# Message Authentication Codes. Lecture Outline

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1 Message Authentication Codes Murat Kantarcioglu Based on Prof. Ninghui Li s Slides Message Authentication Code Lecture Outline 1

2 Limitation of Using Hash Functions for Authentication Require an authentic channel to transmit the hash of a message anyone can compute the hash value of a message, as the hash function is public not always possible How to address this? use more than one hash functions use a key to select which one to use Hash Family A hash family is a four-tuple (X,Y,K,H ), where X is a set of possible messages Y is a finite set of possible message digests K is the keyspace For each K, there is a hash function h K H Each h K : Alternatively, one can think of H as a function K X Y 2

3 Message Authentication Code A MAC scheme is a hash family, used for message authentication MAC = C K (M) The sender and the receiver share K The sender sends (M, C k (M)) The receiver receives (X,Y) and verifies that C K (X)=Y, if so, then accepts the message as from the sender To be secure, an adversary shouldn t be able to come up with (X,Y) such that C K (X)=Y. Constructing MAC from Hash Functions Given a cryptographic (iterative) hash function h, Define C K (M) to be h(m) with K as IV Is this secure? Given a message x and its MAC C K (x), the adversary can construct x and C K (x ) let pad(x) be the padding added to x let x =x pad(x) w, y =x pad(x ) then C K (x ) can be computed from C K (x) 3

4 Model for Iterated Hash Functions original input x append padding bits preprocessing append length formatted input x 1, x 2... x n each x i a t-bit block ƒ x i iterated processing compression function f: {0,1} m+t {0,1} m H i-1 H i H t H 0 =IV H i =f(h i-1,x i ) g output h(x)=g(h n ) Existential Forgery Attack against MAC Let C be a MAC function C K (M) is the MAC for M under K. Challenger Picks K at random q times x i C K (x i ) x,y Adversary Attacker wins game if x {x 1,,x q } and C K (x)=y 4

5 Selective Forgery Attack Against MAC Let C be a MAC function C K (M) is the MAC for M under K. Challenger Picks K at random, Picks a random x q times x x i x C K (x i ) y Adversary Attacker wins game if and C K (x)=y MAC Security The pair (x, z) is called a forgery A (ε,q) forger can produce a forgery with probability ε, after making q queries generally talks about existential forgery The attacker against the MAC scheme C K (M)=h(M) with K as IV is a (1,1) forger 5

6 Constructing MAC using Hash Functions Are the following MAC schemes secure? What kind of forgers exist for them? C K (M) = h(k M), where h is a cryptographic hash function HMAC Goals Use available hash functions without modification. Preserve the original performance of the hash function without incurring a significant degradation. Use and handle keys in a simple way. Allow easy replacement of the underlying hash function in the event that faster or more secure hash functions are later available. Have a well-understood cryptographic analysis of the strength of the authentication mechanism based on reasonable assumptions on the underlying hash function. 6

7 HMAC HMAC K = Hash[(K + opad) Hash[(K + ipad) M)]] K + is the key padded out to input block size of the hash function and opad, ipad are specified padding constants Key size: L/2 < K < L MAC size: at least L/2, where L is the hash output HMAC Overview 7

8 HMAC Security Security of HMAC relates to that of the underlying hash algorithm If used with a secure hash functions (s.t. SHA1) and according to the specification (key size, and use correct output), not known practical attacks against HMAC In general, HMAC be attacked as follows: brute force on the key space attacks on the hash function itself birthday attack, although the use of key makes this attack more difficult attacks against the compression function CBC-MAC Given a block cipher E with block size m Given message M = M 1 M 2 M n MAC of M is E k (M) z 0 =IV=0 m z i = E k (z i-1 M i ) for 1 i n MAC=z n Random IV is needed in CBC encryption to prevent codebook attack on first block, not needed here. 8

9 Encryption Modes: CBC next input depends of previous output Plaintext is M1, M2, M3, M4, Ciphertext is: C 1 = IV E k (M 1 ) C 2 =C 1 E k (M 2 ) C 3 =C 2 E k (M 3 ) C 4 =C 3 E k (M 4 ) M 1 M 2 M 3 IV E k E k E k C 1 C 2 Security of CBC-MAC Secure for messages of a fixed number of blocks assuming the block cipher is PRP Not secure with variable lengths, example attack given three pairs of messages/macs (x1,y1) (x2,y2), (x1 z,y3), then y1= E K [IV x1] y2= E K [IV x2] y3= E K [y1 z]=e K [y2 (z y1 y2)] let z =(z y1 y2), (x2 z,y3) is also a valid pair 9

10 Optional Security Enhancement for CBC-MAC MAC of M is z 0 =IV=0 m z i = E K1 (z i-1 M i ) for 1 i n MAC=E K1 D K2 [z n ] Reduces threat of exhaustive key search Defends against the previous attack Data Integrity Combined with Encryption Encryption alone does not guarantee data integrity Combining encryption with hash C=E K [x h(x)] breaking encryption also compromises integrity may be vulnerable to known-plaintext attack 10

11 MAC with Encryption C=E K [x h K (x)] separate keys used for encryption & for MAC the algorithms E and h should be independent precludes exhaustive key search on MAC key Alternative 1: C=E K [x], h K (E K [x]) allows message authentication without knowing x or K authenticates only the ciphertext Alterative 2: E K [x],h K (x) requires h K (x) does not leak information about x CCM Mode CCM mode is a NIST standard that provides an authenticated encryption MAC is produced as a part of the encryption process CCM mode uses CTR mode for encryption and CBC-MAC for authentication Given message M = M 1 M 2 M n C i = M i E k (ctr+i mod 2 m ) temp=cbc-mac(m,k) and C = temp E k (ctr) Return C 1. C n C 11

12 Number theory Readings: Next Lectures.. Stingson: 5.1, 5.2,

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