hash functions, the md5 algorithm and the future (sha-3)
DESCRIPTION
This was filmed at the Sonoma State University mathematics colloquium on November 5th, 2008. In the talk, Dylan speaks about hash functions, their applications and attacks on them. He specifically focuses on the design of the MD5 algorithm. Dylan also gives a preview of what is in store for the future of hashes- the SHA-3 competition put on by the NIST. For a video of this presentation, visit http://www.vimeo.com/2409021TRANSCRIPT
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Hash Functions,the MD5 Algorithm
and the Future (SHA-3)
Dylan Field, Fall ’08SSU Math Colloquium
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What is a hash?
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First, Consider Humpty Dumpty...
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Humpty Dumpty sat on a wall.
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Humpty Dumpty had a great fall.
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All the king’s horses and all the king’s men
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Couldn’t put Humpty together again.
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X
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h(x)
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BUT h(x) is a one way function
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... so they can’t put Humpty together again.
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x h(x)hash function
Humpty falls
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x h(x)hash function
Humpty falls
‘hello’ MD5
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x h(x)hash function
Humpty falls
‘hello’ MD55d41402abc4b2a76b9719d91
1017c592
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- going backwards -
- going backwards -
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- going backwards -
- going backwards -
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- going backwards -
- going backwards -
NO!!!
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- going backwards -
- going backwards -
5d41402abc4b2a76b9719d91
1017c592
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- going backwards -
- going backwards -
5d41402abc4b2a76b9719d91
1017c592‘hello’
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Requirements
h(x)
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Requirements
h(x)
Given h(x)cannot find x
1
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Requirements
h(x)
Given h(x)cannot find x
1
h(x) isconstant
2
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Requirements
h(x)
Given h(x)cannot find x
1
h(x) isconstant
2
Can’t find x2
so h(x2)=h(x1)
3
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Requirement #3 - Humpty Dumpty Style
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Requirement #3 - Humpty Dumpty Style
≠
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Requirement #3 - Humpty Dumpty Style
≠ ≠
≠ ≠ .........
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so how does it work?
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‘hello’
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5d41402abc4b2a76b9719d911017c592
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we’re going to focus on MD5
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1. Convert ‘x’ to binary
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‘hello’ 0110100001100101011011000110110001101111
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1. Convert ‘x’ to binary2. Pad ‘x’ so that size of x (mod 512) = 0
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0110100001100101011011000110110001101111
1
0000000000 0000000000 0000000000 0000000000 0000000000
0000000000 0000000000 0000000000 0000000000 0000000000
0000000000 0000000000 0000000000 0000000000 0000000000
0000000000 0000000000 0000000000 0000000000 0000000000
0000000000 0000000000 0000000000 0000000000 0000000000
0000000000 0000000000 0000000000 0000000000 0000000000
0000000000 0000000000 0000000000 0000000000 0000000000
0000000000 0000000000 0000000000 0000000000 0000000000
0000000000 0000000000 0000000000 0000000000 000000000000000
0000000000101000
‘hello’ in binary
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0110100001100101011011000110110001101111
1
0000000000 0000000000 0000000000 0000000000 0000000000
0000000000 0000000000 0000000000 0000000000 0000000000
0000000000 0000000000 0000000000 0000000000 0000000000
0000000000 0000000000 0000000000 0000000000 0000000000
0000000000 0000000000 0000000000 0000000000 0000000000
0000000000 0000000000 0000000000 0000000000 0000000000
0000000000 0000000000 0000000000 0000000000 0000000000
0000000000 0000000000 0000000000 0000000000 0000000000
0000000000 0000000000 0000000000 0000000000 000000000000000
0000000000101000
‘hello’ in binary
add ‘1’
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0110100001100101011011000110110001101111
1
0000000000 0000000000 0000000000 0000000000 0000000000
0000000000 0000000000 0000000000 0000000000 0000000000
0000000000 0000000000 0000000000 0000000000 0000000000
0000000000 0000000000 0000000000 0000000000 0000000000
0000000000 0000000000 0000000000 0000000000 0000000000
0000000000 0000000000 0000000000 0000000000 0000000000
0000000000 0000000000 0000000000 0000000000 0000000000
0000000000 0000000000 0000000000 0000000000 0000000000
0000000000 0000000000 0000000000 0000000000 000000000000000
0000000000101000
‘hello’ in binary
add ‘1’
0’s until x mod 512 = 496
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0110100001100101011011000110110001101111
1
0000000000 0000000000 0000000000 0000000000 0000000000
0000000000 0000000000 0000000000 0000000000 0000000000
0000000000 0000000000 0000000000 0000000000 0000000000
0000000000 0000000000 0000000000 0000000000 0000000000
0000000000 0000000000 0000000000 0000000000 0000000000
