Found “chain” loops  in the first 6 letters 4th Letter: FQHPLWOGBMVRXUYCZITNJEASDK 1st Letter: ABCDEFGHIJKLMNOPQRSTUVWXYZ 7 links: C-H-G-O-Y-D-P-C

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Marian Rejewski • Realized the # links in the chain were only caused by the rotors • Could try to break the 105,456 possible rotor settings, not all 10,000,000,000,000,000 possible day keys • 100,000,000,000 times easier By Unknown - Rejewski's daughter's private archive, CC BY-SA 2.5, https://commons.wikimedia.org/w/index.php?curid=216461

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Cyclometer • Team checked each of 105,456 possible settings on replica Enigma machines and recorded which chains were generated by each rotor setting • Took 1 year to complete • Could look up rotor settings by chains found in ﬁrst 6 letters of ciphertext http://www.cryptomuseum.com/crypto/cyclometer/index.htm

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Cyclometer created the first “Rainbow Table” for looking up cryptographic keys

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How to find the plugboard settings out of 100,391,791,500? • Plugboard: Un-plug all • Rotor Arrangement: III, I, II • Initial Rotor Orientations: Q, C, W • Type in ciphertext, see: • “rettew” • Swap R/W = Wetter (weather)

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Polish Cryptographic Bombs • 6 machines for the 6 possible rotor arrangements • Each with 6 full Enigma rotor sets at top for the 6 characters of the repeated message key • Given a number of “females” to ﬁnd, Bomba could recover settings in less than 2 hours

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British Bombes • 36 rotors arrange in 3 banks of 12 • 210 bombes by the end of the war • Operated by 2,000 members of Women’s Royal Navy Service

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Colossus • Inspired by Turings ideas and his bombe • 1,500 electronic valves - faster than electromechanical relay switches • Programmable - ﬁrst computers?

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Ancient Steganography,  Scytale Brute Force Key Search Caesar Shift Non-shifted  Substitution Frequency  Analysis  ~800 AD Homophonic Substitution Renaissance Poly-alphabetic Substitution Le Chiffre Indéchiffrable Assembly-line Frequency Analysis Industrial Babbage Frequency Analysis Enigma ~1925 Colossus Mark 1 1943 Computer

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Computer Cryptography

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In the early days of computing, electrical signals were much harder to measure and control precisely It made more sense to only distinguish between an “on” state and an “off” state

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Like the telegraph required morse to encode messages into electrical signals … In computers, we need a way to encode messages in 1’ and 0’s

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ASCII 1963 Encoding,  not encryption  (like Morse code) E.g., A: 1000001 B: 1000010

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In Binary, we encrypt at the level of 1’s and 0’s

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This is called “bitwise”

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Bitwise anagram For example, consider this short sentence. 01000110011011110111001000100000011001010111100001100001011011010111000001101100011001010010110000100000011000110 11011110110111001110011011010010110010001100101011100100010000001110100011010000110100101110011001000000111001101 101000011011110111001001110100001000000111001101100101011011100111010001100101011011100110001101100101 “Bitwise” rail fence cipher with 2 rails 00010111010101000100011001000110010001100100011001000101011101110101011001000100010101000100011001100101010001010 11001110101010001000101010001110100010001110101010010101011110000001011110010011011110010101011001000001001101110 101101100110101011110000001110100010011101000011011000101111001110000011011011101011101011101010011011

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Bitwise substitution: XOR The XOR operator outputs a 1 whenever the inputs do not match, which occurs when one of the two inputs is exclusively true 0 XOR 0 = 0 0 XOR 1 = 1 1 XOR 0 = 1 1 XOR 1 = 0

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Bitwise substitution: XOR For example, consider this short sentence. 01000110011011110111001000100000011001010111100001100001011011010111000001101100011001010010110000100000011000110 11011110110111001110011011010010110010001100101011100100010000001110100011010000110100101110011001000000111001101 101000011011110111001001110100001000000111001101100101011011100111010001100101011011100110001101100101 Key: “Julius Caesar” 01001010011101010110110001101001011101010111001100100000010000110110000101100101011100110110000101110010 Output 10001100110111101110010001000000110010101111000011000010110110101110000011011000110010100101100001000000110001101 10111101101110011100110110100101100100011001010111001000100000011101000110100001101001011100110010000001110011001 00010000110100001111000011101010101010000000001000101001011010001010100000000000111010000001000010111

