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

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

Jan 17, 2024 41 likes •635 views

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 Rogaways

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Introduction to Modern Cryptography Sharif University Spring 2015

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

Digita Digital l Signa Signatu tures es Instructor: Ahmad Boorghany

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

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Introduction to Modern Cryptography Sharif University Spring 2015

 Syntax and Definition  Building a Digital Signature  Full Domain Hash (FDH)

Outline

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Introduction to Modern Cryptography Sharif University Spring 2015

Syntax and Definition

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Introduction to Modern Cryptography Sharif University Spring 2015

Signing by hand

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Introduction to Modern Cryptography Sharif University Spring 2015

Signing electronically

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Introduction to Modern Cryptography Sharif University Spring 2015

Signing electronically

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Introduction to Modern Cryptography Sharif University Spring 2015

What about a MAC?

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Introduction to Modern Cryptography Sharif University Spring 2015

Digital signatures

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SLIDE 9

Introduction to Modern Cryptography Sharif University Spring 2015

Usage

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Introduction to Modern Cryptography Sharif University Spring 2015

Dissemination of public keys

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Introduction to Modern Cryptography Sharif University Spring 2015

Signatures versus MA schemes

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SLIDE 12

Introduction to Modern Cryptography Sharif University Spring 2015

Security of a DS scheme

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SLIDE 13

Introduction to Modern Cryptography Sharif University Spring 2015

uf-cma adversaries

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Introduction to Modern Cryptography Sharif University Spring 2015

Security of a DS scheme

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Introduction to Modern Cryptography Sharif University Spring 2015

Formalization: UF-CMA

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Introduction to Modern Cryptography Sharif University Spring 2015

A difference with MACs

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Introduction to Modern Cryptography Sharif University Spring 2015

Strong unforgeability

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Introduction to Modern Cryptography Sharif University Spring 2015

Formalization: SUF-CMA

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SLIDE 19

Introduction to Modern Cryptography Sharif University Spring 2015

Building a Digital Signature

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SLIDE 20

Introduction to Modern Cryptography Sharif University Spring 2015

RSA signatures

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SLIDE 21

Introduction to Modern Cryptography Sharif University Spring 2015

Plain RSA signatures: Idea

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Introduction to Modern Cryptography Sharif University Spring 2015

Plain RSA signature scheme

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Introduction to Modern Cryptography Sharif University Spring 2015

Security of plain RSA signatures

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SLIDE 24

Introduction to Modern Cryptography Sharif University Spring 2015

Attacks on plain RSA

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Introduction to Modern Cryptography Sharif University Spring 2015

Homomorphic properties of RSA

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Introduction to Modern Cryptography Sharif University Spring 2015

Another attack on plain RSA

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Introduction to Modern Cryptography Sharif University Spring 2015

Other issues

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Introduction to Modern Cryptography Sharif University Spring 2015

Throwing in a hash function

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Introduction to Modern Cryptography Sharif University Spring 2015

What we need from H

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Introduction to Modern Cryptography Sharif University Spring 2015

Preventing previous attacks

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Introduction to Modern Cryptography Sharif University Spring 2015

RSA PKCS#1 signatures

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Introduction to Modern Cryptography Sharif University Spring 2015

Does 1-wayness prevent forgery?

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Introduction to Modern Cryptography Sharif University Spring 2015

𝑰𝑸𝑳𝑫𝑻 revisited

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Introduction to Modern Cryptography Sharif University Spring 2015

Goal

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Introduction to Modern Cryptography Sharif University Spring 2015

Full Domain Hash (FDH)

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Introduction to Modern Cryptography Sharif University Spring 2015

Full-Domain-Hash (FDH) [BR96]

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Introduction to Modern Cryptography Sharif University Spring 2015

UF-CMA in RO model

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Introduction to Modern Cryptography Sharif University Spring 2015

Security of FDH in RO model

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Introduction to Modern Cryptography Sharif University Spring 2015

Programming the RO

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SLIDE 40

Introduction to Modern Cryptography Sharif University Spring 2015

The case 𝒓𝒕 = 𝟏 and 𝒓𝒊 = 𝟐

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Introduction to Modern Cryptography Sharif University Spring 2015

The case 𝒓𝒕 = 𝟏 and 𝒓𝒊 = 𝟐

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Introduction to Modern Cryptography Sharif University Spring 2015

The inverter for the case 𝒓𝒕 = 𝟏 and 𝒓𝒊 = 𝟐

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Introduction to Modern Cryptography Sharif University Spring 2015

The inverter for the case 𝒓𝒕 = 𝟏 and 𝒓𝒊 = 𝟐

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Introduction to Modern Cryptography Sharif University Spring 2015

The case 𝒓𝒕 = 𝟏 and 𝒓𝒊 > 𝟐

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Introduction to Modern Cryptography Sharif University Spring 2015

The case 𝒓𝒕 = 𝟏 and 𝒓𝒊 > 𝟐

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Introduction to Modern Cryptography Sharif University Spring 2015

The inverter for the case 𝒓𝒕 = 𝟏 and 𝒓𝒊 > 𝟐

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SLIDE 47

Introduction to Modern Cryptography Sharif University Spring 2015

The inverter for the case 𝒓𝒕 = 𝟏 and 𝒓𝒊 > 𝟐

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Introduction to Modern Cryptography Sharif University Spring 2015

The inverter for the case 𝒓𝒕 = 𝟏 and 𝒓𝒊 > 𝟐

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Introduction to Modern Cryptography Sharif University Spring 2015

The case 𝒓𝒕 > 𝟏

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SLIDE 50

Introduction to Modern Cryptography Sharif University Spring 2015

Replying to Sign queries

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SLIDE 51

Introduction to Modern Cryptography Sharif University Spring 2015

Simplification

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Introduction to Modern Cryptography Sharif University Spring 2015

Inverter for the case 𝒓𝒕 > 𝟏

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Introduction to Modern Cryptography Sharif University Spring 2015

Analysis intuition

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Introduction to Modern Cryptography Sharif University Spring 2015

Fundamental Lemma variant

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Introduction to Modern Cryptography Sharif University Spring 2015

Analysis

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Introduction to Modern Cryptography Sharif University Spring 2015

Analysis

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Introduction to Modern Cryptography Sharif University Spring 2015

Security of FDH in RO model

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Introduction to Modern Cryptography Sharif University Spring 2015

Better analysis of FDH in RO model

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Introduction to Modern Cryptography Sharif University Spring 2015

Questions?

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