0000000000 0000000000 0000000000 0000000000 0000000000
0000000000 0000000000 0000000000 0000000000 0000000000
0000000000 0000000000 0000000000 0000000000 0000000000
0000000000 0000000000 0000000000 0000000000 000000000000000
0000000000101000
‘hello’ in binary
add ‘1’
0’s until x mod 512 = 496
add 16 bit binary representation of x
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xpadded = 0110100001100101011011000110110001101111 1 0000000000 0000000000 0000000000 0000000000 0000000000 0000000000 0000000000 0000000000 0000000000 0000000000 0000000000 0000000000 0000000000 0000000000 0000000000 0000000000 0000000000 0000000000 0000000000 0000000000 0000000000 0000000000 0000000000 0000000000 0000000000 0000000000 0000000000 0000000000 0000000000 0000000000 0000000000 0000000000 0000000000 0000000000 0000000000 0000000000 0000000000 0000000000 0000000000 0000000000 0000000000
0000000000 0000000000 0000000000 0000000000 00000 0000000000101000
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1. Convert ‘x’ to binary2. Pad ‘x’ so that size of x (mod 512) = 03. Break ‘x’ into 512 bit sub parts and 32 bit words
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01101000011001010110110001101100
0110100001100101011011000110110001101111 1 0000000000 0000000000 0000000000 0000000000 0000000000 0000000000 0000000000 0000000000 0000000000 0000000000 0000000000 0000000000 0000000000 0000000000 0000000000 0000000000 0000000000 0000000000 0000000000 0000000000 0000000000 0000000000 0000000000 0000000000 0000000000 0000000000 0000000000 0000000000 0000000000 0000000000 0000000000 0000000000 0000000000 0000000000 0000000000 0000000000 0000000000 0000000000 0000000000 0000000000 0000000000
0000000000 0000000000 0000000000 0000000000 00000 0000000000101000
W1 =
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1. Convert ‘x’ to binary2. Pad ‘x’ so that size of x (mod 512) = 03. Break ‘x’ into 512 bit sub parts and 32 bit words4. Assign values to k[i], r[i], w[g], h0, h1, h2 and h3.
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k[i] = |sin(i+1)| x 232 where ‘i’ is in radians
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k[i] = |sin(i+1)| x 232 where ‘i’ is in radians
r[i] = Various round shift amounts
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k[i] = |sin(i+1)| x 232 where ‘i’ is in radians
r[i] = Various round shift amounts
w[g] = Word number (0 – 15)
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k[i] = |sin(i+1)| x 232 where ‘i’ is in radians
r[i] = Various round shift amounts
w[g] = Word number (0 – 15)
h0 = a = 0x67452301
h1 = b = 0xEFCDAB89
h2 = c = 0x98BADCFE
h3 = d = 0x10325476
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1. Convert ‘x’ to binary2. Pad ‘x’ so that size of x (mod 512) = 03. Break ‘x’ into 512 bit sub parts and 32 bit words4. Assign values to k[i], r[i], w[g], h0, h1, h2 and h3.5. Perform 64 rounds on each sub part
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But first... binary operations!
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∧
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∧(AKA ‘AND’)
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p q ∧T T
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p q ∧T T T
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p q ∧T T T
T F
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p q ∧T T T
T F F
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p q ∧T T T
T F F
F T
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p q ∧T T T
T F F
F T F
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p q ∧T T T
T F F
F T F
F F
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p q ∧T T T
T F F
F T F
F F F
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In binary:T = 1F = 0
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p q ∧T T T
T F F
F T F
F F F
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p q ∧T T T
T F F
F T F
F F F
bit 1 bit 2 ∧1 1 1
1 0 0
0 1 0
0 0 0
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∨
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⊕
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bit 1 bit 2 ∨1 1 1
1 0 1
0 1 1
0 0 0
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“XOR is a type of logical disjunction on two operands that results in a value of “true” if and only if exactly one of the operands has a
value of ‘true’”
⊕
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bit 1 bit 2 ∨1 1 1
1 0 1
0 1 1
0 0 0
bit 1 bit 2 ⊕1 1 F
1 0 T
0 1 T
0 0 F
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¬
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¬(not)
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¬1=0¬0=1
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<<(bit shift)
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1 0 1 0 1 0
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0 1 0 1 0 0
0 1 0 1 0
0
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Remember:a,b,c,d are h0-3
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Operation A
f = (b ∧ c) ∨ (¬ b ∧ d)g = i
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Operation B
f = (d ∧ b) ∨ ((¬ d) ∧ c)g = (5i + 1) mod 16
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Operation C
f = b ⊕ c ⊕ dg = (3i + 5) mod 16
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Operation D
f = c ⊕ (b ∨ (¬ d))g = (7i) mod 16
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A B C D
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A B C D
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A B C D
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B
b + {(a + f + k[i] + w[g]) << r[i]}
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b + {(a + f + k[i] + w[g]) << r[i]}
h1 h0
Calculated inOperations A-D
|sin(i+1)| x 232 where ‘i’ is in radians
The gth word(32 bit chunk)
ith pre-designated shift
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After all 64 rounds...
