Hash

Cryptography and Network Security 1
CS549:
Cryptography and Network
Security
© by Xiang-Yang Li
Department of Computer Science,
IIT

Notice©
This lecture note (Cryptography and Network Security) is prepared by
Xiang-Yang Li. This lecture note has benefited from numerous
textbooks and online materials. Especially the “Cryptography and
Network Security” 2nd edition by William Stallings and the
“Cryptography: Theory and Practice” by Douglas Stinson.
You may not modify, publish, or sell, reproduce, create derivative
works from, distribute, perform, display, or in any way exploit any
of the content, in whole or in part, except as otherwise expressly
permitted by the author.
The author has used his best efforts in preparing this lecture note.
The author makes no warranty of any kind, expressed or implied,
with regard to the programs, protocols contained in this lecture
note. The author shall not be liable in any event for incidental or
consequential damages in connection with, or arising out of, the
furnishing, performance, or use of these.

Cryptography and Network
Security
Hash Algorithms
Xiang-Yang Li

Hash Function
 Map a message to a smaller value
 Requirements
 Be applied to a block of data of any size
 Produced a fixed length output
 H(x) is easy to compute (by hardware, software)
 One-way: given code h, it is computationally infeasible
to find x: H(x)=h
 Weak collision resistance: given x, computationally
infeasible to find y so H(x)=H(y)
 Strong collision resistance: Computationally
infeasible to find x, y so H(x)=H(y)

Hash Algorithms
 see similarities in the evolution of hash
functions & block ciphers
 increasing power of brute-force attacks
 leading to evolution in algorithms
 from DES to AES in block ciphers
 from MD4 & MD5 to SHA-1 & RIPEMD-160 in hash
algorithms
 likewise tend to use common iterative
structure as do block ciphers

Basic Uses of Hash Function
 Six basics usages
 Ek(M||H(M))
 Confidentiality and authentication
 M|| Ek(H(M))
 Authentication
 M|| EKRa(H(M))
 Authentication and digital signature
 Ek(M|| EKRa(H(M)))
 Authentication, digital signature and confidentiality
 M||H(M||S)
 Authentication (S shared by both sides)
 Ek(M||H(M||S))
 Confidentiality and authentication

Birthday Attacks
 If 64-bits hash code is used
 On average, how many messages need to try to find one
match the intercepted hash code?
 Birthday paradox
 A will sign a message appended with m-bits hash code
 Attacker generates some variations of fraud message,
also variations of good message
 Find pair of message each from the two sets messages
 Such that they have the same hash code
 Give good message to A to get signature
 Replace good message with fraud message

Analysis
 Using birthday attack, given 64-bits hash
code
 How many message variations needed so the success
probability is large, say 90%?

Examples
 Simple hash functions
 XOR of the input message
 H(M)=X1 X2 … Xm-1 Xm
 But not secure
 Ym=H(M)  Y1 Y2 … Ym-1 has same hash value as
(X1X2 … Xm-1 Xm), where Yi is any value

Cont.
 Based on DES, block chaining technique
 Rabin, 1978
 Divide message M into fix-sized blocks Mi
 Assume total n data blocks
 H0=initial value
 Hi=Emi[Hi-1]
 Hn is the hash value
 Birthday attack still applies
 If still 64-bits code used

More Attacks
 Birthday attack applied if chosen plaintext
 Meet in the middle attack if known
plaintext
 Known signed hash code G
 Construct n-2 desired message block Qi
 Compute Hi=EQi[Hi-1]
 Generate 2m/2 random blocks X
 For each X, Compute Hn-1=EX[Hn-2]
 Generate 2m/2 random blocks Y
 For each Y, Compute H’n-1=DY[G]
 Find X, Y such that Hn-1= H’n-1
 Then Q1, Q2,…Qn-2, X,Y is a fraud message

Security
 The size of hash code determines security
 128bits is not secure
 Currently, most use 160 bits hash code
 Now recommend 256 bits
 Attack MAC
 Objective is to find valid (x, Ck(x)) pair
 Attack the key space: roughly 2k, k =key size
 Attack the MAC value

More Hash Algorithms
 Algorithms
 Message Digest:MD5 (was mostly widely used)
 Secure Hash Algorithm: SHA-1 (from MD4)
 RIPEMD-160
 HMAC

