1. Modern Cryptography

2. The Enigma Machine
German encryption and decryption machine used in WWII
Essentially a complex, automated substitution cipher

3. 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

4. Simplified Enigma A c B a C D d A b B a C d D c A d B c C a D b A b B= = = A b B c C d D a
A a
B b
C c
D d
A a
B b
C c
D d
A a
B b
C c
D d
Every time a key is pressed the rotors spin, so the overall substitution table changes =

5. 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

6. 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

7. The XOR Operation eXclusive OR “should we go left or right?”b a b
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 1 1

8. 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

9. One SPN Round Input to 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
Output from the round
And the output from this round becomes the input to the next round

10. A Simple SPN Cipher Plaintext Block
The overall plaintext is broken into blocks and each block is encrypted with the cipher
Typical SPN ciphers will have 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
Roundkey 1
Round 1
Roundkey 2
Round 2
Roundkey 3
Round 3
Ciphertext Block

11. One Feistel Round Input Left Half Input Right Half
The input to the round is divided in half
Roundkey
The right half is put into a round function with the roundkey
Round
Function
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
Output Left Half
Output Right Half

12. A Simple Feistel Cipher
Plaintext Block
Feistel ciphers need twice as many rounds as SPN ciphers because only half of the input is being encrypted each round
Roundkey 1
Round 1
Works the same as SPN ciphers in terms of transforming one key into subkeys and splitting the plaintext into blocks
Roundkey 2
Round 2
To decrypt, the ciphertext is sent through the same cipher and the roundkeys are used in reverse order
Roundkey 3
Round 3
Ciphertext Block

13. 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 cryptography
DES (Data Encryption Standard)
AES (Advanced Encryption Standard)

14. 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

15. Controversy Surrounding DES
Development process was hidden from public
Suspicions that the government had put in a “backdoor”
Government attempted to shut down research in cryptography

16. 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

17. 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

18. 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

19. 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

20. 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

21. 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

22. 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

23. Using Public Keys Ciphertext Plaintext Plaintext Nonsense Encryption
Decryption
Ciphertext
Plaintext
Plaintext

24. 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

25. Sending a Message What’s your public key? hi
Bob picks a symmetric key and encrypts it using Alice’s public key
Then sends the key to Alice
Alice decrypts the symmetric key using her private key
Bob encrypts his message using the symmetric key
Alice decrypts the message using the symmetric key
Then sends the message to Alice hi

26. 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

27. 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

28. The End