The Blockchain Identitycharvey/Teaching/697...Substitution Cipher Caesar Cipher is early example of using modulo arithmetic. • Let A=0, B=1, …, Z=25 Then: • Encrypted(x) = (x

CryptologyCampbell R. Harvey

Duke University and NBER

Innovation and Cryptoventures

Campbell R. Harvey 2020


Cryptology

Cryptography

Symmetric Ciphers

Asymmetric Ciphers

Protocols

Cryptanalysis

Overview


Cryptology

Cryptography

Symmetric Ciphers

Asymmetric Ciphers

Protocols

Cryptanalysis

Overview

Science of making things secret Science of breaking cryptosystems


Cryptology

Cryptography

Symmetric Ciphers

Asymmetric Ciphers

Protocols

Cryptanalysis

Overview

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

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.

Polybius square

300-400 BCE Polybius advocated a square (originally using the Greek alphabet)• Note that i/j are ambiguous• Read off row, column. CAM = 13, 11, 32


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


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


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 2020Caesar cipher is a special case of an “affine cipher”; more generally encrypted (x) = (ax + k) mod 26; a=1 for Caesar.

Substitution Cipher

Definition• “Plaintext” is the message you want to encrypt (e.g., CAM)• “Ciphertext” is the encrypted message (e.g., FDP)


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


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 ZCipher 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

Substitution Cipher

Many other monoalphabetic ciphers• There are 26! (factorial, i.e. 26x25x24x…x1) ways to reorder • This is a large number (4.032914611x1026 ) 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


Substitution Cipher

Breaking monoalphabetic ciphers• However, you do not need brute force• These ciphers are vulnerable to frequency

analysis


Substitution Cipher

Breaking monoalphabetic ciphers• However, you do not need brute force• These ciphers are vulnerable to frequency

analysis

Campbell R. Harvey 2020https://en.wikipedia.org/wiki/Letter_frequency

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

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


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 YB T C B T C B T C B T C B T C

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”)


Substitution Cipher


“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”)


Substitution Cipher


“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. Campbell R. Harvey 2020

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 YB T C B T C B T C B T C B T C

19+19=38 mod 26 =12(divide 38/26 and remainder is 12)

Excel=mod((ROW1 + ROW2),26)

2 0 12 7 0 17 21 4 24 6 20 8 11 19 24+ 1 19 2 1 19 2 1 19 2 1 19 2 1 19 2

3 19 14 8 19 19 22 23 0 7 13 10 12 12 0= D T O I T T W X A H N K M M A

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)

D T O I T T W X A H N K M M AB T C B T C B T C B T C B T C

3 19 14 8 19 19 22 23 0 7 13 10 12 12 0- 1 19 2 1 19 2 1 19 2 1 19 2 1 19 2

2 0 12 7 0 17 21 4 24 0 6 20 8 11 19 24= C A M H A R V E Y G U I L T Y

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 2610

different tries in brute force (that’s 141 trillion tries)


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)

Campbell R. Harvey 2020*Also known as Lucifer, based on the work of Horst Feistel**Also known as Rijndael, after founders Vincent Rijmen and Joan Daemen

TakeawaysA 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.Campbell R. Harvey 2020

Supplementary material


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 #3 Col #2Campbell R. Harvey 2020

Keyword B T COrder 1 3 2

Y O UR P HO N EI S NO T SE C U

Left over spaces R E A


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



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 YD I C E OA M O N UB O M O RC R P H P

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

C A M H A R V E Y I S S A T O S H I3 1 2 3 1 2 3 1 2 3 1 2 3 1 2 3 1 2M C A R H A Y V E S I S O A T I S H

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


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)

Campbell R. Harvey 2020*Also known as Lucifer, based on the work of Horst Feistel**Also known as Rijndael, after founders Vincent Rijmen and Joan Daemen

Advanced Ciphers


This could be a legit purchase by one of five people that can access my eBay account.

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?

Advanced Ciphers


AES-384

SHA-384

RSA

EC

Advanced Ciphers


Real sender: Someone atbundugamelodge.co.za

Substitution Cipher


SEAN WIEUIIUZH DTG CNP LBHXGK OZ BJQB FEQT XZBW JJOY TK FHR TPZWK PVU RYSQVOUPZXGG OEPH CK UASFKIPW PLVO JIZ HMN NVAEUD XYF DURJ BOVPA SF MLV FYYRDELVPL MFYSIN XY FQEO NPK M OBPC FYXJFHOHT AS ETOV B OCAJDSVQU M ZTZV TPHYDAW FQTI UTTJ J DOGOAIA FLWHTXTI QMTR SEA LVLFLXFO

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

Documents

The Blockchain Identitycharvey/Teaching/697...Substitution Cipher Caesar Cipher is early example of using modulo arithmetic. • Let A=0, B=1, …, Z=25 Then: • Encrypted(x) = (x