• Consider a message 'n' Which is to the encrypted
  • The corresponding block cipher for one application of the DES applications is represented by E_k where K is the corresponding DES key
  • The output of 2-DES is C = E_k2 ( E (m)) to decrypt similarly, m = Dk₁(Dk₂(C))
  • The cipher 2-DES should offer additional security, equivalent to both K₁ & K₂.
  • The cipher 2-DES obtained by the repeated application of DES is called 2DES = DES X DES. This is called a product cipher obtained by the composition of two cipher such an idea can similarly by extended to multiple ciphers
  • The composition of two ciphers with two different keys cannot be obtained by a single application of DES with a key
  • This 2DES is encrypted to provide security equivalent to 56 X 12 = 112 bits
  • But such a cipher can be attached by an attach method which is called meet in the middle ( MIM ) attach
  • As double DES , DES has a problem of the MIM attach, triple DES was developed
  • The expected security of 3-DES is 112 bits

Triple DES

• There are in general two flavors of 3-DES & two ways for implementation of 3-DES
• The first implementation uses three keys K₁,K₂,K₃ the ciphertent of 'm' is thus obtained by

C = DES_K1[DESk₂ ( DESK₃ (m))]

The second way to implement 3-DES is using two keys, thus

C = DES_K1[DES^-1k₂ ( DESK₃ (m))]