Simple Ciphers
– Caesar’s cipher(or, shift cipher):
e.g., A->D, B->E
that is, shift by an offset n:
-(letter + n) mod 26
only 26 possible ways of secret coding
– Monoalphabetic cipher(or, substitution cipher):
generalization, arbitrary mapping of one letter to another
26!, ~4*10^26 or ~ 2^88
Attack with statistical analysis of letter frequencies
Vigenere Cipher
What should be kept secret?
Kerchhoff’s principle
a cryptosystem should be secure even if the attacker knows all details about the system, with exception of the secret key
In practice:
Only use widely known ciphers that have been crypto analyzed for several years by good cryptographers
e.g., established standards
secret key cryptography:
one key same key for encryption and decryption
public key cryptography:
two keys
public for encryption, private for decryption
private for signing and public for verification
Hash Functions
compute message digest of data of any size
fixed length output: 128-512 bits
easy to compute H(m)
Given H(m), no easy way to find m
– one-way function
Given m1, it is computationally infeasible to find m2=m1 s.t. H(m2)= H(m1)
weak collision resistant
Computationally infeasible to find m1 = m2 s.t. H(m1)=H(m2)
strong collision resistant
Hash Functions for passwords
hash function, stored hash of password -> access granted
