Innovation and Cryptoventures. Cryptology. Campbell R. Harvey. Duke University and NBER

Transcription

1 Innovation and Cryptoventures Cryptology Campbell R. Harvey Duke University and NBER

2 Campbell R. Harvey 2018

3 Overview Cryptology Cryptography Cryptanalysis Symmetric Ciphers Asymmetric Ciphers Protocols

4 Overview Cryptology Science of making things secret Cryptography Cryptanalysis Science of breaking cryptosystems Symmetric Ciphers Asymmetric Ciphers Protocols

5 Overview Cryptology Science of making things secret Cryptography Cryptanalysis Science of breaking cryptosystems Symmetric Ciphers Share a secret key Asymmetric Ciphers Share a public key but each has secret private key Protocols Application of cryptographic algos, like TLS

6 Overview Process of concealing messages Greek κρυπτω meaning secret or hidden Used for 4,000 years Early techniques involved concealed writing/symbols Parchments that had to be wrapped around a rod of a specific size to figure out the message Material drawn liberally from M. Cozzens and S. J. Miller, The Mathematics of Encryption, 2013.

7 Polybius square BCE Polybius advocated a square (originally using the Greek alphabet) Note that i/j are ambiguous Read off row, column. CAM = 13, 11, 32

8 Substitution Cipher Caesar Cipher shift letters by fixed number of places (originally 3). Note 3 is called the key. The shift could be arbitrary. +3 CAM=FDP Not very secure

9 Substitution Cipher Caesar Cipher is early example of using modulo arithmetic. If we shifted +26 (or -26), we end up with the regular alphabet If we shifted +27, it is the same as +1 If we shifted +54, it is the same as +2 A clock is modulo 12 Note: Modulo arithmetic very important for advanced encryption

10 Substitution Cipher Caesar Cipher is early example of using modulo arithmetic. Let A=0, B=1,, Z=25 Then: Encrypted(x) = (x + k) mod 26 Here k is the shift or key, mod is the modulo operation (in Python code on earlier slide denoted by % ) Caesar cipher is a special case of an affine cipher ; more generally encrypted (x) = (ax + k) mod 26; a=1 for Caesar.

11 Substitution Cipher Definition Plaintext is the message you want to encrypt (e.g., CAM) Ciphertext is the encrypted message (e.g., FDP)

12 Substitution Cipher Caesar Cipher is a monoalphabetic cipher Each plaintext letter will always have the same ciphertext letter Easy to crack brute force only requires 25 different tries

13 Substitution Cipher It is also possible to use a keyword (with no repeating letters). Suppose keyword = cipher CAM = PCY Normal alphabet 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 Cipher alphabet C I P H E R S T U V W X Y Z A B D F G J K L M N O Q But this is just one of many possible alternative reorderings

14 Substitution Cipher Many other monoalphabetic ciphers There are 26! (factorial, i.e. 26x25x24x x1) ways to reorder This is a large number ( x10 26 ) of distinct ciphers. Brute force: if you could try 1 trillion combinations a second, it would take 12,000 years to brute force all combinations

15 Substitution Cipher Breaking monoalphabetic ciphers However, you do not need brute force These ciphers are vulnerable to frequency analysis

16 Substitution Cipher Breaking monoalphabetic ciphers However, you do not need brute force These ciphers are vulnerable to frequency analysis

17 Properties of Valid Ciphers Properties of a valid encryption scheme Easy to encrypt Easy to transmit Easy to decode If intercepted, should be hard to decode Ideally, source of message should be validated

18 Substitution Cipher Even more advanced uses polyalphabetic substitution Use of Vigenère square (just like Caesar but all possible starting points) Define a keyword (called keystream ) and repeat it to make it as long as your message: suppose my key BTC C A M H A R V E Y G U I L T Y B T C B T C B T C B T C B T C

19 Substitution Cipher Encryption CAM HARVEY BTC BTCBTC For C, go to the row beginning with B (first letter of BTC) and read off the letter corresponding to C in the first row (= D )

20 Substitution Cipher Encryption CAM HARVEY BTC BTCBTC For C, go to the row beginning with B (first letter of BTC) and read off the letter corresponding to C in the first row (= D ) For A go to the row beginning with T and read off A column (= T )

21 Substitution Cipher Encryption CAM HARVEY BTC BTCBTC For C, go to the row beginning with B (first letter of BTC) and read off the letter corresponding to C in the first row (= D ) For A go to the row beginning with T and read off A column (= T ) For M go to the row beginning with C and read off letter under M (= O ) etc.