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1. Convert ‘x’ to binary2. Pad ‘x’ so that size of x (mod 512) = 03. Break ‘x’ into 512 bit sub parts and 32 bit words4. Assign values to k[i], r[i], w[g], h0, h1, h2 and h3.5. Perform 64 rounds on each sub part6. Add a, b, c and d to register values
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h0 = h0 + ah1 = h1 + bh2 = h2 + ch3 = h3 + d
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1. Convert ‘x’ to binary2. Pad ‘x’ so that size of x (mod 512) = 03. Break ‘x’ into 512 bit sub parts and 32 bit words4. Assign values to k[i], r[i], w[g], h0, h1, h2 and h3.5. Perform 64 rounds on each sub part6. Add a, b, c and d to register values7. Append the register values to create digest
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128 bit digest
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‘hello’
![Page 95: Hash Functions, the MD5 Algorithm and the Future (SHA-3)](https://reader037.vdocuments.site/reader037/viewer/2022102521/5464a5e3af7959e2648b5146/html5/thumbnails/95.jpg)
5d41402abc4b2a76b9719d911017c592
![Page 96: Hash Functions, the MD5 Algorithm and the Future (SHA-3)](https://reader037.vdocuments.site/reader037/viewer/2022102521/5464a5e3af7959e2648b5146/html5/thumbnails/96.jpg)
So?
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Applications
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Applications
PasswordProtection
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Applications
PasswordProtection
MessageIntegrity
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Applications
PasswordProtection
MessageIntegrity
DigitalSignatures
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Password Protection
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‘password’MD5
When you registered...
5f4dcc3b5aa765d61d8327deb882cf99
![Page 104: Hash Functions, the MD5 Algorithm and the Future (SHA-3)](https://reader037.vdocuments.site/reader037/viewer/2022102521/5464a5e3af7959e2648b5146/html5/thumbnails/104.jpg)
‘password’MD5
When you registered...
5f4dcc3b5aa765d61d8327deb882cf99
Data Base
![Page 105: Hash Functions, the MD5 Algorithm and the Future (SHA-3)](https://reader037.vdocuments.site/reader037/viewer/2022102521/5464a5e3af7959e2648b5146/html5/thumbnails/105.jpg)
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‘password’
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‘password’MD5
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‘password’MD5
5f4dcc3b5aa765d61d8327deb882cf99
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5f4dcc3b5aa765d61d8327deb882cf99
=
stored, hashed password?
![Page 110: Hash Functions, the MD5 Algorithm and the Future (SHA-3)](https://reader037.vdocuments.site/reader037/viewer/2022102521/5464a5e3af7959e2648b5146/html5/thumbnails/110.jpg)
5f4dcc3b5aa765d61d8327deb882cf99
=
stored, hashed password?
No.
Give ‘incorrect password’ error
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5f4dcc3b5aa765d61d8327deb882cf99
=
stored, hashed password?
No.
Give ‘incorrect password’ error
Yes.
