Cryptographic Hash Functions and Base 64 Notation

Cryptographic Hash Functions

• A hash function is a one-way encryption procedure that takes an arbitrary character string (called the plaintext message) and converts it to a fixed-size bit string called the hash value or digest.
   
• The ideal hash function has these properties:
   
  
  1. it is easy to compute the hash value for a message,
      
  2. it is infeasible to find a message that has the given hash value,
      
  3. it is infeasible to modify a message without changing its hash,
      
  4. it is infeasible to find two different messages with the same hash.
  
  
• An article on cryptographic hash functions
   
  
  en.wikipedia.org/wiki/Cryptographic_hash_function
  
  
• Three popular algorithms for producing hashes are MD5, SHA1, and SHA2.
   
• The Hash Example shows how to use the .Net object HMACSHA1 in C# code to compute the hash of this message:
  

  "the quick brown fox jumped over the lazy dog"
  

  It uses the SHA1 algorithm.
   
• Notice that changing a single character in the message completely changes the hash.
   
• Modern password protection systems never store passwords directly in the database. They always store a cryptographic hash of the password instead. When a user enters a password p, the hash of p is compared with the hash of the password stored in the password table.
   
• Cryptographic hashes are also used for digital signatures.

Base 64 Notation

• Base 64 notation is used to represent binary data in a variety of situations.
   
• Hex to Base 64 Conversion Table
   
• Practice Problem:
   
1. Take a word that contains 4 or more letters:
    
2. Use this ASCII table and Hex Digits Table to convert your word to binary digits.
    
3. Convert these binary digits to base 64, padding with zeros if necessary.

   Original word:               t         e         a         l
   Converted to ASCII hex:    7    4    6    5    6    1    6    c
   Converted to binary:      0111 0100 0110 0101 0110 0001 0110 1100
   Regroup and pad with 0s:  011101 000110 010101 100001 011011 000000
   Look up base 64 values:     d      G      V      h      b      A     = =
   Add == at the end to show two bytes of padding.
   

• In practice strings are not converted to base-64 by hand. This example is just to show you what base-64 encoding is.
   
• Check your work with the C# code in the Base64 Example.