chapter4-1 - Chapter 4 Cryptographic hash function 1 Data...

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1 Chapter 4 Cryptographic hash function
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2 Need a way to ensure that data arrives at destination in its original form as sent by the sender Data Integrity
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3 Data Integrity and Hash function Data integrity: data are intact during the period of storage or transmission Two possibilities of losing data integrity – error occurs during transmission modified by attacker during storage or transmission Solutions to them – error detection/correction, such as CRC (Cyclic Redundancy Code) in every IP packet – Hash function, Message digest, or Message authentication code (MAC)
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4 Hash Functions • Map a message of variable length n bits to fingerprint of fixed length m bits, with m < n (output referred as message digest) A hash is a many-to-one function, so collisions can happen • Two fundamental properties: compression and easy to compute • In general, the hash function is public • Hash functions can be used to detect changes to message
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5 Definition Given two sets, X and Y , a function f : X Y , is a relation which uniquely associates members of set X with members of set Y Terminology X is called domain Y is called range or codomain For y = f(x) where x X and y Y , y is called the image of x and x is called the preimage of y The number of function from X to Y is | Y | | X |
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6 Hash functions • A mapping h : {0,1} * {0,1} n • Message m , hash value h ( m ) (message digest) – Store m in insecure place, but h ( m ) in safe place – Transmission • Send m in insecure manner, h ( m ) in secure manner (e.g., encrypt the h ( m )). • Keyed hashed function, called MAC – hash value can be used for signature
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7 Message Authentication Code (MAC) • Since hash function is public, unkeyed hash value is not secure • Combine secret key information into hash function, called MAC • The key shared between the sender and the receiver is secret
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8 Source Authentication with MACs The output of MAC can not be produced without knowing the secret key Sender computes mac 1 = MAC(M, H, K) and sends it along with the message M Receiver computes mac 2 = MAC(M ' , H, K) and checks if mac 1 = mac 2 ? Yes: accept the message, no: reject • Because the mac 1 could have been generated only by someone that knew the secret key K, this mechanism provides also data source authentication
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9 Hash Family A hash family is a four-tuple ( X , Y , K , H ), where the following conditions are satisfied 1. X is a set of possible messages 2. Y is a finite set of possible message digests or authentication tags 3. K is the keyspace, is a finite set of possible keys 4. For each K K , there is a hash function h K H . Each h K : X Y
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10 Hash Family X could be finite or infinite set; Y is always a finite set if X is a finite set; a hash function is called a compression function – In this situation, we will always assume | X | | Y | (even better, | X | 2| Y |) Let F X Y denote the set of all functions from X to Y – Suppose that | X | = N , | Y |= M , then | F XY | =M N – Any hash family F F X, Y is termed an (N,M)- hash family An unkeyed hash function is a function – h: X Y
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This note was uploaded on 12/25/2010 for the course ALL 0204 taught by Professor 79979 during the Spring '10 term at National Chiao Tung University.

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chapter4-1 - Chapter 4 Cryptographic hash function 1 Data...

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