Let user into website
![Page 112: Hash Functions, the MD5 Algorithm and the Future (SHA-3)](https://reader037.vdocuments.site/reader037/viewer/2022102521/5464a5e3af7959e2648b5146/html5/thumbnails/112.jpg)
![Page 113: Hash Functions, the MD5 Algorithm and the Future (SHA-3)](https://reader037.vdocuments.site/reader037/viewer/2022102521/5464a5e3af7959e2648b5146/html5/thumbnails/113.jpg)
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Attacks
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Rainbow Tables
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omgyouarenevergoingtocrackthis
123
1c9fee8bd70a5afb630fc4f38e97123f
![Page 118: Hash Functions, the MD5 Algorithm and the Future (SHA-3)](https://reader037.vdocuments.site/reader037/viewer/2022102521/5464a5e3af7959e2648b5146/html5/thumbnails/118.jpg)
omgyouarenevergoingtocrackthis
123
1c9fee8bd70a5afb630fc4f38e97123f
![Page 119: Hash Functions, the MD5 Algorithm and the Future (SHA-3)](https://reader037.vdocuments.site/reader037/viewer/2022102521/5464a5e3af7959e2648b5146/html5/thumbnails/119.jpg)
and Brute Force Attacks
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Message Integrity
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digest
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File Verification
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File Verification
Guarding against corruption
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File Verification
Guarding against corruption
Proving you have something
before you release it
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Attacks
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Nostradamus Attack
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![Page 129: Hash Functions, the MD5 Algorithm and the Future (SHA-3)](https://reader037.vdocuments.site/reader037/viewer/2022102521/5464a5e3af7959e2648b5146/html5/thumbnails/129.jpg)
But on November 30th 2007...
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“We have used a Sony Playstation 3 to correctly predict the outcome of the 2008 US presidential elections. In order not to
influence the voters we keep our prediction secret, but commit to it by publishing its cryptographic hash on this website. The
document with the correct prediction and matching hash will be revealed after the elections.”
- Marc Stevens, Arjen Lenstra and Benne de Weger
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3D515DEAD7AA16560ABA3E9DF05CBC80
![Page 132: Hash Functions, the MD5 Algorithm and the Future (SHA-3)](https://reader037.vdocuments.site/reader037/viewer/2022102521/5464a5e3af7959e2648b5146/html5/thumbnails/132.jpg)
But how could they have known!?!?
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But how could they have known!?!?They didn’t.
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3D515DEAD7AA16560ABA3E9DF05CBC80
![Page 135: Hash Functions, the MD5 Algorithm and the Future (SHA-3)](https://reader037.vdocuments.site/reader037/viewer/2022102521/5464a5e3af7959e2648b5146/html5/thumbnails/135.jpg)
Digital Signatures
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MD5hash
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hashMD5
privatekey
encrypted
![Page 139: Hash Functions, the MD5 Algorithm and the Future (SHA-3)](https://reader037.vdocuments.site/reader037/viewer/2022102521/5464a5e3af7959e2648b5146/html5/thumbnails/139.jpg)
hashMD5
privatekey
encryptedpublic
key
hash
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hashMD5
privatekey
encryptedpublic
key
hash
MD5
![Page 141: Hash Functions, the MD5 Algorithm and the Future (SHA-3)](https://reader037.vdocuments.site/reader037/viewer/2022102521/5464a5e3af7959e2648b5146/html5/thumbnails/141.jpg)
hashMD5
privatekey
encryptedpublic
key
hash
MD5
✔
![Page 142: Hash Functions, the MD5 Algorithm and the Future (SHA-3)](https://reader037.vdocuments.site/reader037/viewer/2022102521/5464a5e3af7959e2648b5146/html5/thumbnails/142.jpg)
Attacks
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Collision Attack
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hash
privatekey
encryptedpublic
key
hash
MD5
✔
![Page 145: Hash Functions, the MD5 Algorithm and the Future (SHA-3)](https://reader037.vdocuments.site/reader037/viewer/2022102521/5464a5e3af7959e2648b5146/html5/thumbnails/145.jpg)
hash
encryptedpublic
key
hash✔
Changed Message
MD5
![Page 146: Hash Functions, the MD5 Algorithm and the Future (SHA-3)](https://reader037.vdocuments.site/reader037/viewer/2022102521/5464a5e3af7959e2648b5146/html5/thumbnails/146.jpg)
Very Dangerous!
![Page 147: Hash Functions, the MD5 Algorithm and the Future (SHA-3)](https://reader037.vdocuments.site/reader037/viewer/2022102521/5464a5e3af7959e2648b5146/html5/thumbnails/147.jpg)
Birthday Attack
![Page 148: Hash Functions, the MD5 Algorithm and the Future (SHA-3)](https://reader037.vdocuments.site/reader037/viewer/2022102521/5464a5e3af7959e2648b5146/html5/thumbnails/148.jpg)
Relies on ‘Birthday Paradox’
![Page 149: Hash Functions, the MD5 Algorithm and the Future (SHA-3)](https://reader037.vdocuments.site/reader037/viewer/2022102521/5464a5e3af7959e2648b5146/html5/thumbnails/149.jpg)
First we calculate the chance no one has the same birthday
Relies on ‘Birthday Paradox’
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p(1)=100%
![Page 151: Hash Functions, the MD5 Algorithm and the Future (SHA-3)](https://reader037.vdocuments.site/reader037/viewer/2022102521/5464a5e3af7959e2648b5146/html5/thumbnails/151.jpg)
p(2)=(1)(1 - 1/365)
![Page 152: Hash Functions, the MD5 Algorithm and the Future (SHA-3)](https://reader037.vdocuments.site/reader037/viewer/2022102521/5464a5e3af7959e2648b5146/html5/thumbnails/152.jpg)
p(3)=(1)(1 - 1/365)(1 - 2/365)
![Page 153: Hash Functions, the MD5 Algorithm and the Future (SHA-3)](https://reader037.vdocuments.site/reader037/viewer/2022102521/5464a5e3af7959e2648b5146/html5/thumbnails/153.jpg)
To Generalize...
