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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 kings horses and all the kings men

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Couldnt put Humpty together again.

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X

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h(x)

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BUTh(x) is a one way function

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... so they cant 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 MD5 5d41402abc4b2a76b9719d911017c592

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- going backwards -

-goingbackwards-

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- going backwards -

-goingbackwards-

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- going backwards -

-goingbackwards-

NO!!!

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- going backwards -

-goingbackwards-

5d41402abc4b2a76b9719d91

1017c592

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- going backwards -

-goingbackwards-

5d41402abc4b2a76b9719d91

1017c592hello

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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

Cant find x2so 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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were going to focus on MD5

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1 C t t bi

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1. Convert x to binary

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1 Convert x to binary

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1. Convert x to binary

2. Pad x so that size ofx (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 00000000000000000000 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

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 00000000000000000000 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

hello in binary

add 1

0s untilx 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 00000000000000000000 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

hello in binary

add 1

0s untilx mod 512 = 496

add 16 bit binaryrepresentation of x

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xpadded =0110100001100101011011000110110001101111 1 00000000000000000000 0000000000 0000000000 0000000000 00000000000000000000 0000000000 0000000000 0000000000 00000000000000000000 0000000000 0000000000 0000000000 0000000000

0000000000 0000000000 0000000000 0000000000 00000000000000000000 0000000000 0000000000 0000000000 00000000000000000000 0000000000 0000000000 0000000000 00000000000000000000 0000000000 0000000000 0000000000 00000000000000000000 0000000000 0000000000 0000000000 0000000000

0000000000 0000000000 0000000000 0000000000 000000000000000101000

1 Convert x to binary

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1. Convert x to binary

2. Pad x so that size ofx (mod 512) = 0

3. Break x into 512 bit sub parts and 32 bitwords

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01101000011001010110110001101100

0110100001100101011011000110110001101111 1 0000000000

0000000000 0000000000 0000000000 0000000000 00000000000000000000 0000000000 0000000000 0000000000 00000000000000000000 0000000000 0000000000 0000000000 00000000000000000000 0000000000 0000000000 0000000000 00000000000000000000 0000000000 0000000000 0000000000 00000000000000000000 0000000000 0000000000 0000000000 0000000000

0000000000 0000000000 0000000000 0000000000 00000000000000000000 0000000000 0000000000 0000000000 00000000000000000000 0000000000 0000000000 0000000000 00000

0000000000101000

W1 =

1 Convert x to binary

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1. Convert x to binary

2. Pad x so that size ofx (mod 512) = 0

3. Break x into 512 bit sub parts and 32 bitwords

4. 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 = 0x67452301h1 = b = 0xEFCDAB89h2 = c = 0x98BADCFEh3 = d = 0x10325476

1. Convert x to binary

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1. Convert x to binary

2. Pad x so that size ofx (mod 512) = 0

3. Break x into 512 bit sub parts and 32 bitwords

4. 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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(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 TT F

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p q

T T TT F F

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p q

T T TT F F

F T

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p q

T T TT F F

F T F

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p q

T T TT F F

F T F

F F

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p q

T T TT 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 TT F F

F T F

F F F

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p q

T T TT F F

F T F

F F F

bit 1 bit 2

1 1 11 0 0

0 1 0

0 0 0

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bit 1 bit 2

1 1 11 0 1

0 1 1

0 0 0

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XOR is a type of logical disjunction on two operands that resultsin 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 11 0 1

0 1 1

0 0 0

bit 1 bit 2

1 1 F1 0 T

0 1 T

0 0 F

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(not)

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1=00=1

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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 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])

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b + {(a + f + k[i] + w[g])

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After all 64 rounds...

1. Convert x to binary

2 P d th t i f ( d 512) 0

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2. Pad x so that size ofx (mod 512) = 0

3. Break x into 512 bit sub parts and 32 bitwords

4. 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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1. Convert x to binary

2 P d th t i f (mod 512) 0

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2. Pad x so that size ofx (mod 512) = 0

3. Break x into 512 bit sub parts and 32 bitwords

4. 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

7. Append the register values to create digest

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128 bit digest

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hello

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5d41402abc4b2a76b9719d911017c592

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So?

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Applications

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Applications

PasswordProtection

MessageI i

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Applications

PasswordProtection

Integrity

MessageI i

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Applications

PasswordProtection

Integrity

DigitalSignatures

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Password Protection

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When you registered...

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passwordMD5

5f4dcc3b5aa765d61d8327deb882cf99

When you registered...

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passwordMD5

5f4dcc3b5aa765d61d8327deb882cf99

Data Base

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password

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password

MD5

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password

MD5

5f4dcc3b5aa765d61d8327deb882cf99

5f4dcc3b5aa765d61d8327deb882cf99

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=

stored, hashed password?

5f4dcc3b5aa765d61d8327deb882cf99

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=

stored, hashed password?

No.

Give incorrectpassword error

5f4dcc3b5aa765d61d8327deb882cf99

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=

stored, hashed password?

No.

Give incorrectpassword error

Yes.

Let userinto website

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Attacks

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RainbowTables

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omgyouarenevergoingtocrackthis123

1c9fee8bd70a5afb630fc4f38e97123f

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omgyouarenevergoingtocrackthis123

1c9fee8bd70a5afb630fc4f38e97123f

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and Brute Force

Attacks

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File

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Verification

File

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Verification

Guarding againstcorruption

File

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Verification

Guarding againstcorruption

Proving you

have somethingbefore yourelease it

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Attacks

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Nostradamus Attack

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But on November 30th 2007...

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We have used a Sony Playstation 3 to correctly predict theoutcome of the 2008 US presidential elections. In order not toinfluence 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 berevealed after the elections.

- Marc Stevens, Arjen Lenstra and Benne de Weger

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3D515DEAD7AA16560ABA3E9DF05CBC80

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But how could they have known!?!?

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But how could they have known!?!?They didnt.

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3D515DEAD7AA16560ABA3E9DF05CBC80

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Digital Signatures

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MD5

hash

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hash

MD5

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privatekey

encrypted

hash

MD5

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privatekey

encryptedpublic

key

hash

hash

MD5

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privatekey

encryptedpublic

key

hash

MD5

hash

MD5

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privatekey

encryptedpublic

key

hash

MD5

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Attacks

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Collision Attack

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hashChangedM

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encryptedpublic

key

hash

Message

MD5

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Very Dangerous!

Bi thd Att k

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Birthday Attack

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Relies on Birthday Paradox

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First we calculate the chanceno one has the same birthday

y

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p(1)=100%

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p(2)=(1)(1 - 1/365)

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p(3)=(1)(1 - 1/365)(1 - 2/365)

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To Generalize...

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365! .365n(365-n)!

P(n)=

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23 50% chance

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30 70.6% chance

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50 97% chance

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We can use this property to find

out how many hashes mustbe calculated to find a collision.

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Current State of MD5

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MD5 =

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MD5 = Broken

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The Future of Hashes

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Submissions were due on October 30th

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Currently Submitted

BLAKE

Keccak

MaracaMD6Skein

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Blue Midnight Wish

Boole

CubeHashEdon-R

EnRUPT

ESSENCE

Sgil

Grstl

Keccak

MCSSHA-3

NaSHANKS2D

PonicSHAMATA

WaMM

Waterfall

BLAKE

Keccak

MaracaMD6Skein

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Blue Midnight Wish

Boole

CubeHashEdon-R

EnRUPT

ESSENCE

Sgil

Grstl

Keccak

MCSSHA-3

NaSHANKS2D

PonicSHAMATA

WaMM

Waterfall

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Thank you for coming!

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