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Underlying theories of modern cryptography + Symmetric Cryptography …
Underlying theories of modern cryptography + Symmetric Cryptography
30/09/2019
Information Theory
Known as Shannon's Theory
Computational security vs information theoretic security
Information theory:
deals with two problems
Sending information in "noisy channel"
message might be distorted
Secrecy
Nothing from the plain text can be learned from the cipher text
Ciphers are theoretically breakable with few hundred bits of plain text
the question is if it is computationally secure ( how long it takes to crack the cipher text
A cipher is computationally secure if the best algo requires N operations at least to break it
Provable security
Factorisation
one way function (difficult to revers)
Example
: mix red and blue => purple. But to separate purple to blue and res is difficult
Unconditional security
A system will be unconditional secure if you cannot break it even with infinite computing power
expanding short key (very random) instead of using long key (same length as the plain text)
We need a new key for every message
Only secure if we consider the adversary with bounded computational resources
Issues to consider:
key sizes (issue if the key is too small)
Current algo and harware dev
Broken ciphers:
Vigenère
Enigma
Classical cipher
RC4
DES
Computationally secure:
Triple DES
AES
RSA
EIGamal
Unconditionally secure cipher:
One-time pad
Concepts
Pr(Xi) Probability between 0 and 1
The sum of all the probabilities is one
a crypto system provides perfect secrecy if Pr(p|c) = Pr(p)
Spurious keys
Framing someone
Message can decrypted to multiple version of the plaintext
page 22 second math calculation not in the exam
- Understand the concept
Symmetric cryptography:
One key crypto
Stream Cipher
Block cipher
modes of operations
Strength: how well the key is protected
only kind of public encryption until June 1976
Diffie-Hellman
: "
New directions in Crypthography
"
Advantage: Very efficient and faster to execute
Disadvantage: key management problems n(n-1)/2
Stream Cipher
Break the plaintext into successive bits
Synchronous
Self-synchronous
Ron Rivest 1987
Block Cipher
Block by block instead of bits by bits
block size and key size are not necessarily the same
Feistel Cipher
Invented by Horst Feistel
First seen in IBM's Lucifer cipher in 1970s
Page 52 calculations need not to be remembered, only understood
Sweet32 attack
https://sweet32.info/
Modes of Operation
Deal with block ciphers' limitations
Each block is independent