MD5
 designed by Ronald Rivest (the R in RSA)
 latest in a series of MD2, MD4
 produces a 128-bit hash value
 until recently was the most widely used
hash algorithm
 in recent times have both brute-force & cryptanalytic
concerns
 specified as Internet standard RFC1321

MD5 Overview
1. pad message so its length is 448 mod 512
2. append a 64-bit length value to message
3. initialise 4-word (128-bit) MD buffer
(A,B,C,D)
4. process message in 16-word (512-bit)
blocks:
 using 4 rounds of 16 bit operations on message block
& buffer
 add output to buffer input to form new buffer value
5. output hash value is the final buffer value

MD5 Overview

MD5 Compression Function
 each round has 16 steps of the form:
a = b+((a+g(b,c,d)+X[k]+T[i])<<<s)
 a,b,c,d refer to the 4 words of the buffer,
but used in varying permutations
 note this updates 1 word only of the buffer
 after 16 steps each word is updated 4 times
 where g(b,c,d) is a different nonlinear
function in each round (F,G,H,I)
 T[i] is a constant value derived from sin

MD5 Compression Function

MD4
 precursor to MD5
 also produces a 128-bit hash of message
 has 3 rounds of 16 steps vs 4 in MD5
 design goals:
 collision resistant (hard to find collisions)
 direct security (no dependence on "hard" problems)
 fast, simple, compact
 favours little-endian systems (eg PCs)

Strength of MD5
 MD5 hash is dependent on all message bits
 Rivest claims security is good as can be
 known attacks are:
 Berson 92 attacked any 1 round using differential
cryptanalysis (but can’t extend)
 Boer & Bosselaers 93 found a pseudo collision (again
unable to extend)
 Dobbertin 96 created collisions on MD compression
function (but initial constants prevent exploit)
 conclusion is that MD5 looks vulnerable
soon

Bad news
 Chinese authors (Wang, Feng, Lai, and Yu) reported a
family of collisions in MD5
 (fixing the previous bug in their analysis), and also reported
that their method can efficiently (2^40 hash steps) find a
collision in SHA-0.
 August Crypto 2004,
 MD5 is fatally wounded; its use will be phased out.
SHA-1 is still alive but the vultures are circling. A
gradual transition away from SHA-1 will now start.
The first stage will be a debate about alternatives,
leading to a consensus among practicing
cryptographers about what the substitute will be.

 On 1 March 2005, Arjen Lenstra, Xiaoyun Wang and Benne
de Weger demonstrated[10] construction of two X.509
certificates with different public keys and the same MD5
hash, a demonstrably practical collision. The construction
included private keys for both public keys.
 A few days later, Vlastimil Klima described[11] an improved
algorithm, able to construct MD5 collisions in a few hours on
a single notebook computer.
 On 18 March 2006, Klima published an algorithm[12] that can
find a collision within one minute on a single notebook
computer, using a method he calls tunneling.

Why collisions are bad
 An example of what you might do with this.
 You could request an SSL certificate (for your real identity)
from a certificate authority. After the response comes back,
you can then use that response (which is based on the MD5
of your identity+key) to "authenticate" a carefully chosen
different certificate, one which claims that you are
LargeBankOrSoftwareCorp., but which has the same MD5 as
your real identity. You can then present this to other people
in order to convince them that you are someone whom you
are not.
 Another example,
 core internet routers use md5 to exchange passwords. I
simply sniff the md5sum, and if I can find a string that
generates the same sum, easily, I can send my own routing
update that takes down the internet. More examples, since a
LOT of applications use md5, but you get the idea.

Further detail
 Obviously the above attack isn't quite so simple, but
this research makes it *possible*. Before, it was
believed to be sufficiently difficult to find a collision,
that nobody worried about it. Now they are saying its
feasible to do it in hours.
 The question hanging around right now is that these
researchers managed to find collisions easily, but not
for an artbitrary string. The questions is how long
before someone modifies this method to find any
colllision. That is how much time the world has to
move away.
 More at
 http://www.freedom-to-tinker.com/archives/000664.html

What to do next
 The U.S. National Institute of Standards
and Technology is having a competition for
a new cryptographic hash function.
 The phrase "one-way hash function" might
sound arcane and geeky, but hash functions
are the workhorses of modern
cryptography.
 Submissions will be due in fall 2008, and a
single standard is scheduled to be chosen
by the end of 2011.
 we have an interim solution in SHA-256.