22 Substitution Cipher There are 25 reorderings with Vigenère square But the square is just a visual way of doing modulo arithmetic Let A =0, B =1,, Z =25 C A M H A R V E Y G U I L T Y B T C B T C B T C B T C B T C = D T O I T T W X A H N K M M A 19+19=38 mod 26 =12 (divide 38/26 and remainder is 12) Excel =mod((row1 + ROW2),26)

23 Substitution Cipher There are 25 reorderings with Vigenère square Easy to decipher. Write down code and keystream underneath and subtract D T O I T T W X A H N K M M A B T C B T C B T C B T C B T C = C A M H A R V E Y G U I L T Y Excel =mod((row1 - ROW2),26)

24 One-time Pad Keystream a set of shifts. Keystream length=plaintext length Shifts never fall into a repetitive pattern No frequency differential in terms of letters Ceasar has 26 different encryptions OTP has a Ceasar for every letter. So a 10 letter message would require different tries in brute force (that s 141 trillion tries)

25 Advanced Ciphers Modern ciphers use both substitution and transposition Foundational work by Claude Shannon Modern standards are DES* (Data Encryption Standard from early 1970s and no longer considered secure) and AES** (Advanced Encryption Standard adopted in 2001) *Also known as Lucifer, based on the work of Horst Feistel **Also known as Rijndael, after founders Vincent Rijmen and Joan Daemen

26 Takeaways A basic understanding of cryptography is crucial for not just blockchain but for business in general We have seen that JP Morgan s Quorum uses a blockchain with encrypted data Zcash is a cryptocurrency that is anonymous and uses encryption One issue is the keystream. In order to decrypt, that keystream needs to be communicated and that creates risk. Next, we need to develop a technology where two people can share a secret (like a keystream) by sending information that anyone can intercept (but not be able to deduce the keystream). Modulo arithmetic will come in handy.

27 Supplementary material

28 Transposition Cipher Letters remain the same but the order is scrambled Start with key word, say BTC Write down order of letters in keyword Fill out rectangle with message Read off columns in order YROIOERUHENSUAOPNSTCE Keyword B T C Order Y O U R P H O N E I S N O T S E C U Left over spaces R E A Col #1 Col #3 Col #2

29 Transposition Cipher Letters remain the same but the order is scrambled This type of cipher is immune to an attack based on frequency analysis because the exact same letters are used the order is subject to permutation

30 Transposition Cipher Chinese cipher Fill rectangle with message down far right column and up the next column Read off rows ESSIY DICEO AMONU BOMOR CRPHP = Your phone is compromised(abc) E S S I Y D I C E O A M O N U B O M O R C R P H P

31 Permutation Cipher Mixes up the letters. Example: (1, 2, 3) -> (3, 1, 2) So the word THE would be ETH C A M H A R V E Y I S S A T O S H I M C A R H A Y V E S I S O A T I S H To decrypt, we use the inverse permutation

32 Hill Cipher Uses matrix operations. Choose the length of blocks, say 3 Form 3x1 (3 rows, 1 column) matrices and use numbers for letters, i.e. A=0, B=1 Matrix K is the key and will by 3x3 (3 rows and 3 columns) Multiply each block by K, i.e. b 1 xk (result will be a 3x1) then modulo 26 each element. This produces the Hill Cipher To decipher, multiple each cipher block by the inverse of K, modulo 26

33 Advanced Ciphers Modern ciphers use both substitution and transposition Mixing is called product cipher Mix includes substitution, transformation and modulo operations Foundational work by Claude Shannon Modern standards are DES* (Data Encryption Standard from early 1970s and no longer considered secure) and AES** (Advanced Encryption Standard adopted in 2001) *Also known as Lucifer, based on the work of Horst Feistel **Also known as Rijndael, after founders Vincent Rijmen and Joan Daemen

34 Advanced Ciphers This could be a legit purchase by one of five people that can access my ebay account.

35 Advanced Ciphers This could be a legit purchase by one of five people that can access my ebay account. Why would I buy a 2009 Lenovo in 2017?

36 Advanced Ciphers EC SHA-384 RSA AES-384

37 Advanced Ciphers Real sender: Someone at bundugamelodge.co.za

38 Substitution Cipher SEAN WIEUIIUZH DTG CNP LBHXGK OZ BJQB FEQT XZBW JJOY TK FHR TPZWK PVU RYSQ VOUPZXGG OEPH CK UASFKIPW PLVO JIZ HMN NVAEUD XYF DURJ BOVPA SF MLV FYYRDE LVPL MFYSIN XY FQEO NPK M OBPC FYXJFHOHT AS ETOV B OCAJDSVQU M ZTZV TPHY DAW FQTI UTTJ J DOGOAIA FLWHTXTI QMTR SEA LVLFLXFO

39 Substitution Cipher Civil war message found in river after 147 years Keystream=ManchesterBluff Gen'l Pemberton, You can expect no help from this side of the river. Let Gen'l Johnston know, if possible, when you can attack the same point on the enemy's line. Inform me also and I will endeavour to make a diversion. I have sent you some caps. I subjoin despatch from Gen Johnston. The Confederacy used two main keystreams during the war: ManchesterBluff and CompleteVictory (both 15 characters). As the war ended, their code changed to ComeRetribution