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2 20 January 2006
Cryptographic ToolsThree basic tools are used
– Encryption is used to provide confidentiality
– Digital signatures are used to provide authentication, integrity protection, and non-repudiation
– Checksums/hash algorithms are used to provide integrity protection
However, if the underlying system is unsecure, no amount of cryptography will help.
3 20 January 2006
Cryptographic KeysA long series of binary digits used in various ways to transform a message from its original form, into a stream of seemingly random numbers, and back again.
The strength of a key is roughly based upon the number of bits it has – known as its “length”.
–Here, strength is used to mean how long it would take an attacker to guess the key used to transform or obscure a message.
–This is similar to how the number of teeth in your house key determines the total number of keys there are and, thus, how many keys a burglar might have to try before guessing yours.
4 20 January 2006
In Encryption, Most Folks Say “Key Size Matters!”
In general, the longer the secret key, the harder it will be for an adversary to guess the key’s value and decrypt the secret.
It’s the same as the “teeth” on your house key– The more teeth your house key has, the longer it would
take for persistent criminal to cut various combinations of teeth into test keys in order to find yours.
– e.g., a house key with 8 teeth, each having 3 cut positions, yields 6,500 different keys
5 20 January 2006
Unfortunately, It’s Not That Simple
• Key size gets way too much attention, but it’s the easiest metric• So far, encryption failures have always been due to
– Implementation errors– Protocol errors– Usage errors (cockpit errors)
• Therefore, a more accurate summary would be– In encryption, it’s not the size that matters, it’s the
technique.*
* Ran Canetti of IBM Research
6 20 January 2006
Encryption – Caveat Emptor
Beware of strangers selling “crypto snake oil”– Unbreakable encryption– One-Time Pads– “Military-grade encryption”– “Million-bit” key lengths– Proprietary cryptography
• a.k.a. “I know more than all the world’s cryptographers”
7 20 January 2006
Would You Buy This?
Our unbreakable military-grade 10,240-bit bi-Gaussian encryption system, using a proprietary one-time pad algorithm, has recently been reviewed by the NSA and approved by a Fortune 500 customer and is available both inside and outside of the US.
Adapted from Peter Gutman’s crypto tutorial: http://www.cryptoapps.com/~peter/part6.pdf
8 20 January 2006
In Summary
If you take away anything from this part of today’s talk, it should be these 3 rules:
1. Cryptography is indeed rocket science.2. Proprietary cryptography must be assumed to be
broken, by definition3. Adding cryptography to an unsecure system is like
putting steel doors on a grass hut.
Auguste Kerckhoffs, ‘La cryptographie militaire’, 1883
1. The system must be substantially, if not mathematically, undecipherable;2. The system must not require secrecy and can be stolen by the enemy
without causing trouble;3. It must be easy to communicate and remember the keys without
requiring written notes, it must also be easy to change or modify the keys with different participants;
4. The system ought to be compatible with telegraph communication;5. The system must be portable, and its use must not require more than
one person;6. Finally, regarding the circumstances in which such system is applied, it
must be easy to use and must neither require stress of mind nor the knowledge of a long series of rules.
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Monoalphabetic substitution cipher #1• Pick some number of position to rotate the plaintext
alphabet. Here, we use rot13 : Ac: NOPQRSTUVWXYZABCDEFGHIJKLMequivalent to adding ‘M’ mod 26 to each letter of the message.
• Then use Ac to encipher the plaintext P:Ap: ABCDEFGHIJKLMNOPQRSTUVWXYZ
Ac: NOPQRSTUVWXYZABCDEFGHIJKLM
P: dont forget your towel
C: qbag sbetrg lbhe gbjry
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Monoalphabetic substitution cipher #2
• Pick a keyword to initialize the ciphertext alphabet:Ac: CRYPTOISEZ ABDFGHJKLMNQUVWX
• Then use Ac to encipher the plaintext P:Ap: ABCDEFGHIJKLMNOPQRSTUVWXYZ
Ac: CRYPTOISEZABDFGHJKLMNQUVWX
M: dont forget your towel
C: pgfm ogkitm wgnk mgutb
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How to attack substitution ciphers?
• They don’t obscure the underlying letter frequencies in the plaintext
• Similarly, bigram (a.k.a. digram) and trigram analysis is still quite possible.
