Vlad TEE + PQC (#77)

* TEE file

* enlarged the Post Quantum crypto material

* added links

content/Basic Cryptography/Post-Quantum Cryptography.md

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 # Post-Quantum Cryptography
 
+## Definition
+
+**Post-Quantum Cryptography (PQC)** refers to cryptographic algorithms designed to be secure against the potential threats posed by quantum computers. While classical computers operate on bits (0s and 1s), quantum computers use quantum bits or qubits, which can represent 0 and 1 simultaneously due to superposition. This capability allows quantum computers to solve certain mathematical problems exponentially faster than classical computers, rendering many of today's cryptographic algorithms vulnerable.
+
+PQC aims to develop new cryptographic systems that can run on classical computers but are secure against both classical and quantum attacks. These algorithms are based on mathematical problems believed to be hard for quantum computers to solve efficiently.
+
 ## Quantum Computing and Cryptography
-The public key cryptosystems currently in widespread use are vulnerable to quantum attacks. For example, [[RSA]] relies on integer factorization, which can be easily computed using Shor's algorithm.
+
+### Challenges with Current Cryptographic Algorithms
+
+The public key cryptosystems currently in widespread use, such as [[RSA]], **Elliptic Curve Cryptography (ECC)**, and [[Diffie-Hellman]] **key exchange**, rely on the computational difficulty of certain mathematical problems:
+
+- **Integer Factorization**: The basis for [[RSA]] encryption.
+- **Discrete Logarithm Problem**: Used in [[Diffie-Hellman]] and ECC.
+
+Quantum computers threaten these systems because of algorithms like **Shor's algorithm**, which can solve these problems in polynomial time, effectively breaking the security of these cryptosystems.
+
+#### Shor's Algorithm
+
+- **Developed by**: Peter Shor in 1994.
+- **Capability**: Efficiently factors large integers and computes discrete logarithms.
+- **Impact**: Can break [[RSA]], ECC, and other cryptosystems relying on these hard problems.
+
+#### Grover's Algorithm
+
+- **Developed by**: Lov Grover in 1996.
+- **Capability**: Provides a quadratic speedup for unstructured search problems.
+- **Impact**: Affects symmetric-key algorithms like [[AES]] by effectively halving the key length (e.g., a 256-bit key would offer 128 bits of security against quantum attacks).
+
+### Implications
+
+- **Data Security**: Encrypted data intercepted today could be stored and decrypted in the future once quantum computers become powerful enough—a threat known as "store now, decrypt later."
+- **Urgency for Transition**: There is a need to transition to quantum-resistant algorithms before large-scale quantum computers become operational.
 
 ## Post-Quantum Cryptography
-Post-quantum cryptography aims to develop cryptographic algorithms that are secure against quantum cryptanalysis attacks.
+
+### Goals of Post-Quantum Cryptography
+
+1. **Quantum Resistance**: Develop algorithms that are secure against both classical and quantum attacks.
+2. **Performance**: Ensure that the new algorithms are efficient enough for practical use on existing hardware.
+3. **Ease of Integration**: Design algorithms that can be integrated into current protocols and systems with minimal changes.
+4. **Versatility**: Provide solutions for various cryptographic needs, including encryption, digital signatures, and key exchange.
+
+### Categories of Post-Quantum Algorithms
+
+Post-quantum cryptographic algorithms are based on mathematical problems believed to be resistant to quantum attacks. The main categories include:
+
+1. **Lattice-Based Cryptography**
+
+   - **Mathematical Basis**: Hard problems in lattice structures, such as the Shortest Vector Problem (SVP) and [[Learning With Errors (LWE)]].
+   - **Features**:
+     - Strong security proofs.
+     - Efficiency and scalability.
+     - Supports advanced functionalities like fully homomorphic encryption.
+
+2. **Code-Based Cryptography**
+
+   - **Mathematical Basis**: Error-correcting codes, particularly the difficulty of decoding a general linear code.
+   - **Examples**: McEliece and Niederreiter cryptosystems.
+   - **Features**:
+     - Long-standing security record.
+     - **Drawback**: Large key sizes.
+
+3. **Multivariate Quadratic Equations**
+
+   - **Mathematical Basis**: Solving systems of multivariate quadratic equations over finite fields.
+   - **Features**:
+     - Fast computation.
+     - **Drawback**: Large public keys and complex implementations.
+
+4. **Hash-Based Signatures**
+
+   - **Mathematical Basis**: Security of cryptographic hash functions.
+   - **Examples**: Lamport signatures, Merkle signature schemes, SPHINCS+.
+   - **Features**:
+     - Very strong security assumptions.
+     - Stateless or stateful operations.
+     - **Drawback**: Larger signature sizes.
+
+5. **Isogeny-Based Cryptography**
+
+   - **Mathematical Basis**: Hardness of finding isogenies between elliptic curves.
+   - **Examples**: Supersingular Isogeny Key Exchange (SIKE).
+   - **Features**:
+     - Small key sizes.
+     - Currently less mature and under active research.
+
+6. **Symmetric-Key Quantum Resistance**
+
+   - **Approach**: Doubling key sizes in symmetric algorithms to counteract Grover's algorithm.
+   - **Examples**: Using AES-256 instead of AES-128.
 
