Post on 18-Dec-2015
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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