1. Campbell R. Harvey Duke University and NBER
Innovation and Cryptoventures
Cryptology
Campbell R. Harvey
Duke University and NBER
January 19, 2018

2. Campbell R. Harvey 2018

3. Overview Cryptology Cryptography Symmetric Ciphers Asymmetric Ciphers
Protocols
Cryptanalysis
Campbell R. Harvey 2018

4. Overview Cryptology Cryptography Symmetric Ciphers Asymmetric Ciphers
Protocols
Cryptanalysis
Science of making things secret
Science of breaking cryptosystems
Campbell R. Harvey 2018

5. Overview Cryptology Cryptography Symmetric Ciphers Asymmetric Ciphers
Protocols
Cryptanalysis
Science of making things secret
Science of breaking cryptosystems
Share a secret key
Share a public key but each has secret private key
Application of cryptographic algos, like TLS
Campbell R. Harvey 2018

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.
Campbell R. Harvey 2018

7. Overview We will not talk about steganography
This is the practice of concealing a message
In contrast to cryptography, steganography does not attract any attention
In cryptography, you encrypt the content of the message
In steganography, you focus on hiding the fact that a secret message is even being sent
Campbell R. Harvey 2018

8. 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
Campbell R. Harvey 2018

9. Cipher From Arabic, sifr, meaning “nothing”
Method of concealment where letters are replaced by other letters, numbers or symbols – or the order of the letters is shifted
Code is related but different. Code is a method of concealment that uses words, numbers or syllables to replace original words or phrases (does not appear until modern times). Texting short forms, e.g. ttyl, would not qualify because everyone knows them.
Ciphers traditionally have been broken by frequency analysis. For example, “e” and “t” are the two most common English letters.
Campbell R. Harvey 2018

10. 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
Campbell R. Harvey 2018

11. 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
Campbell R. Harvey 2018

12. Caesar Cipher is early example of using modulo arithmetic.
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 “%”)
Campbell R. Harvey 2018
Caesar cipher is a special case of an “affine cipher”; more generally encrypted (x) = (ax + k) mod 26; a=1 for Caesar.

13. Substitution Cipher Definition
“Plaintext” is the message you want to encrypt (e.g. CAM)
“Ciphertext” is the encrypted message (e.g. FDP)
Campbell R. Harvey 2018

14. Substitution Cipher Caesar Cipher is monoalphabetic cipher
Each plaintext letter will always have the same ciphertext letter
Easy to crack – brute force only requires 25 different tries
Campbell R. Harvey 2018

15. Substitution Cipher
It is also possible to use a keyword (with no repeating letters).
Suppose keyword = cipher
CAM = PCY
But this is just one of many possible alternative reorderings
Campbell R. Harvey 2018

16. Substitution Cipher Many other monoalphabetic ciphers
There are 26! (factorial, i.e. 26x25x24x…x1) ways to reorder
This is a large number ( x1026 ) 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
Campbell R. Harvey 2018

17. Substitution Cipher Breaking monoalphabetic ciphers
However, you do not need brute force
These ciphers are vulnerable to frequency analysis
Campbell R. Harvey 2018

18. Substitution Cipher Breaking monoalphabetic ciphers
However, you do not need brute force
These ciphers are vulnerable to frequency analysis
Campbell R. Harvey 2018

19. 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
Campbell R. Harvey 2018

20. 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
Campbell R. Harvey 2018

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 (which is “D”)
Campbell R. Harvey 2018

22. 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 (which is “D”)
For “A” go to the row beginning with “T” and read off “A” column “T”
Campbell R. Harvey 2018

23. 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 (which is “D”)
For “A” go to the row beginning with “T” and read off first column “T”
For “M” go to the row beginning with “C” and read off letter under “M” which is “O” etc.
Campbell R. Harvey 2018

24. 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
19+19=38 mod 26 =12
(divide 38/26 and remainder is 12)
Excel
=mod((ROW1 + ROW2),26)
Campbell R. Harvey 2018

25. Substitution Cipher There are 25 reorderings with Vigenère square
Easy to decipher. Write down code and keystream underneath and subtract
Excel
=mod((ROW1 - ROW2),26)
Campbell R. Harvey 2018

26. 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
Col #1 Col # Col #2
Campbell R. Harvey 2018

27. 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
Campbell R. Harvey 2018

28. 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)
Campbell R. Harvey 2018

29. Permutation Cipher Mixes up the letters.
Example: (1, 2, 3) -> (3, 1, 2)
So the word “THE” would be “ETH”
To decrypt, we use the inverse permutation
Campbell R. Harvey 2018

30. 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. b1xK (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
Campbell R. Harvey 2018

31. 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
Campbell R. Harvey 2018

32. Advanced Ciphers This could be a legit purchase by one
of five people that can access my eBay account.
Campbell R. Harvey 2018

33. 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?
Campbell R. Harvey 2018

34. Advanced Ciphers EC
SHA-384
RSA
AES-384
Campbell R. Harvey 2018

35. Advanced Ciphers Real sender: Someone at bundugamelodge.co.za
Campbell R. Harvey 2018