Computer Security CS 526 Topic 5 Cryptography: Cryptographic Hash

Computer Security CS 526 Topic 5 Cryptography: Cryptographic Hash Functions And Message Authentication Code CS526 Topic 5: Hash Functions and Message Authentication 1

Announcements HW1 due on Sept 5 Quiz 1 will be on Sept 10, covering topics 1-5 Both projects will be allow a team of two – May want to start forming teams Mid-term exam tentatively scheduled to be Tuesday Oct 15, during lecture time CS526 Topic 5: Hash Functions and Message Authentication 2

Readings for This Lecture Wikipedia Cryptographic Hash Function s Message Authentication Cod e CS526 Topic 5: Hash Functions and Message Authentication 3

Data Integrity and Source Authentication Encryption does not protect data from modification by another party. Why? Need a way to ensure that data arrives at destination in its original form as sent by the sender and it is coming from an authenticated source. CS526 Topic 5: Hash Functions and Message Authentication 4

Hash Functions A hash function maps a message of an arbitrary length to a m-bit output – output known as the fingerprint or the message digest What is an example of hash functions? – Give a hash function that maps Strings to integers in [0,2 {32}-1] Cryptographic hash functions are hash functions with additional security requirements CS526 Topic 5: Hash Functions and Message Authentication 5

Using Hash Functions for Message Integrity Method 1: Uses a Hash Function h, assuming an authentic (adversary cannot modify) channel for short messages – Transmit a message M over the normal (insecure) channel – Transmit the message digest h(M) over the secure channel – When receiver receives both M’ and h, how does the receiver check to make sure the message has not been modified? This is insecure. How to attack it? A hash function is a many-to-one function, so collisions can happen. CS526 Topic 5: Hash Functions and Message Authentication 6

Security Requirements for Cryptographic Hash Functions Given a function h:X Y, then we say that h is: preimage resistant (one-way): if given y Y it is computationally infeasible to find a value x X s.t. h(x) y 2-nd preimage resistant (weak collision resistant): if given x X it is computationally infeasible to find a value x’ X, s.t. x’ x and h(x’) h(x) collision resistant (strong collision resistant): if it is computationally infeasible to find two distinct values x’,x X, s.t. h(x’) h(x) CS526 Topic 5: Hash Functions and Message Authentication 7

Usages of Cryptographic Hash Functions Software integrity – E.g., tripwire Timestamping – How to prove that you have discovered a secret on an earlier date without disclosing it? Covered later – Message authentication – One-time passwords – Digital signature CS526 Topic 5: Hash Functions and Message Authentication 8

Bruteforce Attacks on Hash Functions Attacking one-wayness – Goal: given h:X Y, y Y, find x such that h(x) y – Algorithm: pick a random value x in X, check if h(x) y, if h(x) y, returns x; otherwise iterate after failing q iterations, return fail – The average-case success probability is q q 1 1 1 Y Y – Let Y 2m, to get to be close to 0.5, q 2m-1 CS526 Topic 5: Hash Functions and Message Authentication 9

Bruteforce Attacks on Hash Functions Attacking collision resistance – Goal: given h, find x, x’ such that h(x) h(x’) – Algorithm: pick a random set X0 of q values in X for each x X0, computes yx h(x) if yx yx’ for some x’ x then return (x,x’) else fail – The average success probability is 1 1 1 Y q ( q 1) 2 1 e q ( q 1) 2 Y – Let Y 2m, to get to be close to 0.5, q 2m/2 – This is known as the birthday attack. CS526 Topic 5: Hash Functions and Message Authentication 10

Well Known Hash Functions MD5 – output 128 bits – collision resistance completely broken by researchers in China in 2004 SHA1 – output 160 bits – no collision found yet, but method exist to find collisions in less than 2 80 – considered insecure for collision resistance – one-wayness still holds SHA2 (SHA-224, SHA-256, SHA-384, SHA-512) – outputs 224, 256, 384, and 512 bits, respectively – No real security concerns yet CS526 Topic 5: Hash Functions and Message Authentication 11

