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