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### Transcript of Authentication Function 2: Message Authentication Code

Authentication Function 2: Message Authentication Code

Message Authentication Code (MAC) generated by an algorithm that creates a small fixed-sized block depending on both message and some key like encryption though need not be reversible (receiver also recomputes it. No decryption needed) appended to message as a signature receiver performs same computation on message and checks it matches the MAC provides assurance that message is unaltered and comes from sender Message: M Shared secret key: K MAC function: C

Message Authentication Code (MAC) If we assume that only receiver and sender knows the key, and if received MAC matches the calculated MAC, then

3. the receiver is assured that the message has not been altered 4. the receiver is assured that the message is from alleged sender. 5. the attacker cannot alter the sequence number

Message Authentication Code (I)

MAC

MAC=

Message Authentication Code (II)

MAC

MAC=

Message Authentication Code (III)

MAC

MAC=

Importance of MAC

as shown the MAC provides confidentiality can also use encryption for secrecy generally use separate keys for each can compute MAC either before or after encryption is generally regarded as better if done before why use a MAC? sometimes only authentication is needed

Uses of MAC Same message is broadcasts to a number of destinations. eg. alarm signal in a military control server. Time can be reduced in case of decrypting all incoming messages. It can save the processor resource and give assurance of the integrity of the program

MAC Properties a MAC is a cryptographic checksum MAC = CK(M) condenses a variable-length message M using a secret key K to a fixed-sized authenticator is a many-to-one function potentially many messages have same MAC

Properties of MAC Function A MAC function is similar to encryption. But, it need not be reversible, as it must be for decryption. For n-bit MAC, there are 2n possible MACs. But there might be N >> 2n possible messages. So, it is a many-toone function. e.g. 100-bit messages and we use a 10-bit MAC. There are 2100 different messages but only 210 different MACs. On average, each MAC represents 2100/210=290 different messages. It turned out that MAC is less vulnerable to be broken than encryption.

Requirements for MAC Functions taking into account the types of attacks Brute-force technique to discover the authentication key is as hard as decryption without key Suppose key size > MAC size (k>n). Given a known plaintext M1 and its MAC1=CK(M1): attacker may generate MACi=CKi(Mi) for all 2k keys. The opponent generates 2k MACs. But there are only 2n real MAC values. On average a total of 2k/2n=2(k-n) keys will produce a match

Requirements for MAC Functions cont and the opponent wouldnt know which one is correct. m round where k=m.n is needed to find the key. Need the MAC to satisfy the following: 1.knowing a message and MAC, is infeasible to find another message with same MAC 2.MACs should be uniformly distributed 3.MAC should depend equally on all bits of the message

Hash Functions A one-way hash function can be used as the message authentication code. Other names: compression function, contraction function, message digest, fingerprint, cryptographic checksum, message integrity check (MIC), modification detection code (MDC). condenses arbitrary message to fixed size, H(M) usually assume that the hash function is public and not keyed Contrary to the MAC which is keyed hash used to detect changes to message

Hash Functions (I)

Hash Functions (II)

Hash Functions (III)

Hash Functions (IV)

Hash Functions (V)

S: Common secret value (If attacker can do H-1(C)=S||M, then having also M, he can easily find S)

Hash Functions (VI)

S: Common secret value

Hash Function Properties a Hash Function produces a fingerprint of some file/message/data h = H(M) condenses a variable-length message M to a fixed-sized fingerprint assumed to be public

Requirements for Hash Functions1. 2. 3. 4. can be applied to any sized message M produces fixed-length output h is easy to compute h=H(M) for any message M given h is infeasible to find x s.t. H(x)=h one-way property (level of effort needed by attacker 2m for hash code of length m) 5. given x is infeasible to find y s.t. H(y)=H(x) weak collision resistance (level of effort needed 2m) 6. is infeasible to find any x,y s.t. H(y)=H(x) strong collision resistance (level of effort needed 2m/2)

Simple Hash Functions are several proposals for simple functions based on XOR of message blocks e.g. longitudinal redundancy check is a simple parity for each bit position Ci=bi1 bi2 bim not secure since can manipulate bits (bij) in message that either not change hash code (C) or change the hash itself need a stronger cryptographic function (Chapter 12)

The Secure Hash Algorithm (SHA-1)SHA-1 A message composed of b bits 160-bit message digest

Step 1 -- PaddingPadding the total length of a padded message is multiple of 512 Every message is

Padding (cont.)Message 1 zeros Message length

1 bit

64 bits

Multiple of 512

Padding (cont.) Padding is done by appending to the input: A single bit, 1 Enough additional bits, all 0, to make the final 512 block exactly 448 bits long A 64-bit integer representing the

M = 01100010 11001010 1001 (20 bits) Padding is done by appending to the input: A single bit, 1 427 0s A 64-bit integer representing 20 Pad(M) = 01100010 11001010 10011000 00010100

Example

Example Length of M = 500 bits Padding is done by appending to the input: A single bit, 1 459 0s A 64-bit integer representing 500 Length of Pad(M) = 1024 bits

Message Digest Generation Using SHA-1

SHA-1 Processing of single 512Bit Block

SHA Overview pad message so that we have: length mod 512 = 448 or equivalently length 448 (mod 512) append a 64-bit length value to message initialize 5-word (160-bit) buffer (A,B,C,D,E) to the following using big-endian format: (67452301, efcdab89, 98badcfe, 10325476, c3d2e1f0) process message in 16-word (512-bit) chunks: expand 16 words into 80 words by mixing & shifting use 4 rounds of 20 bit operations on message block & buffer add output to input to form new buffer value output hash value is the final buffer value

4.

5.

Single 512-Bit Block Function in SHA-1

Summary of SHA-1 Behavior The SHA-1 behaviour can be summarized as: CV0 = IV CVq+1= SUM32 [CVq, ABCDEq] MD = CVL Where: IV: Initial value (stored in ABCDE buffers) ABCDEq: the output of the last round of processing in the qth 512-bit block of the message L: number of blocks in the message (including padding and the length fields) CVq: chaining variable processed with the qth block SUM32: addition mod 232 performed separately on each word of the pair of inputs MD: final message digest value

SHA-1 Compression Function each round has 20 steps which replaces the 5 buffer words thus: [A,B,C,D,E] [(E+f(t,B,C,D)+S5(A)+Wt+Kt),A,S30(B),C,D] a,b,c,d refer to the 4 words of the buffer t is the step number (0t79) Sk: circular left-shift (rotation) of the 32-bit argument by k bits (same as