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Bitwise substitution: XOR For example, consider this short sentence. 010001100110111101110010001000000110010101111000011000010110110101110000011011000110010100101100001000000110001101 101111011011100111001101101001011001000110010101110010001000000111010001101000011010010111001100100000011100110110 1000011011110111001001110100001000000111001101100101011011100111010001100101011011100110001101100101 Key: “random” 1|0’s length of plaintext 000000111010001101000011010010111001100100000011100110110100001101111011100100111010000100000011100110110010101101 110011101000110010101101110011000110110010101000110011011110111001000100000011001010111100001100001011011010111000 0011011000110010100101100001000000110001101101111011011100111001101101001011001000110010101110010001 Output 100011001101111011100100010000001100101011110000110000101101101011100000110110001100101001011000010000001100011011 011110110111001110011011010010110010001100101011100100010000001110100011010000110100101110011001000000111001100100 010000110100001111000011101010101010000000001000101001011010001010100000000000111010000001000010111

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Bitwise substitution: XOR For example, consider this short sentence. 010001100110111101110010001000000110010101111000011000010110110101110000011011000110010100101100001000000110001101 101111011011100111001101101001011001000110010101110010001000000111010001101000011010010111001100100000011100110110 1000011011110111001001110100001000000111001101100101011011100111010001100101011011100110001101100101 Key: “random” 1|0’s length of plaintext 000000111010001101000011010010111001100100000011100110110100001101111011100100111010000100000011100110110010101101 110011101000110010101101110011000110110010101000110011011110111001000100000011001010111100001100001011011010111000 0011011000110010100101100001000000110001101101111011011100111001101101001011001000110010101110010001 Output 100011001101111011100100010000001100101011110000110000101101101011100000110110001100101001011000010000001100011011 011110110111001110011011010010110010001100101011100100010000001110100011010000110100101110011001000000111001100100 010000110100001111000011101010101010000000001000101001011010001010100000000000111010000001000010111

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Horst Feistel 1971: Published “Lucifer” cipher for computer encryption First(?) Block Cipher

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XOR S-box Permutation

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SP Network

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Lucifer Cipher: “block” cipher Break message into 128-bit blocks 128-bit key 16 rounds: Break block in half the f-function is calculated using that round's subkey and the left half of the block. The result is then XORed to the right half of the block, which is the only part of the block altered for that round. After every round except the last one, the right and left halves of the block are swapped.

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256 bit message (in ASCII) 01010100011010000110010100100000010101010101001101000001001000000100111001010011 01000001001000000111001101110100011011110111001001100101011100110010000001111001 01101111011101010111001000100000011101000111011101100101011001010111010001110011 0010000100100001

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Break into 128-bit blocks 01010100011010000110010100100000010101010101001101000001001000000100111001010011010000010010000001110011011101000110111101110010 01100101011100110010000001111001011011110111010101110010001000000111010001110111011001010110010101110100011100110010000100100001 The USA NSA stor es your tweets!!

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Generate 128-bit key awesomepassword! 01100001011101110110010101110011011011110110110101100101011100000110000101110011011100110111011101101111011100100110010000100001

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Break block in half 01010100011010000110010100100000010101010101001101000001 The USA NSA stor 0100111001010011010000010010000001110011011101000110111101110010

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Generate 72-bit sub-key awesomepassword! 01100001011101110110010101110011011011110110110101100101011100000110000101110011011100110111011101101111011100100110010000100001 a a 01100001 01100001 wesomep 01110111011001010111001101101111011011010110010101110000

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Rotate key left 7 bytes password!awesome 01110000011000010111001101110011011101110110111101110010011001000010000101100001011101110110010101110011011011110110110101100101 7 bytes

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…

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Data Encryption Standard (DES) 1977 Lucifer with 56-bit keys So the NSA could brute force keys if they “needed” to

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Ancient Steganography,  Scytale Brute Force Key Search Caesar Shift Non-shifted  Substitution Frequency  Analysis Homophonic Substitution Renaissance Poly-alphabetic Substitution Le Chiffre Indéchiffrable Assembly-line Frequency Analysis Industrial Babbage Frequency Analysis One-Time Pad Enigma Cryptanalytic “Bombs”: Polish, British, US Lucifer, DES 1971-1977 Computer

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How hard is it to ﬁnd a  binary 56-bit key?

