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

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DES

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),( 11

1

iiii

ii

KRfLR

RL

Single Iteration of DES Algorithm

Algorithm in Details

Initial Permutation (see the permutation tables)• The output bit 1 for example is the input bit

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• If we take the inverse permutation:

It can be seen that the original ordering is

restored.

)(MIPX

))(()( 11 MIPIPXIPY

Permutation Tables of DES

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.

iK

iK

Calculation of f (R,k)

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

iS

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

Definition of DES S-Boxes

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Function f

S-Box Detail (Row 0 of S1)

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Sub-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 i=1,2,9,16– Else cyclic shift two positions left

Key Generation

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.

Table Used for DES Key Calculation

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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:

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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

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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

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

iK

16K

15K

DES Encryption and Decryption

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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)

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.

Time To Break A Code(106 decryption/ s)

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DES Attacks

1998:The EFF's US$250,000 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.

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DES Attacks:

The COPACOBANA machine, built for US$10,000 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

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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.

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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

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 562= 112 bits

]][[12PEEC KK

]][[21CDDP KK

Double Encryption

E E CPX

K1 K2

Encryption

D D PCX

K2 K1

Decryption

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Double DES

• Using two encryption stages and two keys– C=Ek2(Ek1(P))

– P=Dk1(Dk2(C))

• It is proved that there is no key k3 such that– C=Ek2(Ek1(P))=Ek3(P)

• But Meet-in-the-middle attack

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Meet-in-the-Middle Attack

• Assume C=Ek2(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

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.

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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

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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