Data Encryption Standard (DES)

1
Data Encryption Standard (DES)

• Most widely used block cipher in the world
• Adopted in 1977 by National Bureau Standards
  (NBS)
• Encrypts 64-bit data using 56-bit key
• Has widespread use
• Has been considerable controversy over its
  security

2
DES
3
Details of A Single Iteration

• First the left and right half of each 64-bit are
  treated as separate 32-bit quantities labelled L
  (left) and R (Right).
• The overall process at each iteration can be
  summarized in
• Where denotes the bitwise XOR function

4
Single Iteration of DES Algorithm
5
Algorithm in Details

• Initial Permutation (see the permutation tables)
• The output bit 1 for example is the input bit 58
• If we take the inverse permutation
• It can be seen that the original ordering is
• restored.

6
Permutation Tables of DES
7
Calculation of f (R,K) and S-Boxes

• First R input is expanded to 48 bit to be equal
  to the iteration key by using the
  permutation table.
• The resulting 48-bit of R is XOR ed with the key
  and the result passes through a substitution
  function (S-box) that produces 32-bit output.
• The 32-bit output is permuted as defined in the
  permutation table also to produce the output.

8
Calculation of f (R,k)
9
S-Box Detail

• The input to each S-Box is 6 bits and the output
  is 4 bits.
• The first and last bits of the input to box
  from a 2-bit binary number to select a particular
  row in the DES S-Box table.
• The middle 4 bit selects a particular column.
• The decimal value in the selected cell is
  converted to a 4-bit binary output

10
Continue

• Example
• The input of 011011, the row is 01(row 1).
• The column is 1101 (column 13).
• The value in the row 1 and column 13 in the S-Box
  table cell is 5 , so the output is (0101).
• The first and the last bit of the output select
  one of four permutations for rows of the S-Box
  table

11
Definition of DES S-Boxes
12
Function f
13
S-Box Detail (Row 0 of S1)
14
Sub-key Generation
Key Generation

• Given a 64 bits key (with parity-check bit)
• Discard the parity-check bits
• Permute the remaining bits using fixed table P1
• Let C0D0 be the result (total 56 bits)
• Let Ci Shifti(Ci-1) Di Shifti(Di-1) and Ki be
  another permutation P2 of CiDi (total 56 bits)
• Where cyclic shift one position left if
  i1,2,9,16
• Else cyclic shift two positions left

15
Key Generation

• First the 56-bit key is subjected to a
  permutation governed by the DES key calculation
  table.
• Then the 56-bit is treated as 28-bit quantities
  labelled Co and Do.
• C and D are separately subjected to a circular
  shift or rotation of 1 or 2 bit governed by the
  DES key calculation table.
• They are also serve as input to another
  permutation to produce the 48-bit output.

16
Table Used for DES Key Calculation
17
DES Weak Keys

• With many block ciphers there are some keys that
  should be avoided, because of reduced cipher
  complexity
• These keys are such that the same sub-key is
  generated in more than one round, and they
  include

18
Continue.

• Weak keys
• The same sub-key is generated for every round
• DES has 4 weak keys
• Semi-weak keys
• Only two sub-keys are generated on alternate
  rounds
• DES has 12 of these (in 6 pairs)
• Demi-semi weak keys
• Have four sub-keys generated

19
Continue.

• None of these causes a problem since they are a
  tiny fraction of all available keys
• However they MUST be avoided by any key
  generation program

20
DES Decryption

• The process of decryption is the same as the
  encryption process.
• The rule is as follows use the cipher text as
  input to the DES algorithm but use the keys
  in reverse order. That is use on the first
  iteration and on the second and son on

21
DES Encryption and Decryption
22
DES in Practice

• DEC (Digital Equipment Corp. 1992) built a chip
  with 50k transistors
• Encrypt at the rate of 1G/second
• Clock rate 250 Mhz
• Cost about 300
• Applications
• ATM transactions (encrypting PIN and so on)

23
The Strength of DES

• Concerns about the strength of DES fall into two
  categories
• Concerns about the algorithm itself (nothing so
  far).
• Concerns about the use of 56-bit key.
• Electronic Frontier Foundation (EFF) announced
  that it had broken a new DES encryption using a
  DES Cracker machine for less than 250,000.
• A 128 bit key is guaranteed for unbreakable
  algorithm by Brute-Force.

24
Time To Break A Code(106 decryption/ ?s)
25
DES Attacks
1998 The EFF's US250,000 DES cracking machine
contained 1,536 custom chips and could brute
force a DES key in a matter of days the photo
shows a DES Cracker circuit board fitted with
several Deep Crack chips.
26
DES Attacks
The COPACOBANA machine, built for US10,000 by
the Universities of Bochum and Kiel, contains 120
low-cost FPGAs and can perform an exhaustive key
search on DES in 9 days on average. The photo
shows the backplane of the machine with the FPGAs
27
Attack Faster than Brute Force

• Differential cryptanalysis
• was discovered in the late 1980s by Eli Biham and
  Adi Shamir, although it was known earlier to both
  IBM and the NSA and kept secret. To break the
  full 16 rounds, differential cryptanalysis
  requires 247 chosen plaintexts. DES was designed
  to be resistant to DC.
• Linear cryptanalysis
• was discovered by Mitsuru Matsui, and needs 243
  known plaintexts (Matsui, 1993) the method was
  implemented (Matsui, 1994), and was the first
  experimental cryptanalysis of DES to be reported.
  There is no evidence that DES was tailored to be
  resistant to this type of attack.

28
Possible Techniques for Improving DES

• Multiple enciphering with DES
• Extending DES to 128-bit data paths and 112-bit
  keys
• Extending the key expansion calculation

29
Double DES

• The simplified form of multiple encryption has
  two encryption stage and two keys.
• Given a plaintext P and two keys K1 and K2 one
  can generate a cipher text C as
• Decryption equation is
• The key length is 56?2 112 bits

30
Double Encryption
K1
K2
X
C
P
E
E
Encryption
K2
K1
X
P
C
D
D
Decryption
31
Double DES

• Using two encryption stages and two keys
• CEk2(Ek1(P))
• PDk1(Dk2(C))
• It is proved that there is no key k3 such that
• CEk2(Ek1(P))Ek3(P)
• But Meet-in-the-middle attack

32
Meet-in-the-Middle Attack

• Assume CEk2(Ek1(P))
• Given the plaintext P and ciphertext C
• Encrypt P using all possible keys k1
• Decrypt C using all possible keys k2
• Check the result with the encrypted plaintext
  lists
• If found match, they test the found keys again
  for another plaintext and ciphertext pair
• If it turns correct, then find the keys
• Otherwise keep decrypting C

33
Continue.

• Given a known pair (P,C), the attack proceeds as
  follows
• Encrypt all the 256 possible values of K1store
  the results in a table.
• Next decrypt C using all the 256 possible values
  of K2 .
• Check the matching between the two tables. If the
  matching occurs then you recognized the two keys.

34
Triple DES

• DES variant
• Standardized in ANSI X9.17 ISO 8732 and in PEM
  for key management
• Proposed for general EFT standard by ANSI X9
• Backwards compatible with many DES schemes
• Uses 2 or 3 keys

35
Continue.

• No known practical attacks
• Brute force search impossible (very hard)
• Meet-in-the-middle attacks need 256
  Plaintext-Cipher text pairs per key
• Popular current alternative