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1001101010011010100110101001 1010100110101001101010011010 Unique Possible Permutations 256 72,057,594,037,927,936 72 quadrillion (million billion) In 1976, estimated to cost $20M to build a computer to crack such a key Affordable to the NSA

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DES 1971-1977 Computer- powered Brute Force Key Search

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By Max Roser - https://ourworldindata.org/uploads/2019/05/Transistor-Count-over-time-to-2018.png, CC BY-SA 4.0, https://commons.wikimedia.org/w/index.php?curid=79751151

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1100110101001101010011010100 1101010011010100110101001101 0 Unique Possible Permutations 256 72,057,594,037,927,936 72 quadrillion (million billion) 257 144,115,188,075,855,870 144 quadrillion (million billion)

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DES 1971-1977 Computer-powered Brute Force Key Search Moore’s Law

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3DES EDE:  DES: Encrypt, Decrypt, Encrypt https://www.researchgate.net/ﬁgure/Flowchart-of-3DES-encryption-and-decryption-algorithm-40_ﬁg4_322277374

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What about messages that are longer than the key?

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Block cipher  mode of operation

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Electronic Codebook (ECB) https://en.wikipedia.org/wiki/Block_cipher_mode_of_operation

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https://en.wikipedia.org/wiki/Block_cipher_mode_of_operation

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Attribution, https://commons.wikimedia.org/w/index.php?curid=828161

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Cipher Block Chaining (CBC) https://en.wikipedia.org/wiki/Block_cipher_mode_of_operation

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Attribution, https://commons.wikimedia.org/w/index.php?curid=828161

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DES Computer-powered Brute Force Key Search Moore’s Law 3DES + CBC

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The forever problem of cryptography: Key distribution

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Banks literally ﬂew people around with code-books of keys

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We need a way to communicate secret keys over non-secret channels.

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Whitﬁeld Difﬁe Stanford AI Lab 1974

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Martin Hellman IBM Watson Research Center 1968-1969

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New Directions in Cryptography Published 1976

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Alice, Bob, and Eve Alice and Bob need to communicate securely They need to share a secret They only have public channels between them “Eve is always eavesdropping” How can they share a secret without sharing it with Eve?

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Difﬁe-Hellman Key Establishment

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https://www.khanacademy.org/computing/computer-science/cryptography/modern-crypt/v/difﬁe-hellman-key-exchange-part-1

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https://www.khanacademy.org/computing/computer-science/cryptography/modern-crypt/v/difﬁe-hellman-key-exchange-part-1

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https://www.khanacademy.org/computing/computer-science/cryptography/modern-crypt/v/difﬁe-hellman-key-exchange-part-1

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https://www.khanacademy.org/computing/computer-science/cryptography/modern-crypt/v/difﬁe-hellman-key-exchange-part-1 + ____ ____ +

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The key can be anything that can encode to 1’s and 0’s So, anything … like a number.

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And in MATH! , we have some 1-way functions!

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Modular Arithmetic aka “Clock” arithmetic https://www.khanacademy.org/computing/computer-science/cryptography/modern-crypt/v/discrete-logarithm-problem

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To ﬁnd 46 mod 12 … https://www.khanacademy.org/computing/computer-science/cryptography/modern-crypt/v/discrete-logarithm-problem

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Wrap a cord 46 “hours” long around a 12-hour clock … … and it ends on 10

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Easy to perform … 46 mod 12 is “congruent” to 10 generator Modulus

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? mod 12 ≡ 10 … hard to reverse

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? mod 12 ≡ 10 22 mod 12 ≡ 10 34 mod 12 ≡ 10 46 mod 12 ≡ 10 58 mod 12 ≡ 10 70 mod 12 ≡ 10 .. mod 12 ≡ 10 … impossible to reverse!

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… impossible for recipient too!

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Alice picks an exponent https://www.khanacademy.org/computing/computer-science/cryptography/modern-crypt/v/difﬁe-hellman-key-exchange-part-2 Prime Modulus “n” generator “g”

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Alice keeps her exponent secret https://www.khanacademy.org/computing/computer-science/cryptography/modern-crypt/v/difﬁe-hellman-key-exchange-part-2 Prime Modulus “n” generator “g”

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“Discrete Logarithm” problem https://www.khanacademy.org/computing/computer-science/cryptography/modern-crypt/v/difﬁe-hellman-key-exchange-part-2

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“Discrete Logarithm” problem Have to resort to “brute force” guessing the exponent

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For small numbers, it’s easy, but not for a large prime modulus. https://www.khanacademy.org/computing/computer-science/cryptography/modern-crypt/v/difﬁe-hellman-key-exchange-part-2

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How can we turn that single exponent secret into 2 secrets?