• Straightforward programs can solve these with several dozen characters of ciphertext.– ETOAIN SHRDLU– SS, EE, TT, FF, TH, ER, ON
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Polyalphabetic Substitution Cipher:
Vigenère Cipher
This is the Vignere Square, or Tabula Recta.
P =SAMBRADFORD
KEY=HEISMANHEIS
C= ZEUTDAQMSZV
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Breaking a Vigenère cipher
• Look for sequences that repeat• Example cracking tool from Simon Singh
Transposition cipher:Columnar transposition
THISISATESTOFTHEEARLYWARNINGSYSTEM
Becomes
TEENE HSAIM ITRNSOLGIF YSSTW YAHASTERT
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ROTOR Machines
• Variation of Vigenère• Series of rotors each with an arbitrary
permutation of the alphabet.• Output of one rotor connected to inputs of
next
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Rotor machines:ENIGMA
After the A is encrypted as a G, the rightmost rotor is advanced one position.
Then another A is encrypted, but this time as a C.
The breaking of the ENIGMA code is said to have ended the European war by two years (WWII).
18Wikimedia Commons
Simple XOR$ ./xor abcd xor.c xorx /* abcd is 0x61626364 */
$ hexdump xor.c | head -2
23 69 6e 63 6c 75 64 65 20 3c 73 74 64 69 6f 2e
68 3e 0a 0a 76 6f 69 64 20 6d 61 69 6e 20 28 69
$ hexdump xorx | head -2
42 0b 0d 07 0d 17 07 01 41 5e 10 10 05 0b 0c 4a
09 5c 69 6e 17 0d 0a 00 41 0f 02 0d 0f 42 4b 0d
$ ./xor abcd xorx xorxx
$ hexdump xorxx | head -2
23 69 6e 63 6c 75 64 65 20 3c 73 74 64 69 6f 2e
68 3e 0a 0a 76 6f 69 64 20 6d 61 69 6e 20 28 69
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Feistel network generalized
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Feistel Networks
Guaranteed to be invertible
Original diagram from WikiCommons, modified here
L1L1 R1
R1
L2L2 R2
R2
LdLd RdRd
Ld-1Ld-1Rd-1
Rd-1
Ld-2Ld-2Rd-2
Rd-2
Then you can add encryption decryption to the F’s.
LdLdRdRd
Li = Ri-1
Ri = Li-1 XOR f(Ri-1),thenRi = Li-1 XOR f(Ri-1,Ki) )
DESIP occurs before round 1, transposing the input block in specific manner
In each round, the key bits are shifted, and 48 bits are selected from the 56 bits of the key
The data is split in half, with permutations and substitutions applied to the right half.
After 16 rounds, the FP (inverse of IP) is applied.
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AES
Here’s a super animation of AES
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Modes of operation: ECB(Electronic Code Book)
25Wikimedia Commons
ECB can leave data patterns behind
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Tux the Penguin, the Linux mascot. Created by Larry Ewing with The GIMP.Other two images are from Wikipedia Commons
Encrypted using ECBEncrypted using other modes
Initialization Vector (IV)
• All the modes of operation besides ECB need their pumps to be primed with a random block of data.
• No need for secrecy, but an IV should only be used once for a given key.
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28Wikimedia Commons
Modes of operation: CBC(Cipher-Block Chaining)
Ci = EK (Pi Ci-1)
Pi = Ci-1 DK (Ci)
Modes of operation: CFB (Cipher Feedback)
29Wikimedia Commons
Ci = Pi EK (Ci-1)
Pi = Ci DK (Ci-1)
Cryptographic Hash Function
30Wikimedia Commons
Message Authentication Codes
31Wikimedia Commons
Vernam Cipher
If a binary message m1m2...mt is operated on by a binary key string k1k2…kt of the same length to produce a ciphertext c1c2…ct where
ci = mi ki , 1 ≤ i ≤ t
If the key string is randomly chosen and never used again, the cipher is a one-time pad.
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Russian One-Time Pad captured by MI5
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Playfair Cipher
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E C H O S
M I T A B
D F G J K
L N P R U
V W X Y Z
Key is: ECHOSMITH
http://www.simonsingh.net/The_Black_Chamber/playfair_cipher.html