Secure Hash Algorithm (SHA-1)
 SHA was designed by NIST & NSA in
1993, revised 1995 as SHA-1
 US standard for use with DSA signature
scheme
 standard is FIPS 180-1 1995, also Internet RFC3174
 nb. the algorithm is SHA, the standard is SHS
 produces 160-bit hash values
 now the generally preferred hash algorithm
 based on design of MD4 with key
differences

SHA Overview
3. initialise 5-word (160-bit) buffer (A,B,C,D,E)
to
(67452301,efcdab89,98badcfe,10325476,c3d2e1f0)
4. 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

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)+(A<<5)+Wt+Kt),A,(B<<30),C,D)
 a,b,c,d refer to the 4 words of the buffer
 t is the step number
 f(t,B,C,D) is nonlinear function for round
 Wt is derived from the message block
 Kt is a constant value derived from sin

SHA-1 Compression Function

SHA-1 verses MD5
 brute force attack is harder (160 vs 128
bits for MD5)
 not vulnerable to any known attacks
(compared to MD4/5)
 a little slower than MD5 (80 vs 64 steps)
 both designed as simple and compact
 optimised for big endian CPU's (vs MD5
which is optimised for little endian CPU’s)

Revised Secure Hash Standard
 NIST have issued a revision FIPS 180-2
 adds 3 additional hash algorithms
 SHA-256, SHA-384, SHA-512
 designed for compatibility with increased
security provided by the AES cipher
 structure & detail is similar to SHA-1
 hence analysis should be similar

 See
 http://en.wikipedia.org/wiki/SHA_hash_fu
nctions
 For history of attaching this one.

RIPEMD-160
 RIPEMD-160 was developed in Europe as part of
RIPE project in 96
 by researchers involved in attacks on MD4/5
 initial proposal strengthen following analysis to
become RIPEMD-160
 somewhat similar to MD5/SHA
 uses 2 parallel lines of 5 rounds of 16 steps
 creates a 160-bit hash value
 slower, but probably more secure, than SHA

RIPEMD-160 Overview
3. initialise 5-word (160-bit) buffer (A,B,C,D,E) to
(67452301,efcdab89,98badcfe,10325476,c3d2e1f0)
4. process message in 16-word (512-bit) chunks:
 use 10 rounds of 16 bit operations on message block & buffer –
in 2 parallel lines of 5
 add output to input to form new buffer value

RIPEMD-160 Round

RIPEMD-160 Compression Function

RIPEMD-160 Design Criteria
 use 2 parallel lines of 5 rounds for
increased complexity
 for simplicity the 2 lines are very similar
 step operation very close to MD5
 permutation varies parts of message used
 circular shifts designed for best results

RIPEMD-160 verses MD5 & SHA-1
 brute force attack harder (160 like SHA-1
vs 128 bits for MD5)
 not vulnerable to known attacks, like SHA-1
though stronger (compared to MD4/5)
 slower than MD5 (more steps)
 all designed as simple and compact
 SHA-1 optimised for big endian CPU's vs
RIPEMD-160 & MD5 optimised for little
endian CPU’s

Keyed Hash Functions as MACs
 have desire to create a MAC using a hash
function rather than a block cipher
 because hash functions are generally faster
 not limited by export controls unlike block ciphers
 hash includes a key along with the message
 original proposal:
KeyedHash = Hash(Key|Message)
 some weaknesses were found with this
 eventually led to development of HMAC

HMAC
 specified as Internet standard RFC2104
 uses hash function on the message:
HMACK = Hash[(K+ XOR opad) ||
Hash[(K+ XOR ipad)||M)]]
 where K+ is the key padded out to size
 and opad, ipad are specified padding constants
 overhead is just 3 more hash calculations than the
message needs alone
 any of MD5, SHA-1, RIPEMD-160 can be used

HMAC Overview

HMAC Security
 know that the security of HMAC relates to
that of the underlying hash algorithm
 attacking HMAC requires either:
 brute force attack on key used
 birthday attack (but since keyed would need to observe
a very large number of messages)
 choose hash function used based on speed
verses security constraints

Summary
 have considered:
 some current hash algorithms: MD5, SHA-1, RIPEMD-
160
 HMAC authentication using hash function

Hash

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