Merkle-Damgard Construction for Hash Functions Message is divided into fixed-size blocks and padded Uses a compression function f, which takes a chaining variable (of size of hash output) and a message block, and outputs the next chaining variable Final chaining variable is the hash value M m1m2 mn; C0 IV, Ci 1 f(Ci,mi); H(M) Cn CS526 Topic 5: Hash Functions and Message Authentication 12

NIST SHA-3 Competition NIST is having an ongoing competition for SHA-3, the next generation of standard hash algorithms 2007: Request for submissions of new hash functions 2008: Submissions deadline. Received 64 entries. Announced first-round selections of 51 candidates. 2009: After First SHA-3 candidate conference in Feb, announced 14 Second Round Candidates in July. 2010: After one year public review of the algorithms, hold second SHA-3 candidate conference in Aug. Announced 5 Third-round candidates in Dec. 2011: Public comment for final round 2012: October 2, NIST selected SHA3 – Keccak (pronounced “catch-ack”) created by Guido Bertoni, Joan Daemen and Gilles Van Assche, Michaël Peeters CS526 Topic 5: Hash Functions and Message Authentication 13

The Sponge Construction: Used by SHA-3 Each round, the next r bits of message is XOR’ed into the first r bits of the state, and a function f is applied to the state. After message is consumed, output r bits of each round as the hash output; continue applying f to get new states SHA-3 uses 1600 bits for state size CS526 Topic 5: Hash Functions and Message Authentication 14

Choosing the length of Hash outputs The Weakest Link Principle: – A system is only as secure as its weakest link. Hence all links in a system should have similar levels of security. Because of the birthday attack, the length of hash outputs in general should double the key length of block ciphers – SHA-224 matches the 112-bit strength of triple-DES (encryption 3 times using DES) – SHA-256, SHA-384, SHA-512 match the new key lengths (128,192,256) in AES CS526 Topic 5: Hash Functions and Message Authentication 15

Limitation of Using Hash Functions for Authentication Require an authentic channel to transmit the hash of a message – Without such a channel, it is insecure, because anyone can compute the hash value of any message, as the hash function is public – Such a channel may not always exist How to address this? – use more than one hash functions – use a key to select which one to use CS526 Topic 5: Hash Functions and Message Authentication 16

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 K, there is a hash function hK H . Each hK: X Y Alternatively, one can think of H as a function K X Y CS526 Topic 5: Hash Functions and Message Authentication 17

Message Authentication Code A MAC scheme is a hash family, used for message authentication MAC(K,M) HK(M) The sender and the receiver share secret K The sender sends (M, Hk(M)) The receiver receives (X,Y) and verifies that HK(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 HK(X’) Y’. CS526 Topic 5: Hash Functions and Message Authentication 18

Security Requirements for MAC Resist the Existential Forgery under Chosen Plaintext Attack – Challenger chooses a random key K – Adversary chooses a number of messages M1, M2, ., Mn, and obtains tj MAC(K,Mj) for 1 j n – Adversary outputs M’ and t’ – Adversary wins if j M’ Mj, and t’ MAC(K,M’) Basically, adversary cannot create the MAC for a message for which it hasn’t seen an MAC CS526 Topic 5: Hash Functions and Message Authentication 19

Constructing MAC from Hash Functions Let h be a one-way hash function MAC(K,M) h(K M), where denote concatenation – Insecure as MAC – Because of the Merkle-Damgard construction for hash functions, given M and t h(K M), adversary can compute M’ M Pad(M) X and t’, such that h(K M’) t’ CS526 Topic 5: Hash Functions and Message Authentication 20

HMAC: Constructing MAC from Cryptographic Hash Functions HMACK[M] Hash[(K opad) Hash[(K ipad) M)]] K is the key padded (with 0) to B bytes, the input block size of the hash function ipad the byte 0x36 repeated B times opad the byte 0x5C repeated B times. At high level, HMACK[M] H(K H(K M)) CS526 Topic 5: Hash Functions and Message Authentication 21

HMAC Security If used with a secure hash functions (e.g., SHA-256) and according to the specification (key size, and use correct output), no known practical attacks against HMAC CS526 Topic 5: Hash Functions and Message Authentication 22

Coming Attractions Cryptography: Public Key Cryptography CS526 Topic 5: Hash Functions and Message Authentication 23