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Mehrdad Nourani

Data & Network SecurityData & Network Security

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Hash Algorithms

Session 14Session 14

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Well-known Hash Functions

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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

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MD5/MD4 Algorithm

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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

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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

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MD5 Overview (cont.)• Step 3: initialize 4-word (128-bit) MD buffer

(A,B,C,D) to given values:—A=67452301, B=EFCDAB89, C=98BADCFE, D=10325476 Save the values in little-endian format (the least significant

byte of a word in the low-address position)—Word A= 01 23 45 67, Word B= 89 AB CD EF, —Word C= FE DC BA 98 , Word D= 76 54 32 10

• 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).

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MD5 Structure

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Single 512-bit (HMD5) Block

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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

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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

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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’)

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Matrix T in MD5

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MD5 Compression Function - Single Step

Circular Left Shift (rotation) by s bits

Part of Message

Constants

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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)

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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

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SHA-1 Algorithm

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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 180-1 1995, 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

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SHA Overview1. pad message so that we have: length

mod 512 = 448 or equivalently length ≡ 448 (mod 512)

2. append a 64-bit length value to message3. initialize 5-word (160-bit) buffer (A,B,C,D,E) to

the following using big-endian format:(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

5. output hash value is the final buffer value

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Single 512-Bit Block Function in SHA-1

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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

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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

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SHA-1 Compression Function

Circular Left Shift (rotation) by k bits

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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

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Additive Constant Kt

• Only 4 distinct constants are used:

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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)

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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)

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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

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Summary of SHA-256

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Summary of SHA-384

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Summary of SHA-512

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RIPEMD-160 Algorithm

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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

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RIPEMD-160 Overview1. pad message so that: length mod 512 = 4482. append a 64-bit length value to message3. initialize 5-word (160-bit) buffer (A,B,C,D,E) to the

following in little-endian format:(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

5. output hash value is the final buffer value

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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’

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RIPEMD-160 Compression Function

Circular Left Shift (rotation) by k determined by s(j)

A 32-bit from current 512-bit block; chosen by a permutation function r(j)

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Constants

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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’)

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Other Elements in RIPEMD-160

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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

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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

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RIPEMD-160 versus MD5 & SHA-1 (cont.)

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HMAC Algorithm

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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.)

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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

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HMAC Overview1. Append zeros to the

left end of K to create a b-bit string K+

2. XOR K+ with ipad to produce b-bit block Si

3. Append M to Si

4. Apply H to the stream generated in step 3

5. XOR K+ with opad to produce b-bit block So

6. Append the hash result from step 4 to So

7. Apply H to the stream generated in step 6 and output the final result.

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Efficient Implementation of HMAC

f(cv,block) is the compression function for the hash function (the precomputed values substitute IV).

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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

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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. 264 * 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!!)

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Summary• have considered:

—some current hash algorithms: – MD5/MD4– SHA-1– RIPEMD-160

—HMAC authentication using hash function