Cryptography Algorithms: Explore New Algorithms in Zero-knowledge, Homomorphic Encryption, and Quantum Cryptography. 2 Ed

Preface....10

Who this book is for....12

What this book covers....13

Section 1: A Brief History and Outline of Cryptography....14

Section 2: Classical Cryptography (Symmetric and Asymmetric Encryption)....15

Section 3: New Cryptography Algorithms and Protocols....16

Section 4: Quantum Cryptography....17

To get the most out of this book....17

Get in touch....18

Section 1: A Brief History and Outline of Cryptography....23

Deep Dive into Cryptography....24

An introduction to cryptography....25

Binary numbers, ASCII code, and notations....31

Fermat’s Last Theorem, prime numbers, and modular mathematics....33

A brief history and a panoramic overview of cryptographic algorithms....40

Rosetta Stone....41

The Caesar cipher....43

ROT13....47

The Beale ciphers....49

The Vernam cipher....58

Notes on security and computation....62

Summary....68

Section 2: Classical Cryptography (Symmetric and Asymmetric Encryption)....70

Symmetric Encryption Algorithms....71

Notations and operations in Boolean logic....72

DES algorithms....80

Simple DES....81

Bit initialization....83

Bit expansion....84

Key generation....86

Bit encryption....87

DES....89

Key generation in DES....90

Analysis of the DES algorithm....98

Violation of DES....101

Triple DES....103

DESX....105

AES Rijndael....106

Description of AES....108

Attacks and vulnerabilities in AES....114

Summary....120

Asymmetric Encryption Algorithms....123

Introduction to asymmetric encryption....124

The pioneers....125

The Diffie-Hellman algorithm....128

The discrete logarithm....130

Explaining the D-H algorithm....134

Analyzing the algorithm....135

Possible attacks and cryptanalysis on the D-H algorithm....136

RSA....140

Explaining RSA....142

Analyzing RSA....144

Conventional attacks on the algorithm....145

The application of RSA to verify international treaties....148

Unconventional attacks....151

PGP....155

The ElGamal algorithm....156

Summary....161

Hash Functions and Digital Signatures....163

A basic explanation of hash functions....164

Overview of the main hash algorithms....168

Logic and notations to implement hash functions....170

Explanation of the SHA-1 algorithm....177

Notes and example on SHA-1....183

Example of one block encoded with SHA- 1....185

Authentication and digital signatures....189

RSA digital signatures....191

Why do digital signatures work?....196

Digital signatures with the ElGamal algorithm....197

Blind signatures....201

Blind signature with RSA....202

Notes on the blind signature protocol....205

Summary....207

Section 3: New Cryptography Algorithms and Protocols....209

Zero-Knowledge Protocols....210

The main scenario of a ZKP – the digital cave....212

Non-interactive ZKPs....214

Demonstration of a non-interactive ZKP....218

Demonstrating an attack on an RSA ZKP....219

Schnorr’s interactive ZKP....223

A demonstration of an interactive ZKP....224

A challenge for a disruptive attack on an interactive ZKP....228

One-round ZKP....229

How it works mathematically....231

Numerical example....231

Notes on the one-round protocol....233

An introduction to zk-SNARKs – spooky moon math....235

Understanding how a zk-SNARK works....237

Demonstrating an attack on a zk-SNARK protocol....239

ZK13 – a ZKP for authentication and key exchange....242

ZK13 explained....245

Demonstrating the ZK13 protocol....248

Notes and possible attacks on the ZK13 protocol....249

Possible attacks on ZK13....250

Summary....250

New Inventions in Cryptography and Logical Attacks....253

The genesis of the MB09 algorithm and blockchain....254

Introducing the MB09 algorithm and an attempt at demonstrating Fermat’s Last Theorem....260

An extensive explanation of the MB09 algorithm....267

Introducing the MBXI algorithm....277

A numerical example of MBXI....281

Notes on the MBXI algorithm and the prelude to an attack on RSA....283

Unconventional attacks and self-reverse decryption on RSA....285

A new protocol to protect RSA and asymmetric algorithms from spying....294

Digital signatures on MBXI....296

A direct signature method in MBXI....299

The appendix signature method with MBXI....301

A mathematical demonstration of the MBXI digital signature algorithm....303

The evolution of MB09 and MBXI: an introduction to MBXX....307

An explanation of the MBXX protocol....312

Notes on the MBXX protocol....319

Conclusions on the MBXX protocol....321

Lightweight encryption....322

Encryption with Cybpher....326

Summary....331

Elliptic Curves....334

An overview of elliptic curves....335

Operations on elliptic curves....336

Scalar multiplication....343

Implementing the D-H algorithm on elliptic curves....346

Elliptic curve secp256k1: the Bitcoin digital signature....354

Step 1: Generating keys....357

Step 2: Performing the digital signature in secp256k1....358

Step 3: Verifying the digital signature....359

A numerical exercise on a digital signature on secp256k1....360

Attacks on ECDSA and the security of elliptic curves....367

Step 1: Discovering the random key, [k]....367

Step 2: Recovering the private key, [d]....368

Considerations about the future of ECC....371

Summary....372

Homomorphic Encryption and Crypto Search Engine....374

Introduction to CSE: homomorphism....375

Partial homomorphism in RSA....379

Analysis of homomorphic encryption and its implications....383

Math and logic behind search engines....386

Introduction to trees: graph theory....393

Huffman code....395

Hash and Boolean logic....399

CSE explained....401

The innovation in CSE....404

Computational analysis on CSE....408

Example of computational brute-force cracking....411

Applications of CSE....415

The new frontier of CSE and a new quantum algorithm for message transmission: QTM....418

