Digita Digital l Signa Signatu tures es Instructor: Ahmad - PowerPoint PPT Presentation

Data and Network Security Lab Sharif University of Technology Department of Computer Engineering Digita Digital l Signa Signatu tures es 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 / 59

Outline  Syntax and Definition  Building a Digital Signature  Full Domain Hash (FDH) Sharif University Introduction to Modern Cryptography Spring 2015 2 / 59

Syntax and Definition Sharif University Introduction to Modern Cryptography Spring 2015 3 / 59

Signing by hand Sharif University Introduction to Modern Cryptography Spring 2015 4 / 59

Signing electronically Sharif University Introduction to Modern Cryptography Spring 2015 5 / 59

Signing electronically Sharif University Introduction to Modern Cryptography Spring 2015 6 / 59

What about a MAC? Sharif University Introduction to Modern Cryptography Spring 2015 7 / 59

Digital signatures Sharif University Introduction to Modern Cryptography Spring 2015 8 / 59

Usage Sharif University Introduction to Modern Cryptography Spring 2015 9 / 59

Dissemination of public keys Sharif University Introduction to Modern Cryptography Spring 2015 10 / 59

Signatures versus MA schemes Sharif University Introduction to Modern Cryptography Spring 2015 11 / 59

Security of a DS scheme Sharif University Introduction to Modern Cryptography Spring 2015 12 / 59

uf-cma adversaries Sharif University Introduction to Modern Cryptography Spring 2015 13 / 59

Security of a DS scheme Sharif University Introduction to Modern Cryptography Spring 2015 14 / 59

Formalization: UF-CMA Sharif University Introduction to Modern Cryptography Spring 2015 15 / 59

A difference with MACs Sharif University Introduction to Modern Cryptography Spring 2015 16 / 59

Strong unforgeability Sharif University Introduction to Modern Cryptography Spring 2015 17 / 59

Formalization: SUF-CMA Sharif University Introduction to Modern Cryptography Spring 2015 18 / 59

Building a Digital Signature Sharif University Introduction to Modern Cryptography Spring 2015 19 / 59

RSA signatures Sharif University Introduction to Modern Cryptography Spring 2015 20 / 59

Plain RSA signatures: Idea Sharif University Introduction to Modern Cryptography Spring 2015 21 / 59

Plain RSA signature scheme Sharif University Introduction to Modern Cryptography Spring 2015 22 / 59

Security of plain RSA signatures Sharif University Introduction to Modern Cryptography Spring 2015 23 / 59

Attacks on plain RSA Sharif University Introduction to Modern Cryptography Spring 2015 24 / 59

Homomorphic properties of RSA Sharif University Introduction to Modern Cryptography Spring 2015 25 / 59

Another attack on plain RSA Sharif University Introduction to Modern Cryptography Spring 2015 26 / 59

Other issues Sharif University Introduction to Modern Cryptography Spring 2015 27 / 59

Throwing in a hash function Sharif University Introduction to Modern Cryptography Spring 2015 28 / 59

What we need from H Sharif University Introduction to Modern Cryptography Spring 2015 29 / 59

Preventing previous attacks Sharif University Introduction to Modern Cryptography Spring 2015 30 / 59

RSA PKCS#1 signatures Sharif University Introduction to Modern Cryptography Spring 2015 31 / 59

Does 1-wayness prevent forgery? Sharif University Introduction to Modern Cryptography Spring 2015 32 / 59

𝑰 𝑸𝑳𝑫𝑻 revisited Sharif University Introduction to Modern Cryptography Spring 2015 33 / 59

Goal Sharif University Introduction to Modern Cryptography Spring 2015 34 / 59

Full Domain Hash (FDH) Sharif University Introduction to Modern Cryptography Spring 2015 35 / 59

Full-Domain-Hash (FDH) [BR96] Sharif University Introduction to Modern Cryptography Spring 2015 36 / 59

UF-CMA in RO model Sharif University Introduction to Modern Cryptography Spring 2015 37 / 59

Security of FDH in RO model Sharif University Introduction to Modern Cryptography Spring 2015 38 / 59

Programming the RO Sharif University Introduction to Modern Cryptography Spring 2015 39 / 59

The case 𝒓 𝒕 = 𝟏 and 𝒓 𝒊 = 𝟐 Sharif University Introduction to Modern Cryptography Spring 2015 40 / 59

The case 𝒓 𝒕 = 𝟏 and 𝒓 𝒊 = 𝟐 Sharif University Introduction to Modern Cryptography Spring 2015 41 / 59

The inverter for the case 𝒓 𝒕 = 𝟏 and 𝒓 𝒊 = 𝟐 Sharif University Introduction to Modern Cryptography Spring 2015 42 / 59

The inverter for the case 𝒓 𝒕 = 𝟏 and 𝒓 𝒊 = 𝟐 Sharif University Introduction to Modern Cryptography Spring 2015 43 / 59

The case 𝒓 𝒕 = 𝟏 and 𝒓 𝒊 > 𝟐 Sharif University Introduction to Modern Cryptography Spring 2015 44 / 59

The case 𝒓 𝒕 = 𝟏 and 𝒓 𝒊 > 𝟐 Sharif University Introduction to Modern Cryptography Spring 2015 45 / 59

The inverter for the case 𝒓 𝒕 = 𝟏 and 𝒓 𝒊 > 𝟐 Sharif University Introduction to Modern Cryptography Spring 2015 46 / 59

The inverter for the case 𝒓 𝒕 = 𝟏 and 𝒓 𝒊 > 𝟐 Sharif University Introduction to Modern Cryptography Spring 2015 47 / 59

The inverter for the case 𝒓 𝒕 = 𝟏 and 𝒓 𝒊 > 𝟐 Sharif University Introduction to Modern Cryptography Spring 2015 48 / 59

The case 𝒓 𝒕 > 𝟏 Sharif University Introduction to Modern Cryptography Spring 2015 49 / 59

Replying to Sign queries Sharif University Introduction to Modern Cryptography Spring 2015 50 / 59

Simplification Sharif University Introduction to Modern Cryptography Spring 2015 51 / 59

Inverter for the case 𝒓 𝒕 > 𝟏 Sharif University Introduction to Modern Cryptography Spring 2015 52 / 59

Analysis intuition Sharif University Introduction to Modern Cryptography Spring 2015 53 / 59

Fundamental Lemma variant Sharif University Introduction to Modern Cryptography Spring 2015 54 / 59

Analysis Sharif University Introduction to Modern Cryptography Spring 2015 55 / 59

Analysis Sharif University Introduction to Modern Cryptography Spring 2015 56 / 59

Security of FDH in RO model Sharif University Introduction to Modern Cryptography Spring 2015 57 / 59

Better analysis of FDH in RO model Sharif University Introduction to Modern Cryptography Spring 2015 58 / 59

Questions? Sharif University Introduction to Modern Cryptography Spring 2015 59 / 59