 ## NIST Post-Quantum Cryptography Standardization Program
-The NIST Post-Quantum Cryptography Standardization Program and competition are intended to update the NIST standards to include post-quantum cryptography. This program is conducting a call for proposals for digital signatures and key encapsulation mechanisms.
 
-## NIST's Announcement of the First Winners in 2020
-In 2020, NIST announced the first winners:
-- **CRYSTALS-Kyber (PKE/KEM)**
-- **CRYSTALS-Dilithium**
-- **FALCON**
-- **SPHINCS (Signature)**
+### Overview
+
+The **National Institute of Standards and Technology** [NIST](https://www.nist.gov/) initiated the Post-Quantum Cryptography Standardization Program in 2016 to evaluate and standardize one or more quantum-resistant public-key cryptographic algorithms.
+
+### Objectives
+
+- **Identify Secure Algorithms**: Find algorithms that can withstand quantum attacks.
+- **Standardization**: Develop new standards to replace vulnerable cryptographic algorithms.
+- **Industry Adoption**: Encourage the integration of these algorithms into existing systems.
+
+### Process
+
+1. **Call for Proposals (2016)**
+
+   - NIST invited submissions of quantum-resistant cryptographic algorithms.
+   - Received 82 initial submissions.
+
+2. **Evaluation Rounds**
+
+   - **Round 1 (2017-2019)**: 69 candidates accepted for initial evaluation.
+   - **Round 2 (2019-2020)**: Narrowed down to 26 candidates based on security and performance.
+   - **Round 3 (2020-2022)**: Further reduced to 15 finalists (7 finalists and 8 alternates).
+
+3. **Criteria for Evaluation**
+
+   - **Security**: Resistance to classical and quantum attacks.
+   - **Performance**: Computational efficiency, key and signature sizes.
+   - **Implementation Considerations**: Ease of implementation, resistance to side-channel attacks.
+   - **Algorithm Maturity**: Extent of analysis and peer review.
+
+## NIST's Announcement of the First Winners in 2022
+
+In July 2022, NIST announced the selection of four algorithms for standardization:
+
+1. [CRYSTALS-Kyber](https://csrc.nist.gov/pubs/fips/203/ipd) (Public-Key Encryption/KEM)
+2. [CRYSTALS-Dilithium](https://csrc.nist.gov/pubs/fips/204/ipd) (Digital Signature)
+3. [FALCON](https://csrc.nist.gov/pubs/fips/205/ipd) (Digital Signature)
+4. [SPHINCS+](https://csrc.nist.gov/CSRC/media/Presentations/SPHINCS/images-media/SPHINCS-Plus-April2018.pdf) (Digital Signature)
+
+### CRYSTALS-Kyber
+
+- **Type**: Public-Key Encryption and Key-Encapsulation Mechanism (KEM).
+- **Basis**: Lattice-based, relying on the hardness of the [[Learning With Errors (LWE)]] problem.
+- **Features**:
+  - **Efficiency**: Offers a good balance between security and performance.
+  - **Small Key Sizes**: Relatively compact public and private keys.
+  - **Applications**: Suitable for general encryption needs, including securing internet traffic.
+
+### CRYSTALS-Dilithium
+
+- **Type**: [[Digital Signature]] Scheme.
+- **Basis**: Lattice-based, using Module-LWE and Module-SIS problems.
+- **Features**:
+  - **Strong Security**: Based on well-studied hard lattice problems.
+  - **Performance**: Efficient signing and verification processes.
+  - **Applications**: Code signing, authentication protocols.
+
+### FALCON
+
+- **Type**: [[Digital Signature]] Scheme.
+- **Basis**: Lattice-based, specifically [NTRU lattices](https://www.ntru.org/f/hps98.pdf).
+- **Features**:
+  - **Compact Signatures**: Smaller signature sizes compared to other lattice-based schemes.
+  - **Efficient Verification**: Fast verification times.
+  - **Applications**: Ideal for applications where bandwidth or storage is limited.
+
+### SPHINCS+
+
+- **Type**: [[Digital Signature]] Scheme.
+- **Basis**: Hash-based, relying solely on the security of underlying hash functions.
+- **Features**:
+  - **Conservative Security**: Minimal assumptions beyond the hash function's security.
+  - **Stateless Operation**: Simplifies implementation by avoiding the need to maintain state.
+  - **Drawbacks**: Larger signature sizes and slower performance compared to lattice-based schemes.
+  - **Applications**: Situations requiring high security assurances.
+
+### Significance of the Selection
+
+- **Diversity**: NIST chose algorithms from different families to mitigate the risk of a single point of failure.
+- **Focus on Lattice-Based Cryptography**: The prominence of lattice-based algorithms underscores their importance in PQC.
+- **Preparation for Transition**: Provides the industry with concrete options to begin transitioning to quantum-resistant cryptography.
+
+## Conclusion
+
+Post-Quantum Cryptography is a critical field addressing the imminent threat that quantum computing poses to current cryptographic systems. By developing and standardizing algorithms resistant to quantum attacks, PQC ensures the confidentiality, integrity, and authenticity of digital communications in the quantum era.
 
