Has Hash h Fu Func nction tions Instructor: Ahmad Boorghany Most - - PowerPoint PPT Presentation

▶
has hash h fu func nction tions instructor ahmad boorghany
SMART_READER_LITE
LIVE PREVIEW

Has Hash h Fu Func nction tions Instructor: Ahmad Boorghany Most - - PowerPoint PPT Presentation

Mar 15, 2023 111 likes •555 views

Data and Network Security Lab Sharif University of Technology Department of Computer Engineering Has Hash h Fu Func nction tions Instructor: Ahmad Boorghany Most of the slides are obtained from Bellare and Rogaways Introduction to

slide-1
SLIDE 1

Introduction to Modern Cryptography Sharif University Spring 2015

Data and Network Security Lab Sharif University of Technology Department of Computer Engineering

Has Hash h Fu Func nction tions Instructor: Ahmad Boorghany

1 / 43

Most of the slides are obtained from Bellare and Rogaway’s “Introduction to Modern Cryptography” course.

slide-2
SLIDE 2

Introduction to Modern Cryptography Sharif University Spring 2015

 Collision Resistant Hash Functions  Merkle–Damgård Construction  One-wayness

Outline

2 / 43

slide-3
SLIDE 3

Introduction to Modern Cryptography Sharif University Spring 2015

Collision Resistant Hash Functions

3 / 43

slide-4
SLIDE 4

Introduction to Modern Cryptography Sharif University Spring 2015

What is a hash function?

4 / 43

slide-5
SLIDE 5

Introduction to Modern Cryptography Sharif University Spring 2015

Collision resistance (CR)

5 / 43

slide-6
SLIDE 6

Introduction to Modern Cryptography Sharif University Spring 2015

Function families

6 / 43

slide-7
SLIDE 7

Introduction to Modern Cryptography Sharif University Spring 2015

CR of function families

7 / 43

slide-8
SLIDE 8

Introduction to Modern Cryptography Sharif University Spring 2015

CR of function families

8 / 43

slide-9
SLIDE 9

Introduction to Modern Cryptography Sharif University Spring 2015

Example

9 / 43

slide-10
SLIDE 10

Introduction to Modern Cryptography Sharif University Spring 2015

Example

10 / 43

slide-11
SLIDE 11

Introduction to Modern Cryptography Sharif University Spring 2015

Birthday attack

11 / 43

slide-12
SLIDE 12

Introduction to Modern Cryptography Sharif University Spring 2015

Analysis of birthday attack

12 / 43

slide-13
SLIDE 13

Introduction to Modern Cryptography Sharif University Spring 2015

Analysis of birthday attack

13 / 43

slide-14
SLIDE 14

Introduction to Modern Cryptography Sharif University Spring 2015

Analysis of birthday attack

14 / 43

slide-15
SLIDE 15

Introduction to Modern Cryptography Sharif University Spring 2015

Analysis of birthday attack

15 / 43

slide-16
SLIDE 16

Introduction to Modern Cryptography Sharif University Spring 2015

Birthday attack times

16 / 43

slide-17
SLIDE 17

Introduction to Modern Cryptography Sharif University Spring 2015

Merkle–Damgård Construction

17 / 43

slide-18
SLIDE 18

Introduction to Modern Cryptography Sharif University Spring 2015

Compression functions

18 / 43

slide-19
SLIDE 19

Introduction to Modern Cryptography Sharif University Spring 2015

The MD transform

19 / 43

slide-20
SLIDE 20

Introduction to Modern Cryptography Sharif University Spring 2015

The MD transform

20 / 43

slide-21
SLIDE 21

Introduction to Modern Cryptography Sharif University Spring 2015

MD preserves CR

21 / 43

slide-22
SLIDE 22

Introduction to Modern Cryptography Sharif University Spring 2015

MD preserves CR

22 / 43

slide-23
SLIDE 23

Introduction to Modern Cryptography Sharif University Spring 2015

How 𝐵ℎ works

23 / 43

slide-24
SLIDE 24

Introduction to Modern Cryptography Sharif University Spring 2015 24 / 43

slide-25
SLIDE 25

Introduction to Modern Cryptography Sharif University Spring 2015 25 / 43

slide-26
SLIDE 26

Introduction to Modern Cryptography Sharif University Spring 2015

How are compression functions designed?

26 / 43

slide-27
SLIDE 27

Introduction to Modern Cryptography Sharif University Spring 2015

How are compression functions designed?

27 / 43

slide-28
SLIDE 28

Introduction to Modern Cryptography Sharif University Spring 2015

How are compression functions designed?

28 / 43

slide-29
SLIDE 29

Introduction to Modern Cryptography Sharif University Spring 2015

How are compression functions designed?

29 / 43

slide-30
SLIDE 30

Introduction to Modern Cryptography Sharif University Spring 2015

One-wayness

30 / 43

slide-31
SLIDE 31

Introduction to Modern Cryptography Sharif University Spring 2015

One-wayness

31 / 43

slide-32
SLIDE 32

Introduction to Modern Cryptography Sharif University Spring 2015

One-wayness adversaries

32 / 43

slide-33
SLIDE 33

Introduction to Modern Cryptography Sharif University Spring 2015

Issues in formalizing one-wayness

33 / 43

slide-34
SLIDE 34

Introduction to Modern Cryptography Sharif University Spring 2015

Formal definition of one-wayness

34 / 43

slide-35
SLIDE 35

Introduction to Modern Cryptography Sharif University Spring 2015

Does CR imply OW?

35 / 43

slide-36
SLIDE 36

Introduction to Modern Cryptography Sharif University Spring 2015

Does CR imply OW?

36 / 43

slide-37
SLIDE 37

Introduction to Modern Cryptography Sharif University Spring 2015

CR ⇏ OW

37 / 43

slide-38
SLIDE 38

Introduction to Modern Cryptography Sharif University Spring 2015

CR ⇒ OW for functions that compress

38 / 43

slide-39
SLIDE 39

Introduction to Modern Cryptography Sharif University Spring 2015

Proof of Theorem

39 / 43

slide-40
SLIDE 40

Introduction to Modern Cryptography Sharif University Spring 2015

Advantage of B

40 / 43

slide-41
SLIDE 41

Introduction to Modern Cryptography Sharif University Spring 2015

Advantage of B

41 / 43

slide-42
SLIDE 42

Introduction to Modern Cryptography Sharif University Spring 2015

Advantage of B

42 / 43

slide-43
SLIDE 43

Introduction to Modern Cryptography Sharif University Spring 2015

Questions?

43 / 43