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 Rogaway’s “Introduction to Modern Cryptography” course. Sharif University Introduction to Modern Cryptography Spring 2015 1 / 43
Outline Collision Resistant Hash Functions Merkle – Damgård Construction One-wayness Sharif University Introduction to Modern Cryptography Spring 2015 2 / 43
Collision Resistant Hash Functions Sharif University Introduction to Modern Cryptography Spring 2015 3 / 43
What is a hash function? Sharif University Introduction to Modern Cryptography Spring 2015 4 / 43
Collision resistance (CR) Sharif University Introduction to Modern Cryptography Spring 2015 5 / 43
Function families Sharif University Introduction to Modern Cryptography Spring 2015 6 / 43
CR of function families Sharif University Introduction to Modern Cryptography Spring 2015 7 / 43
CR of function families Sharif University Introduction to Modern Cryptography Spring 2015 8 / 43
Example Sharif University Introduction to Modern Cryptography Spring 2015 9 / 43
Example Sharif University Introduction to Modern Cryptography Spring 2015 10 / 43
Birthday attack Sharif University Introduction to Modern Cryptography Spring 2015 11 / 43
Analysis of birthday attack Sharif University Introduction to Modern Cryptography Spring 2015 12 / 43
Analysis of birthday attack Sharif University Introduction to Modern Cryptography Spring 2015 13 / 43
Analysis of birthday attack Sharif University Introduction to Modern Cryptography Spring 2015 14 / 43
Analysis of birthday attack Sharif University Introduction to Modern Cryptography Spring 2015 15 / 43
Birthday attack times Sharif University Introduction to Modern Cryptography Spring 2015 16 / 43
Merkle – Damgård Construction Sharif University Introduction to Modern Cryptography Spring 2015 17 / 43
Compression functions Sharif University Introduction to Modern Cryptography Spring 2015 18 / 43
The MD transform Sharif University Introduction to Modern Cryptography Spring 2015 19 / 43
The MD transform Sharif University Introduction to Modern Cryptography Spring 2015 20 / 43
MD preserves CR Sharif University Introduction to Modern Cryptography Spring 2015 21 / 43
MD preserves CR Sharif University Introduction to Modern Cryptography Spring 2015 22 / 43
How 𝐵 ℎ works Sharif University Introduction to Modern Cryptography Spring 2015 23 / 43
Sharif University Introduction to Modern Cryptography Spring 2015 24 / 43
Sharif University Introduction to Modern Cryptography Spring 2015 25 / 43
How are compression functions designed? Sharif University Introduction to Modern Cryptography Spring 2015 26 / 43
How are compression functions designed? Sharif University Introduction to Modern Cryptography Spring 2015 27 / 43
How are compression functions designed? Sharif University Introduction to Modern Cryptography Spring 2015 28 / 43
How are compression functions designed? Sharif University Introduction to Modern Cryptography Spring 2015 29 / 43
One-wayness Sharif University Introduction to Modern Cryptography Spring 2015 30 / 43
One-wayness Sharif University Introduction to Modern Cryptography Spring 2015 31 / 43
One-wayness adversaries Sharif University Introduction to Modern Cryptography Spring 2015 32 / 43
Issues in formalizing one-wayness Sharif University Introduction to Modern Cryptography Spring 2015 33 / 43
Formal definition of one-wayness Sharif University Introduction to Modern Cryptography Spring 2015 34 / 43
Does CR imply OW? Sharif University Introduction to Modern Cryptography Spring 2015 35 / 43
Does CR imply OW? Sharif University Introduction to Modern Cryptography Spring 2015 36 / 43
CR ⇏ OW Sharif University Introduction to Modern Cryptography Spring 2015 37 / 43
CR ⇒ OW for functions that compress Sharif University Introduction to Modern Cryptography Spring 2015 38 / 43
Proof of Theorem Sharif University Introduction to Modern Cryptography Spring 2015 39 / 43
Advantage of B Sharif University Introduction to Modern Cryptography Spring 2015 40 / 43
Advantage of B Sharif University Introduction to Modern Cryptography Spring 2015 41 / 43
Advantage of B Sharif University Introduction to Modern Cryptography Spring 2015 42 / 43
Questions? Sharif University Introduction to Modern Cryptography Spring 2015 43 / 43
Recommend
More recommend