![Page 154: Hash Functions, the MD5 Algorithm and the Future (SHA-3)](https://reader037.vdocuments.site/reader037/viewer/2022102521/5464a5e3af7959e2648b5146/html5/thumbnails/154.jpg)
365! .365n(365-n)!
P(n)=
![Page 155: Hash Functions, the MD5 Algorithm and the Future (SHA-3)](https://reader037.vdocuments.site/reader037/viewer/2022102521/5464a5e3af7959e2648b5146/html5/thumbnails/155.jpg)
23 50% chance
![Page 156: Hash Functions, the MD5 Algorithm and the Future (SHA-3)](https://reader037.vdocuments.site/reader037/viewer/2022102521/5464a5e3af7959e2648b5146/html5/thumbnails/156.jpg)
30 70.6% chance
![Page 157: Hash Functions, the MD5 Algorithm and the Future (SHA-3)](https://reader037.vdocuments.site/reader037/viewer/2022102521/5464a5e3af7959e2648b5146/html5/thumbnails/157.jpg)
50 97% chance
![Page 158: Hash Functions, the MD5 Algorithm and the Future (SHA-3)](https://reader037.vdocuments.site/reader037/viewer/2022102521/5464a5e3af7959e2648b5146/html5/thumbnails/158.jpg)
We can use this property to find out how many hashes must
be calculated to find a collision.
![Page 159: Hash Functions, the MD5 Algorithm and the Future (SHA-3)](https://reader037.vdocuments.site/reader037/viewer/2022102521/5464a5e3af7959e2648b5146/html5/thumbnails/159.jpg)
Current State of MD5
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MD5 =
![Page 161: Hash Functions, the MD5 Algorithm and the Future (SHA-3)](https://reader037.vdocuments.site/reader037/viewer/2022102521/5464a5e3af7959e2648b5146/html5/thumbnails/161.jpg)
MD5 = Broken
![Page 162: Hash Functions, the MD5 Algorithm and the Future (SHA-3)](https://reader037.vdocuments.site/reader037/viewer/2022102521/5464a5e3af7959e2648b5146/html5/thumbnails/162.jpg)
The Future of Hashes
![Page 163: Hash Functions, the MD5 Algorithm and the Future (SHA-3)](https://reader037.vdocuments.site/reader037/viewer/2022102521/5464a5e3af7959e2648b5146/html5/thumbnails/163.jpg)
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Submissions were due on October 30th
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Currently Submitted
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BLAKE
Blue Midnight Wish
Boole
CubeHashEdon-R
EnRUPT
ESSENCE
Sgàil
Grøstl
Keccak
Maraca
MCSSHA-3
MD6
NaSHANKS2D
PonicSHAMATA
Skein
WaMM
Waterfall
![Page 167: Hash Functions, the MD5 Algorithm and the Future (SHA-3)](https://reader037.vdocuments.site/reader037/viewer/2022102521/5464a5e3af7959e2648b5146/html5/thumbnails/167.jpg)
BLAKE
Blue Midnight Wish
Boole
CubeHashEdon-R
EnRUPT
ESSENCE
Sgàil
Grøstl
Keccak
Maraca
MCSSHA-3
MD6
NaSHANKS2D
PonicSHAMATA
Skein
WaMM
Waterfall
![Page 168: Hash Functions, the MD5 Algorithm and the Future (SHA-3)](https://reader037.vdocuments.site/reader037/viewer/2022102521/5464a5e3af7959e2648b5146/html5/thumbnails/168.jpg)
![Page 169: Hash Functions, the MD5 Algorithm and the Future (SHA-3)](https://reader037.vdocuments.site/reader037/viewer/2022102521/5464a5e3af7959e2648b5146/html5/thumbnails/169.jpg)
Thank you for coming!
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Any Questions?