1. Data & Network Security
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Data & Network Security
Mehrdad Nourani

2. 4/23/2017
Session 14
Hash Algorithms

3. Well-known Hash Functions
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Well-known Hash Functions

4. see similarities in the evolution of hash functions & block ciphers
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

5. 4/23/2017
MD5/MD4 Algorithm

6. designed by Ronald Rivest (the R in RSA – Rivest-Shamir-Adleman)
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MD5
designed by Ronald Rivest (the R in RSA – Rivest-Shamir-Adleman)
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 is the current, and very widely used, member of Rivest’s family of hash functions.

7. Step 1: pad message so that we have:
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MD5 Overview
Step 1: pad message so that we have:
length mod 512 = 448 or equivalently length ≡ 448 (mod 512)
The above makes the length of padded message to be 64 bits less than an integer multiple of 512 bits.
Padding is always added even if the message is already of the desired length. e.g. if the message is 448 bits long, it is padded by 512 bits to a length of 960 bits.
Number of padding bits is in range of 1 to 512 bits.
Padding is a single “1” followed by the necessary number of “0”s
Step 2: append a 64-bit length value to message
This is K mod 264 where k is the length of message
The padded message is broken into 512-bit blocks, processed along with the buffer value using 4 rounds, and the result added to the input buffer to make the new buffer value. Repeat till run out of message, and use final buffer value as hash. nb. due to padding always have a full final block (with length in it).

8. 4/23/2017
MD5 Overview (cont.)
Step 3: initialize 4-word (128-bit) MD buffer (A,B,C,D) to given values:
A= , B=EFCDAB89, C=98BADCFE, D=
Save the values in little-endian format (the least significant byte of a word in the low-address position)
Word A= , Word B= 89 AB CD EF,
Word C= FE DC BA 98 , Word D=
Step 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
Step 5: After all L 512-bit blocks have been processed the output from the Lth stage is the 128-bit message digest (hash code).
The padded message is broken into 512-bit blocks, processed along with the buffer value using 4 rounds, and the result added to the input buffer to make the new buffer value. Repeat till run out of message, and use final buffer value as hash. nb. due to padding always have a full final block (with length in it).

9. 4/23/2017
MD5 Structure
Stallings Fig 12.1

10. Single 512-bit (HMD5) Block
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Single 512-bit (HMD5) Block
Stallings Fig 12.2

11. Summary of MD5 Behavior Where: The MD5 behaviour can be summarized as:
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Summary of MD5 Behavior
The MD5 behaviour can be summarized as:
CV0 = IV
CVq+1= SUM32[CVq,RFI(Yq,RFH(Yq,RFG(Yq,RFF(Yq,CVq))))]
MD = CVL-1
Where:
IV: Initial value (stored in ABCD buffers)
Yq: the qth 512-bit block of the message
L: number of blocks in the message
CVq: chaining variable processed with the qth block
RFx: round function using primitive logical function x
SUM32: addition mod 232 performed separately on each word of the pair of inputs
MD: final message digest value
Note that SUM32 symbol here is the same as what picture in pp. 10 shows.
CVq is 128 bits and splits into 4 32-bits parts.

12. MD5 Compression Function
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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) (see book for details)
X[k]=M[q*16+k]=the kth 32-bit word in the qth 512-bit block of the message
T[i] is a constant value derived from sin, that is T[i] = 232 * abs[sin(i)] and can be found in a lookup table (matrix T)
<<< s is circular shift of the 32-bit argument by s bits
All additions are modulo 232
Each round mixes the buffer input with the next "word" of the message in a complex, non-linear manner. A different non-linear function is used in each of the 4 rounds (but the same function for all 16 steps in a round). The 4 buffer words (a,b,c,d) are rotated from step to step so all are used and updated. g is one of the primitive functions F,G,H,I for the 4 rounds respectively. X[k] is the kth 32-bit word in the current message block. T[i] is the ith entry in the matrix of constants T. The addition of varying constants T and the use of different shifts helps ensure it is extremely difficult to compute collisions.

13. MD5’s Logical Functions
In terms of logical operations:
F(b,c,d) = bc + b’c
G(b,c,d) = bd + cd’
H(b,c,d) = b  c  d
I(b,c,d) = c  (b + d’)

14. Matrix T in MD5

15. MD5 Compression Function - Single Step
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MD5 Compression Function - Single Step
Part of Message
Constants
Circular Left Shift (rotation) by s bits
S (the amount of circular shift) is determined according to RFC See pp. 355 of text.