Summary....419

Section 4: Quantum Cryptography....422

Quantum Cryptography....423

Introduction to Q-Mechanics and Q-Cryptography....424

An experiment that changed the story of quantum....425

An imaginary experiment to understand the elements of Q-Mechanics....427

Step 1: superposition....428

Step 2: the indeterminacy principle....431

Step 3: spin and entanglement....434

Origin of Q-Cryptography: quantum money....439

QKD: BB84....443

Step 1: initializing the quantum channel....446

Step 2: transmitting the photons....447

Step 3: determining the shared key....448

Analysis of attack and technical issues....451

Quantum computing....458

Shor’s algorithm....462

Hypothesis and thesis....463

Step 1: initializing the qubits....464

Step 2: choosing the random number, (a)....465

Step 3: quantum measurement....466

Step 4: finding the right candidate, (r)....468

QFT....469

Step 5: factorizing (n)....475

Notes on Shor’s algorithm....476

Post-Q-Cryptography....476

Summary....478

Quantum Search Algorithms and Quantum Computing....481

An overview of Grover’s algorithm....482

Elements of quantum programming: quantum information and circuits....486

Classical information....487

Quantum information, gates, and circuits....492

Pauli gates (X, Z)....493

Identity gate....497

Hadamard gate....497

Deep dive into Grover’s algorithm....500

Pseudocode for running Grover’s algorithm....504

Step 1: Allocate the register of qubits in superposition....505

Step 2: Iterations on Grover’s operator: G....509

The unique search problem and the amplitude amplification probability....513

Step 1: The promise of the inputs....514

Step 2: Grover’s operation G....515

Step 3: Quantum measurement....522

Summary....523

Other Books You May Enjoy....526

Index....531

Master real-world cryptography with updated algorithms, enhanced encryption techniques, and modern defenses in this latest edition of Cryptographic Algorithms

Purchase of the print or Kindle book includes a free eBook in PDF format.

Key Features

• Gain expertise in cryptographic algorithms from classical encryption to quantum-resistant security.
• Become a forward-thinking cryptographer by diving into next-gen encryption with zero-knowledge proofs, homomorphic encryption, and post-quantum cryptographic techniques.
• Analyze vulnerabilities and see how cryptographic algorithms protect against modern cyber threats.

Book Description

As cyber threats evolve, so must our cryptographic defenses. This updated edition of Cryptographic Algorithms delves into the latest advancements in encryption, cybersecurity, and data protection, ensuring you stay ahead in this rapidly changing field. Whether you're an aspiring or seasoned cybersecurity professional, this book equips you with the expertise to confidently tackle modern security challenges.

Written by Dr. Massimo Bertaccini—a cryptography researcher, inventor, and cybersecurity expert—this book goes beyond theory, offering real-world applications backed by his inventions and patents. His expertise in zero-knowledge proofs, homomorphic encryption, and blockchain security makes this an essential resource for mastering cryptographic security.

With updated algorithms, in-depth explanations, and a comprehensive overview of next-gen cryptographic advancements, this second edition provides the tools to protect sensitive data, implement secure cryptographic systems, and defend against emerging cybersecurity threats.

By the end of this book, you’ll have hands-on expertise in modern cryptographic techniques—empowering you to build robust security solutions and stay at the forefront of cybersecurity innovation.

What you will learn

• Become proficient in key cryptographic algorithms, including AES, RSA, and quantum-resistant encryption
• Identify vulnerabilities in symmetric and asymmetric encryption to strengthen security defenses
• Apply zero-knowledge protocols to enhance privacy and authentication
• Implement homomorphic encryption for secure data processing
• Evaluate emerging cryptographic inventions to counter evolving threats
• Identify and defend against logical attacks in cryptographic systems
• Analyze quantum cryptography through the Shor and Grover algorithms

Who this book is for

This book is for cybersecurity professionals, enthusiasts, and anyone looking to master modern cryptography and advance their cybersecurity career. It covers key cryptographic algorithms, mathematical concepts, and emerging technologies. The book addresses mathematical issues related to the algorithms that may arise. A background in university-level mathematics, algebra, modular arithmetic, finite fields theory, and knowledge of elliptic curves and quantum computing, will help readers get the most out of this book.