CS 150 – Computing: From Ada to the Web

Cryptography

Protecting Information

• Frame message– Indicates what the message is

• Outer message– Tells how to interpret the message

• Inner message– The content of the message

• How do we protect the message from eavesdropping?

At War

• The earliest need for encryption came from war.

• Sending orders by carrier that could be captured was dangerous at best.

• Need to protect the message!• (Another early use: the Kama Sutra describes

it as a way to have an affair without “inconvenient discovery.”)

The Caesar Cipher

• The network: The Roman roads• The message: Orders to Roman troops• Also known as a Rotation Cipher, you simply

replace a letter with another letter that is a certain number of letters away.

• Technically, a Caesar Cipher is a Rotation Cipher where n = 3.

• Popularly, you can find this cipher today as a simple “decoder ring.”

Rotation Cipher

ABCDEFGHIJKLMNOPQRSTUVWXYZ

JIDKQACRSHLGWNFEXUZVTPMYOB

encrypt decr

ypt

CS DZ

Worked okay for 44BC, but…

• Language is not random!• Random strings: the probability of two letters

in the two messages matching is 1/26 (number of letters in alphabet)

• Same-encrypted strings: the output letters will match when the input letters match– This happens much more frequently because

some letters (e.g., “e” is ~13% of all letters) are more common

Vigenere Cipher

• Blaise de Vigenère in the 19th century• Used during the Confederacy during the Civil

War• Keyword rotational cipher• Plaintext: ATTACKATDAWN• Key: LEMONLEMONLE• Ciphertext: LXFOPVEFRNHR

Enigma• Invented commercially, 1923• German Navy, Army, Air Force• About 50,000 in use (many were

captured by Allies)• Modified throughout WWII, Germans

believed perfectly secure• Kahn’s Codebreakers (1967) didn’t

know it was broken• Turing’s 1940 Treatise on Enigma

declassified in 1996

Enigma machine at Bletchley Park

Rotor WheelsSimplesubstitution

Latch turns next rotor once per rotation

Imag

e fro

mht

tp://

en.w

ikip

edia

.org

/wik

i/Im

age:

Enig

ma-

actio

n.pn

g

Enigma’s Rotating Substitutions

ABCDEFGHIJKLMNOPQRSTUVWXYZ

JIDKQACRSHLGWNFEXUZVTPMYOB

SQHLZNYKXUWVJRDFBETIMOGACP

ABCDEFGHIJKLMNOPQRSTUVWXYZ

Whe

el 1

: Ro

tate

one

po

sitio

n ev

ery

lette

r

Whe

el 2

: Ro

tate

one

po

sitio

n ev

ery

26 le

tters

ABCDEFGHIJKLMNOPQRSTUVWXYZUAVGRDCBESYHLZOQKXTIMNJWFP

Whe

el 3

: Ro

tate

one

po

sitio

n wh

en

whee

l 2 c

ycle

s

Enigma’s Problems

• Each day, a new set of initial settings were used…– …and these were stored in a book that was stolen.

• Each network had a different setup for the machine…– …which was also stolen.

• For each message, a random set of three characters would be used to decipher the text…– …but people were lazy and used the same letters and

also repeated them at the beginning of the message

The best thing about bad encryption?

• We won WWII.• D-Day would not have happened without the

cracking of the Enigma.

Modern Ciphers

• RSA – popular public key cryptographic algorithm

• Found in common products• Not “perfect,” but “good enough” if the key is

long enough• Each entity needs a public and private key

RSA Key Generation• Choose two distinct large random prime numbers p and q• Compute n = pq

– n is used as the modulus for both the public and private keys• Compute the totient: φ(n) = (p − 1)(q − 1).• Choose an integer e such that 1 < e < φ(n), and e and φ(n)

share no factors other than 1 (i.e. e and φ(n) are coprime)– e is released as the public key exponent – 2^16 + 1 = 65537 is a

popular choice• Compute d such that d*e = 1 + kφ(n) for some integer k.

– d is kept as the private key exponent• Public key = (n, e)

Encrypting and Decrypting

• Encrypt: c = m^e mod n• Decrypt: m = c^d mod n

Example• Choose two prime numbers

– p = 61 and q = 53

• Compute n = p q– n = 61 * 53 = 3233

• Compute φ (n) = (p-1)(q-1) – φ(n) = (61 - 1)(53 - 1) = 3120

• Choose e > 1 coprime to 3120– e = 17

• Compute d, such that d*e = 1 + kφ(n) – d = 2753– 17 * 2753 = 46801 = 1 + 15 * 3120.

Example• The public key is (n = 3233, e = 17). For a message m, the

encryption function is:– c = m^e mod n= m^{17} mod {3233}.

• The private key is (n = 3233, d = 2753). The decryption function is:– m = c^d mod n = c^{2753} mod {3233}.

• For example, to encrypt m = 123, we calculate– c = 123^{17} mod {3233} = 855.

• To decrypt c = 855, we calculate– m = 855^{2753} mod {3233} = 123.

Key Exchange

• Alice comes up with a key– She puts the key in a box and locks it with her padlock

• Alice sends the box to Bob– Bob can’t get in the box, but he adds his padlock to

the box• Bob sends the box back to Alice– Alice removes her padlock

• Alice sends the box one more time to Bob– Bob removes his padlock and gets the key

Key Exchange

• PGP– Pretty Good Privacy– Usually used for email– Uses RSA (sometimes)

• X.509– Server certificate keys– Can generate your own, or get one from a

certificate authority

Point-to-point security

• Using this type of exchange provides point-to-point security for traffic

• But what if the other end doesn’t support any encryption?

• http://gmail.com vs https://gmail.com• Both are valid – one is encrypted!

Tunneling

• If you don’t trust the network you’re on (such as open wireless or hotspot) tunneling might be a good option.

• Create a secure connection through which all traffic passes through.

• SSH and VPN use this concept.• You connect to a computer and network you

do trust and then release your traffic.

SSH and VPN

• SSH is a secure shell connection that can tunnel other traffic.

• VPN stands for Virtual Private Network• Hotspotvpn is a good option• Back to my Mac is another