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“Commutative” Arithmetic:  Order of operands doesn’t matter 3 + 5 5 + 3 = = 8 3 * 5 = = 15 5 * 3

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“Commutative” Arithmetic:  Order of operands doesn’t matter 323 332 = = 729 3 + 5 5 + 3 = = 8 3 * 5 = = 15 5 * 3

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Alice and Bob publicly agree on a generator and prime modulus https://www.khanacademy.org/computing/computer-science/cryptography/modern-crypt/v/difﬁe-hellman-key-exchange-part-2

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Alice picks a private number, and sends the result to Bob https://www.khanacademy.org/computing/computer-science/cryptography/modern-crypt/v/difﬁe-hellman-key-exchange-part-2

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Bob picks a private number, and sends the result to Alice https://www.khanacademy.org/computing/computer-science/cryptography/modern-crypt/v/difﬁe-hellman-key-exchange-part-2

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Now the cool part … https://www.khanacademy.org/computing/computer-science/cryptography/modern-crypt/v/difﬁe-hellman-key-exchange-part-2

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Alice raises Bob’s result to her private exponent and gets 10

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Bob raises Alice’s mixture to his private exponent and also gets 10!

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Because their results were calculated from the shared public generator and prime modulus

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So, they did the same calculation with exponents in different order, which doesn’t affect the result

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Public Key Cryptography!

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Difﬁe-Hellman  Key Establishment 3DES +

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DES Computer-powered Brute Force Key Search Moore’s Law 1970+ 3DES + CBC DH + 3DES + CBC 1976

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Use Difﬁe-Hellman Exchange to make a key … … for Triple-DES … … with Cipher Block Chaining mode. … Encrypt-Decrypt-Encrypt …

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What’s RSA?

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Difﬁe-Hellman makes a new key between every 2 people! https://www.khanacademy.org/computing/computer-science/cryptography/modern-crypt/v/intro-to-rsa-encryption

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https://www.khanacademy.org/computing/computer-science/cryptography/modern-crypt/v/intro-to-rsa-encryption

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Clifford Cox 1971 Trap Door  One-way Function By Royal Society uploader - Own work, CC BY-SA 4.0, https://commons.wikimedia.org/w/index.php?curid=43268163

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https://www.khanacademy.org/computing/computer-science/cryptography/modern-crypt/v/intro-to-rsa-encryption

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The “e” means encrypt! “d” is for decrypt! https://www.khanacademy.org/computing/computer-science/cryptography/modern-crypt/v/intro-to-rsa-encryption

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https://www.khanacademy.org/computing/computer-science/cryptography/modern-crypt/v/intro-to-rsa-encryption

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https://www.khanacademy.org/computing/computer-science/cryptography/modern-crypt/v/intro-to-rsa-encryption

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Bob's number

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Ron Rivest, Adi Shamir, Leonard Adelman

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DES Computer-powered Brute Force Key Search Moore’s Law 1970+ 3DES + CBC DH/RSA + 3DES + CBC 1976

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Public Key Certiﬁcates https://www.youtube.com/watch?v=704dudhA7UI Alice's Alice's Alice's

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Look! The public exponent and modulus!

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Another RSA public exponent and modulus

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Quantum Computing For fun, proﬁt, and breaking the whole world

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Public Key Certiﬁcates https://www.youtube.com/watch?v=704dudhA7UI Alice's Alice's Alice's Quantum- cracked

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DES Computer-powered Brute Force Key Search Moore’s Law 3DES + CBC DH/RSA + 3DES + CBC Quantum Computing

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2048-bit RSA key needs  4096-qubit computer to crack

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DES Computer-powered Brute Force Key Search Moore’s Law 3DES + CBC DH/RSA + 3DES + CBC Quantum Computing Post-Quantum Cryptography

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Don’t invent your own crypto

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Mind your keys

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https://techcrunch.com/2019/10/21/nordvpn-conﬁrms-it-was-hacked/

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Questions? Scytale Caesar Cipher Unshifted cipher Frequency Analysis Poly-alphabetic cipher Vigenere Square Enigma Lucifer/DES Modes of Encryption Difﬁe-Hellman RSA Quantum speakerdeck.com/groovecoder