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

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