1 The Data Encryption Standard

2 Outline 4.1 Introduction 4.4 DES 4.5 Modes of Operation 4.6 Breaking DES 4.7 Meet-in-the-Middle Attacks

3 4.1 Introduction In 1973, NBS, later to become NIST, issued a public request seeking a crypto algo to become a national standard. In 1974, IBM submitted an algo called LUCIFER. The NBS forwarded it to NSA, which reviewed it and, after some modifications, returned a version that was essentially the DES. In 1975, NBS released DES, as well as a free license for its use. In 1977, NBS made it the official data encryption standard.

4 Introduction From 1975 on, there has been controversy surrounding DES. Some regarded the key size as too small. Many were worried about NSA’s involvement. In 1990, Eli Biham and Adi Shamir showed how their method of differential cryptanalysis could be used to attack DES. The DES algo involves 16 rounds; differential cryptanaysis would be more efficient than exhaustively searching all possible keys if the algo used at most 15 rounds.

5 Introduction The DES has lasted for a long time, but is becoming outdated. Brute force searches (see Sec 4.6), though expensive, can now break the system. Therefore, NIST replaced it with a new system in the year The DES is a block cipher; namely, it breaks the plaintext into blocks of 64 bits, and encrypts each block separately.

6 4.4 DES Description of DES DES is a special type of iterated cipher called a Feistel cipher. In a Feistel cipher, each state u i is divided into two halves of equal length, say L i and R i. Round function g: g(L i-1, R i-1, K i )=(L i, R i ), where Invertible:

7 Overview of DES One round

8 DES Initial permutation IP : IP(x)=L 0 R 0 Inverse permutation IP -1 : y=IP -1 (R 16 L 16 ) Note L 16 and R 16 are swapped before IP -1 is applied. Each L i and R i is 32 bits in length. The function takes as input a 32-bit string (the right half of the current state) and a round key. Key schedule (K 1,K 2,…,K 16 ) consists of 48-bit round keys that are derived from the 56-bit key, K.

9 DES Suppose we denote the first argument of f function ( Figure A ) by A, and the second argument by J. A is expanded to 48-bit according to a fixed expansion function E. Compute and write the result as concatenation of eight 6-bit strings B=B 1 B 2 B 3 B 4 B 5 B 6 B 7 B 8. The next step uses eight S-boxes (S 1, …,S 8 ), Given a bitstring of length 6, B j =b 1 b 2 b 3 b 4 b 5 b 6. b 1 b 6 determine the row r of S j, and b 2 b 3 b 4 b 5 determine the column c of S j. We compute C j =S j (B j ). The bitstring C=C 1 C 2 C 3 C 4 C 5 C 6 C 7 C 8 is permuted according to the permutation P. Then f ( A, J )= P (C).

10 A E(A) J f(A,J) E + B1B1 B2B2 B3B3 B4B4 B5B5 B6B6 B7B7 B8B8 S1S1 S2S2 S3S3 S4S4 S5S5 S6S6 S7S7 S8S8 C1C1 C2C2 C3C3 C4C4 C5C5 C6C6 C7C7 C8C8 P Figure A The DES f function

11 S1S S2S S3S S4S S-boxes Example B

12 S5S S6S S7S S8S S-boxes

13 DES Example B: We show how to compute an output of S-box S 1 with input b 1 b 6 =10 which is 2 b 2 b 3 b 4 b 5 =0100 which is 4 Output is row 2 and column 4 of S 1. Note: rows are numbered 0,1,2,3 and columns are 0,1,2, … 15 So the output is 13 which is 1101 in binary.

14 DES The expansion function E is specified by the following table: If A=(a 1,a 2, …,a 32 ) then E (A)=(a 32,a 1,a 2,a 3,a 4,a 5,a 4, …,a 31,a 32,a 1 ). E bit-selection table

15 DES The permutation P is as follows: If C=(c 1,c 2, …,c 32 ) then P (C)=(c 16,c 7,c 20,c 21,c 29, …,c 11,c 4,c 25 ). P

