Security

1
Security
2
Cipher Modes

• ECB Electronic Code Book Mode. Break the entire
  file into blocks, and encode every block
  individually.
• Problems. The example in the book. You can
  replace a block if it is good for you.

3
CBC Cipher block chaining

• Encryption
• C0 E(P0 xor IV).
• C1 E(P1 xor C0), and so on.
• IV is transmitted in plain text.
• Decryption
• P0 IV xor D(C0)
• P1 C0 xor D(C1), and so on.
• So, same message wont result in the same code.

4
Stream Cipher Mode

• T0 E(IV).
• T1 E(T0), and so on.
• C P xor T.
• Dont use the same stream twice.

5
Counter mode

• Ti E(IVi).
• Ci Pi xor Ti.
• The advantage is that you can randomly access any
  block.
• Used by Skype. Often called ICM (Integer counter
  mode).
• ECB also supports random access. Does it have the
  same problem as ECB? No, because the Ivs are
  different.

6
Public Key / Private Key

• Talking about Skype, how do you think that two
  Skype users can share the same AES key?

7
Public Key / Private Key

• Everyone has a public key and private key.
• With Bs public key (pkB) A can encode data that
  only B can decode with his private key (skB)
  because other people does not have Bs private
  key.
• D_skBE_pkB(W) W
• E_pkBD_skB(W) W

8
Public Key /Private key

• So, A can choose a 128-bit string W as the
  session key and send E_pkB(W) to B. B runs the
  decryption algorithm to get D_skBE_pkB(W) W.
• Skype actually asks two ends to both contribute
  128 bits to make the 256-bit session key.

9
The RSA algorithm

• Most common, the RSA algorithm is used to get the
  public key/private key.
• Choose two large primes, p and q.
• Compute npq and z(p-1)(q-1).
• Choose a large number relatively prime to z and
  call it d.
• Find e such that ed 1 mod z. (such e must
  exist)
• (e,n) is the public key for encoding and (d,n) is
  the private key for decoding.

10
The RSA algorithm

• To encrypt a message M, CMe mod n.
• To decrypt from C, M Cd mod n.
• D_skBE_pkB(M) M
• E_pkBD_skB(M) M.

11
Why is RSA secure?

• The problem is, given (d,n), can you figure out
  e?
• It is difficult.
• You can try to find p and q given n. If you
  indeed can, then you get z. Given z and d, you
  get e.
• But it is difficult to factor large numbers.