Cryptography

1. Symmetric Ciphers

   Annotations:

   • Because both D and E use the same secret key; K
   1. E; Encryption algorithm
   2. D; Dicription algorithm
2. 1. Substitution ciphers

   Annotations:

   • substituting one letter with another
   1. Solving- cipher text only attack
      1. frequency of english letters
         1. E: 12.7%
         2. T: 9.1%
         3. A: 8.1%
         4. The rest appear similarly
      2. frequency of pairs of letters
         1. 'he', 'ar', 'in', 'th'
   2. size of key space
      1. 26!
3. Caesar cipher
   1. Not a cipher- doesn't have a key
   2. A fixed substitution
   3. Easy to solve because it's not random
4. 2. Vigener cipher (16th century, Rome)
   1. k= cipher text (e.g. crypto) repeated
   2. m= message
   3. c= k+m
   4. Solving
      1. length of the key, e.g. 6
      2. break c into groups of 6
      3. work out the most common letter in the set and substract by E
5. 3. Rotor machines (1870-1943)

   Annotations:

   • ciphers used to decode an electric mechine
   1. Disk rotates by one
   2. Enigma machine
6. 4. Data encryption standards; DES (1974)

   Annotations:

   • Federal law- a standard for encryptions DES: key = 2^56, block size = 64 bits>> currently insecure
   1. Today
      1. AES (2001)
      2. Salsa20 (2008)

1. Encryption of files
2. Protection
3. User authentication
4. Limitations
   1. Not a solution for all security problems
   2. Useless unless implemented correctly

1. Single use

   Annotations:

   • used to encrypt one message
2. Multiple use

   Annotations:

   • can be used to encrypt multiple messages- needs more machinery and security 

Annotations:

• how to create a digital signature that will be hard to forge

1. Mix net

   Annotations:

   • when sending messages they get encrypted in the process, so a person would only be able to tell the output and not the identity of the sender
2. bidirectional
3. anonymous digital cash

   Annotations:

   • Need to prevent double spending-  If someone spends more than once the identity becomes revealed
4. Secure Multi-party computation
   1. 'Trusted party'

      Annotations:

      • So there is a middle party which gets all the data before revealing the output
   2. No trusted party

      Annotations:

      • There is always a way to compute the output without a middle party 

1. Precisely specific threat model

   Annotations:

   • What an attacker can do to an encryption >> make it unforgable
2. Provide a construction
3. Proving that breaking a construction under threat model will solve an underlying hard problem

   Annotations:

   • If an attacker can break the construction they can use that to make it harder to break

1. Privately outsourcing computation

   Annotations:

   • allows to compute encrypted data- e.g. running a search on google on encryption data
2. Zero knowledge

   Annotations:

   • Proving you solved something without providing the solution >> e.g. proving that you know what the prime numbers are of a certain value N-pxq