Modern Cryptography

The Enigma Machine

German encryption and decryption machine used in WWII

Essentially a complex, automated substitution cipher

How did Enigma work?

Rotors have different wiring connecting input to output

Rotors move after each keypress

The key is the initial position of the three rotors

Simplified EnigmaA a

B b

C c

D d

=

A c

B a

C c

D d

A a

B b

C c

D d

A a

B b

C c

D d

=

A b

B a

C d

D c

=

A d

B c

C a

D b

Every time a key is pressed the rotors spin, so the overall substitution table changes

A a

B b

C c

D d

A a

B b

C c

D d

A a

B b

C c

D d

=

A b

B c

C d

D a

Breaking the Enigma

Britain set up its cryptanalysis team in Bletchley Park

They consistently broke German codes throughout the war

Provided the intelligence codenamed ULTRA

Important location in the history of computing Alan Turing COLOSSUS

Cryptography in the Computer Age

Working with binary instead of letters

We can do things many, many times Think of an Enigma machine that has 2128 pairs of

symbols on each rotor, and 20 rotors

Other than that, the basic principles are the same as classical cryptography

The XOR Operation

eXclusive OR “should we go left or

right?” Can do one or the other, but

not both

Useful in cryptography for mixing two binary strings together

0 0

0 1

1 0

1 1

0

1

1

0

a b a b

Modern Ciphers

We design one relatively simple scrambling method (called a round) and repeat it many times Think of each round as a rotor on the Enigma One round may be easy to break, but when you put them all

together it becomes very hard

Almost all ciphers follow one of two structures SPN (Substitution Permutation Network) Feistel Network These describe the basic structure of a round

One SPN RoundInput to the round

Output from the round

First, the input is XORed with the round subkey

Second, the input is split into pieces (usually of one byte) and put through a substitution

Finally, the pieces are swapped around

And the output from this round becomes the input to the next round

A Simple SPN Cipher

Round 1

Round 2

Round 3

Plaintext Block

Ciphertext Block

Roundkey 1

Roundkey 2

Roundkey 3

The overall plaintext is broken into blocks and each block is encrypted with the cipher

Typical SPN ciphers will have 10-14 rounds

Alice and Bob only need one key, and the cipher will transform that key into subkeys for each round

To decrypt, Alice just does everything in the reverse order

One Feistel RoundInput Left Half Input Right Half

RoundFunction

Output Left Half Output Right Half

The input to the round is divided in half

The right half is put into a round function with the roundkey

The output of the round function is XORed with the left half

The two halves switch sides to become the input to the next round

Only the left half of the input has been modified

Roundkey

A Simple Feistel CipherPlaintext Block

Ciphertext Block

Round 1

Round 2

Round 3

Feistel ciphers need twice as many rounds as SPN ciphers because only half of the input is being encrypted each round

Works the same as SPN ciphers in terms of transforming one key into subkeys and splitting the plaintext into blocks

To decrypt, the ciphertext is sent through the same cipher and the roundkeys are used in reverse order

Roundkey 1

Roundkey 2

Roundkey 3

Modern Ciphers in Practice

Follow SPN/Feistel structure in general, but with added twists for security

There are two important ciphers in the history of modern cryptographyDES (Data Encryption Standard)AES (Advanced Encryption Standard)

DES

U.S. Government recognized the need to have a standardized cipher for secret documents

DES was developed by IBM in 1976 Feistel structure Key length of 56 bits, block size of 64 bits 16 rounds

Analysis of DES was the beginning of modern cryptographic research

Controversy Surrounding DES

Development process was hidden from publicSuspicions that the government had put in a

“backdoor”

Government attempted to shut down research in cryptography

Breaking DES

The key length of DES was too short If a key is 56 bits long, that means there are 256

possible keys “DES Cracker” machines were designed to simply

brute force all possible keys

People began encrypting the plaintext multiple times with different keys in order to increase the number of keys that need to be checked

Breaking DES cont.

DES was further weakened by the discovery of differential cryptanalysis Biham and Shamir in 1990 The most significant advance in cryptanalysis since frequency analysis

Ideally a ciphertext should be completely random, there should be no connection to its matching plaintext Differential analysis exploits the fact that this is never actually the case Uses patterns between plaintext and ciphertext to discover the key

There is evidence that IBM knew about differential cryptanalysis back when they were designing DES in 1976

Developing the AES

With DES effectively broken, a new standard was needed

U.S. Government made it an open application/review process this time, and received many submissions

In 2001, after five years, the Rijndael cipher was selected to become the Advanced Encryption Standard

AES (Rijndael)

Developed by Vincent Rijmen and Joan Daemen

SPN structure Block size of 128 bits Key size of 128, 192, or 256 bits 10, 12, or 14 rounds depending on the key

size

Current attacks against AES

On AES with 128-bit keys, a brute force attack would require 2128 work Any technique that can decrypt a ciphertext with less

than 2128 work is considered an attack

Currently the best attacks on AES use variations of differential cryptanalysis None of them could actually be completed before the

sun burns out None of them work on the full number of rounds

The Problem of Symmetric Key Cryptography Up until now we’ve been talking about symmetric

key cryptography Alice and Bob are using the same key to

encrypt/decrypt

Problem: How does Bob get the key to Alice when Eve is eavesdropping?

Up until 1976 the only solution was to physically give Alice the key in a secure environment

Public Key Cryptography

Diffie and Hellman published a paper in 1976 providing a solution

We use one key for encryption (the public key), and a different key for decryption (the private key)

Everyone knows Alice’s public key, so they can encrypt messages and send them to her But only Alice has the key to decrypt those messages

No one can figure out Alice’s private key even if they know her public key

Using Public Keys

Plaintext

Ciphertext DecryptionEncryption

Plaintext

Nonsense

Public Key Cryptography in Practice The problem is that public key algorithms are too

slow to encrypt large messages Instead Bob uses public key algorithms to send Alice

the symmetric key, and then uses symmetric key algorithms to send the message

Bob and Alice have to be careful when sending these communications back and forth that Eve can’t overhear anything that would allow her to decrypt the message

Sending a Message What’s your public key?

Bob picks a symmetric key and encrypts it using Alice’s public key

Alice decrypts the symmetric key using her private key

Bob encrypts his message using the symmetric key

Then sends the key to Alice

Then sends the message to Alice

Alice decrypts the message using the symmetric key

hi

The RSA Public Key Cipher

The most popular algorithm is RSA, developed in 1977 Named after its creators: Rivest, Shamir, and Adleman

Alice picks two large primes and finds their product She then uses this product to create the public and private keys She sends the product and the public key to Bob, who can use them

to encrypt messages Even if Eve knows the product and the public key, she can’t figure

out the private key unless she can factor the product There is no known way to do this efficiently

Are we all secure now?

Unfortunately not, there are still many problems that need to be dealt with How does Bob know that he’s really talking to Alice? How does Alice know that the message she receives

hasn’t been tampered with? How does Alice know the message was sent by Bob?

These are questions addressed by other areas of cryptography

The End