Dr. Jinyuan (Stella) Sun Dept. of Electrical Engineering and Computer Science University of Tennessee Fall 2010
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1 CS 494/594 Computer and Network Security Dr. Jinyuan (Stella) Sun Dept. of Electrical Engineering and Computer Science University of Tennessee Fall
2 Hashes and Message Digests What hashes can do MD2 MD4, MD5, SHA-1 HMAC 2
3 Hash Functions Aka: message digests, one-way transformations Take a message m of arbitrary length (transformed into a string of bits) and computes from it a fixed-length (short) number h(m) Properties: - easy-to-compute: for any message m, it is relatively easy to compute h(m) - non-reversible: given h(m), there is no way to find an m that hashes to h(m) except trying all possibilities of m - computationally infeasible to find m and m such that h(m)=h(m ) and m!=m 3
4 Notion of Randomness Any particular bit in the outputs should have 50% chance to be on Each output should have about half the bits on, w.h.p Any two outputs should be completely uncorrelated, no matter how similar the inputs are 4
5 General Structure Repeated use of a compression function, f, that takes two inputs (the chaining variable and input block), and produces an n-bit output 5
6 Birthday Paradox If there are 23 or more people in a room, there is better than 50% chance that two of them will have the same birthday Assume n inputs (number of people) and k possible outputs (365 days) If n > k 1/2, there is a good chance of finding a matching pair 6
7 Length of Digest If the length of the digest is n-bit long: It takes O(2 n ) to find a message with a given digest It takes O(2 n/2 ) to find two messages with the same digest (the length of digest should be sufficient to resist this attack) 7
8 Length of Digest (Cont d) Due to birthday attack, the length of the digest in general should be twice the length of the key in block ciphers For example, SHA-256, SHA-384, and SHA-512 to match the key lengths 128, 192, and 256 in AES 8
9 What Hashes Can Do Authentication Integrity check (MAC) Encryption 9
10 Authentication Authentication with SKC (previous example) Authentication with message digest 10
11 Message Authentication Code (MAC) MD (KAB m): only those knowing the secret KAB can compute/verify the MAC (Problem?) See Problem With Keyed Hash and Solutions 11
12 Encryption Generate one-time pad: (similar to OFB) b1 = MD(KAB IV), b2 = MD(KAB b1), b3 = MD(KAB b2), XOR the message with the one-time pad bit sequence (Problem with one-time pad?) Mixing in the plaintext: (similar to CFB) b1 = MD(KAB IV), c1 = m1 XOR b1, b2 = MD(KAB c1), c2 = m2 XOR b2, b3 = MD(KAB c2), c3 = m3 XOR b3, 12
13 Replacing Hash with SKC Unix password hash: password is converted into a secret key, which is input into DES to encrypt the constant 0, producing a hashed password Hashing large messages: (Problem? See Figure 5-2, pp. 128) 13
14 MD2, MD4, MD5, SHA-1 Message digest (MD), designed by Ron Rivest MD2: 1989, operates on 8-bit octets MD4: 1990, operates on 32-bit words MD5: 1991, operates on 32-bit words Secure hash algorithm (SHA), proposed by NIST SHA-1: 1995, operates on 32-bit words 14
15 MD2 Input: arbitrary number of octets Output: 128-bit message digest Step 1: Pad the message to be a multiple of 16 octets Step 2: Append a 16-octet checksum to the message Step 3: Process the message, 16 octets at a time, to produce the message digest 15
16 Step 1: Padding 16 octets of padding are added if the message is initially a multiple of 16 octets Otherwise, r octets of padding are added to make the message a multiple of 16 octets 16
17 Step 2: Checksum Computation Checksum: 16-octet quantity, appended to the message m m checksum is processed by MD2 to obtain the actual message digest 17
18 π Substitution Table 18
19 Final Pass: Producing Digest 19
20 MD4, MD5, SHA-1 Input: arbitrary number of bits Output: 128 bits for MD4 and MD5, 160 bits for SHA-1 Step 1: Pad the message to be a multiple of 512 bits (16 words, 64 octets) Step 2: Process the message, 512 bits at a time, to produce the message digest 20
21 Step 1: Padding Padding for MD4, MD5, SHA-1 21
22 Step 2: Producing Message Digest Overview of MD4, MD5, SHA-1 22
23 SHA-1 vs. MD5 SHA-1 has 160-bit digest and MD5 128-bit, making SHA-1 more secure against brute-force SHA-1 involves more stages and bigger buffer, and thus executes more slowly than MD5 MD5 is considered broken in 2004 SHA-1 is considered broken in 2005 SHA-2: four digest sizes 224, 256, 384, 512 bits 23
24 Problem With Keyed Hash Keyed hash: h(key m) An attacker gets m and h(key m) First pads m according to the used hash function, and then adds another message m at the end, the result is m pad m h(key m pad m ) can be calculated from h(key m pad) which is the intermediate digest 24
25 Solutions Use h(m key) Use only half the bits of h(key m) Use h(key m key) HMAC 25
26 HMAC 26
27 Reading Assignments [Kaufman] Chapter 5 27
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