16. also produces a 128-bit hash of message
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MD4
precursor to MD5
also produces a 128-bit hash of message
has 3 rounds of 16 steps versus 4 in MD5
design goals:
collision resistant (hard to find collisions)
direct security (no dependence on "hard" problems)
fast, simple, compact
favours little-endian (the least significant bytes in the low-address byte position) systems (e.g. Intel’s 80xxx and Pentium)
MD4 is the precursor to MD5, and was widely used. It uses 3 instead of 4 rounds, and the round functions are a little simpler. In creating MD5 Rivest aimed to strengthen the algorithms by introducing the extra round, and varying the constants used.
Sun architecture uses big-endian and thus needs to reverse order. This is no problem as the big-endian machines are often historically faster and can afford this computation overhead.

17. Strength and Weakness of MD5
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Strength and Weakness 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
Two new alternatives: SHA-1 and RIPEMD-160
Some progress has been made analysing MD5, which along with the hash size of 128-bits means its starting to look too small. Hence interest in hash functions that create larger hashes.

18. 4/23/2017
SHA-1 Algorithm

19. Secure Hash Algorithm (SHA-1)
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Secure Hash Algorithm (SHA-1)
SHA was designed by National Institute of Standards and Technology (NIST) & NSA in 1993, revised 1995 as SHA-1
US standard for use with DSA signature scheme
standard is FIPS , also Internet RFC3174
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 a few key differences
SHA is one of the newer generation of hash functions, more resistant to cryptanalysis, and now probably preferred for new applications.

20. append a 64-bit length value to message
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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:
( , efcdab89, 98badcfe, , 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
Note that the SHA-1 Overview is very similar to that of MD5.

21. Single 512-Bit Block Function in SHA-1
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Single 512-Bit Block Function in SHA-1

22. Summary of SHA-1 Behavior
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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

23. SHA-1 Compression Function
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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 (0≤t≤79)
Sk: circular left-shift (rotation) of the 32-bit argument by k bits (same as “<<< k”)
f(t,B,C,D) is a nonlinear function for round
Wt is derived from the message block
Kt is a additive constant value derived from integer part of 232 x i0.5 for i=2,3,5,10.
All +’s are modulo 232 additions
Can see SHA shares much in common with MD4/5, but with 20 instead of 16 steps in each of the 4 rounds. Note the 4 constants are based on sqrt(2,3,5,10). Note also that instead of just splitting the input block into 32-bit words and using them directly, SHA-1 shuffles and mixes them using rotates & XOR’s to form a more complex input, and greatly increases the difficulty of finding collisions.

24. SHA-1 Compression Function
Circular Left Shift (rotation) by k bits

25. Logical Functions f In terms of logical operations:
0≤t≤19 f1= f(t,B,C,D)= BC + B’D
20≤t≤39 f2= f(t,B,C,D)= B  C  D
40≤t≤59 f3= f(t,B,C,D)= BC + BD + CD
60≤t≤79 f4= f(t,B,C,D)= B  C  D

26. Additive Constant Kt
Only 4 distinct constants are used:

27. 4/23/2017
32-Bit Word Values Wt
The first 16 values are taken directly from the 16 words of the current blocks.
The remaining values are computed as:
Wt = S1 (Wt-16  Wt-14  Wt-8  Wt-3)

28. brute force attack is harder (160 vs 128 bits for MD5)
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SHA-1 versus 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
optimized for big-endian CPU's (vs MD5 which is optimised for little-endian CPU’s)
Compare using the design goals listed earlier.
SHA-1 is probably the preferred hash function for new applications. Currently no problems are known with it.

29. Revised Secure Hash Standard
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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 Stallings Tables 12.3 and 12.4 for details.

30. 4/23/2017
Summary of SHA-256
See Stallings Tables 12.3 and 12.4 for details.

31. 4/23/2017
Summary of SHA-384
See Stallings Tables 12.3 and 12.4 for details.

32. 4/23/2017
Summary of SHA-512
See Stallings Tables 12.3 and 12.4 for details.

33. 4/23/2017
RIPEMD-160 Algorithm

34. RIPEMD-160
RIPEMD-160 was developed in Europe as part of RIPE (RACE Integrity Primitive Evaluation) project in 1996
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 than MD5, but probably more secure than SHA and MD5

35. RIPEMD-160 Overview pad message so that: length mod 512 = 448
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RIPEMD-160 Overview
pad message so that: length mod 512 = 448
append a 64-bit length value to message
initialize 5-word (160-bit) buffer (A,B,C,D,E) to the following in little-endian format:
( , efcdab89, 98badcfe, , c3d2e1f0)
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
output hash value is the final buffer value
Note that the overall structure is quite similar to MD4/5 and SHA-1. Indeed the initialization constants are the same as SHA-1.