16 DES Key scheduling:

17 DES

Modes of Operation Four modes of operation for DES: Electronic codebook mode ( ECB mode) Cipher feedback mode ( CFB mode) Cipher block chaining mode ( CBC mode) Output feedback mode ( OFB mode) ECB mode corresponds to the naive use of a block cipher: x 1,x 2, … of 64-bit plaintext blocks, encrypted with the same key K, producing a string of ciphertext blocks, y 1,y 2, …

19 Modes of Operation CBC mode: initialization vector IV and y 0 =IV IV=y 0 + x1x1 eKeK y1y1 + x2x2 eKeK y2y2 encrypt IV=y 0 + y1y1 dKdK x1x1 + y2y2 dKdK x2x2 decrypt Figure 3.9 CBC mode

20 Modes of Operation OFB mode: a synchronous stream cipher (cf. section 1.1.7) z 0 =IV, then keystream z 1 z 2 … encryption: IV=z 0 eKeK + x1x1 y1y1 eKeK + x2x2 y2y2 encrypt IV=z 0 eKeK + y1y1 x1x1 eKeK + y2y2 x2x2 decrypt

21 Modes of Operation CFB mode: y 0 =IV keystream: encryption: IV=y 0 eKeK + x1x1 y1y1 eKeK + x2x2 y2y2 encrypt IV=y 0 eKeK + y1y1 x1x1 eKeK + y2y2 x2x2 decrypt Figure 3.10 CFB mode

22 Modes of Operation Some properties: In ECB and OFB modes, changing one 64-bit plaintext block, x i, causes the corresponding ciphertext block, y i, to be altered, but other ciphertext blocks are not affected. It is useful in some cases, like communicating on an unreliable channel. In CBC and CFB modes, if a plaintext block x i is changed, then y i and all subsequent ciphertext blocks will be affected. These modes can be used to produce a message authentication code ( MAC ).

Breaking DES The S-boxes, being the non-linear components of the cryptosystem, are vital to its security. DES was to make differential cryptanalysis infeasible. Differential cryptanalysis was known to IBM when they design DES, but it was kept secret for almost 20 years until Biham and Shamir invented the technique in the early 1990 ’ s. The most pertinent criticism of DES is that the size of the keyspace, 2 56, is too small.

24 Breaking DES Many people try to design a special purpose machine to do exhaustive key search. Eg: “ DES Cracker ” contained 1536 chips and could search 88 billion keys per second. It won RSA Laboratory ’ s “ DES Challenge II-2 ” by successfully finding a DES key in 56 hours.

25 Breaking DES Other than exhaustive key search, differential cryptanalysis and linear cryptanalysis are the most important attacks. (linear attack is more efficient) In 1994, Matsui implemented the attack by using 2 43 plaintext-ciphertext pairs with the same key. It took 40 days to generate the pairs and 10 days to find the key. DES is still secure theoretically due to the extremely large number of pairs required. An adversary is impossible to collect that amount of pairs.

26 Breaking DES There are two main approaches to achieving increased security. 1. Use DES multiple times – Triple DES 2. Find a new system that employs a larger key size than 56 bits – AES (Rijndael) The idea behind multiple DES schemes: 1. Double DES encrypts the plaintext by first encrypting with one key and then encrypting again using a different key.(one might guess that Double DES should double the keyspace to However, this in not true! See Sec 4.7)

27 Breaking DES 2. Triple DES (a level of security eq. to a 112-bit key) There are two ways Triple DES can be implemented: (1) Choose three keys, K 1, K 2, K 3 and perform E K1 (E K2 (E K3 (m))). (2) Choose two keys, K 1 and K 2, and perform E K1 (D K2 (E K1 (m)) Both versions of Triple DES are resistant to meet-in-the-middle attacks. However, there are other attacks on (2).

Meet-in-the-Middle Attacks Starting with plaintext message m, the ciphertext is c=E k2 (E k1 (m)). To decrypt, simply compute m=D k1 (D k2 (c)). Eve will need to discover both k1 and k2 to decrypt their messages. Does this provide greater security? No

Meet-in-the-Middle Attacks Assume Eve has intercepted a message m and a doubly encrypted ciphertext c=E k2 (E k1 (m)). She wants to find k 1 and k 2. She first computes and stores E k (m) for all possible keys k. She then computes D k (c) for all possible keys k. Finally, she compares the two lists. If there are several matches, she then takes another plaintext-ciphertext pair and do further test …