36. RIPEMD-160 Round
Each round take as inputs the current 512-bit block (Yq) and the 160-bit buffer ABCDE (left line) or A’B’C’D’E’ (right line) and updates the content of the buffer
Overall:
CVq+1(0)=CVq(1)+C+D’
CVq+1(1)=CVq(2)+D+E’
CVq+1(2)=CVq(3)+E+A’
CVq+1(3)=CVq(4)+A+B’
CVq+1(4)=CVq(0)+B+C’

37. RIPEMD-160 Compression Function
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RIPEMD-160 Compression Function
A 32-bit from current 512-bit block; chosen by a permutation function r(j)
Circular Left Shift (rotation) by k determined by s(j)
The compression function is rather more complex than SHA-1. See Stallings for details.

38. Constants

39. Functions f In terms of logical operations:
0≤t≤15 f1= f(t,B,C,D)= B  C  D
16≤t≤31 f2= f(t,B,C,D)= BC + B’D
32≤t≤47 f3= f(t,B,C,D)= (B + C’)  D
48≤t≤63 f4= f(t,B,C,D)= BD + CD’
64≤t≤79 f5= f(t,B,C,D)= B  (C + D’)

40. Other Elements in RIPEMD-160
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Other Elements in RIPEMD-160
The compression function is rather more complex than SHA-1. See Stallings for details.

41. 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

42. RIPEMD-160 versus MD5 & SHA-1
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RIPEMD-160 versus 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 optimized for big-endian CPU's vs RIPEMD-160 & MD5 optimized for little-endian CPU’s
RIPEMD-160 is probably the most secure of the hash algorithms, so would be chosen if that is of major concern.

43. RIPEMD-160 versus MD5 & SHA-1 (cont.)
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RIPEMD-160 versus MD5 & SHA-1 (cont.)
RIPEMD-160 is probably the most secure of the hash algorithms, so would be chosen if that is of major concern.

44. 4/23/2017
HMAC Algorithm

45. Keyed Hash Functions as MACs
have desire to create a MAC using a hash function rather than a block cipher
because hash functions (e.g. MD5 and SHA-1) are generally faster than symmetric block cipher like DES
library code for cryptographic hash functions is widely available
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 (now mandatory for IP Security protocols, SSL, etc.)

46. specified as Internet standard RFC2104
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HMAC Algorithm
specified as Internet standard RFC2104
uses hash function on the message:
HMACK(M)= H[(K+  opad)|| H[(K+  ipad)|| M)]]
where K is the secret key and K+ is the key padded out with 0’s to size b (b is the number of bits in a block)
and opad (5C hex), ipad (36 hex) are specified padding constants repeated b/8 times
overhead is just 3 more hash calculations than the message needs alone
any of MD5, SHA-1, RIPEMD-160 can be used
The idea of a keyed hash evolved into HMAC, designed to overcome some problems with the original proposals. Further have a design that has been shown to have the same security as the underlying hash alg. The hash function need only be used on 3 more blocks than when hashing just the original message (for the two keys + inner hash). Choose hash alg to use based on speed/security concerns.

47. HMAC Overview
Append zeros to the left end of K to create a b-bit string K+
XOR K+ with ipad to produce b-bit block Si
Append M to Si
Apply H to the stream generated in step 3
XOR K+ with opad to produce b-bit block So
Append the hash result from step 4 to So
Apply H to the stream generated in step 6 and output the final result.

48. Efficient Implementation of HMAC
f(cv,block) is the compression function for the hash function (the precomputed values substitute IV).

49. attacking HMAC requires either:
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. This is in order of 2n where n is the chaining variable bit-width.
birthday attack (but since keyed would need to observe a very large number of messages). Like MD5 this is in order of 2n/2 for a hash length of n.
choose hash function used based on speed versus security constraints

50. Note that HMAC is more secure than MD5 for birthday attack.
HMAC Security (cont.)
Note that HMAC is more secure than MD5 for birthday attack.
In MD5 the attacker can choose any set of messages to find a collision (i.e. H(M)=H(M’)).
In HMAC since the attacker does not know K, he cannot generate messages offline. For a hash code of 128 bits, this requires 264 observed blocks (i.e * 29=273 bits) generated using the same key. On a 1 Gbps line, this requires monitoring stream of messages with no change of the key for 250,000 years (quite infeasible!!)

51. Summary have considered: some current hash algorithms:
MD5/MD4
SHA-1
RIPEMD-160
HMAC authentication using hash function