-Among these, all algorithms except SPHINCS are lattice-based. SPHINCS is a hash-based algorithm.

content/Privacy Enhancing Technologies (PET)/Trusted Execution Environment/TEE.md

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+# Trusted Execution Environment (TEE)
+
+## Definition
+
+A **Trusted Execution Environment (TEE)** is a secure area within a processor that ensures code and data are executed and stored in isolation from the main operating system. TEEs enable sensitive computations to be performed securely, even on a device that may be compromised. The primary goal of a TEE is to provide a secure enclave where private data can be processed without being exposed to unauthorized parties, including the operating system and other applications.
+
+## Use Cases
+
+TEEs are utilized in various applications where privacy and data integrity are crucial:
+
+- **Mobile Payments**: Securely storing and processing payment information and cryptographic keys on smartphones.
+- **Digital Identity Management**: Managing biometric data and private information for identity verification.
+- **Secure Cryptographic Operations**: Managing private keys and signing transactions securely in blockchain and cryptocurrency applications.
+- **Healthcare**: Processing sensitive patient data without exposing it to unauthorized parties.
+- **Internet of Things (IoT)**: Protecting IoT devices from being compromised by providing a secure execution environment.
+
+## Advantages
+
+1. **Data Privacy**: Ensures that sensitive data is never exposed, even to the operating system or malicious applications.
+2. **Isolation**: Operates independently from the rest of the system, providing a secure environment for sensitive computations.
+3. **Tamper Resistance**: Designed to be resistant to attacks attempting to alter or retrieve data from the secure enclave.
+4. **Secure Key Management**: Securely stores cryptographic keys, ensuring they are only used for their intended purposes.
+5. **Regulatory Compliance**: Helps organizations comply with data protection regulations by safeguarding sensitive data.
+
+## Popular TEE Implementations
+
+- **ARM TrustZone**: Creates a secure world alongside the normal operating system for ARM processors.
+- **Intel SGX**: Provides applications the ability to create secure enclaves for code and data on Intel processors.
+- **AMD SEV**: Encrypts virtual machine memory, protecting it from unauthorized access on AMD platforms.
+
+> **Info**  
+> To learn more about different types of TEEs and their applications, refer to [Intel SGX Documentation](https://software.intel.com/content/www/us/en/develop/articles/intel-software-guard-extensions.html).
+
+## Applying TEE to Blockchain and Cryptography
+
+### Challenges with Blockchain Privacy
+
+Blockchain technology ensures data integrity through decentralization and transparency. However, the public nature of blockchains means all transaction data is visible on the ledger, posing privacy risks. Sensitive information, such as user balances and transaction details, can be exposed to the public.
+
+### How TEEs Enhance Blockchain Privacy
+
+By integrating TEEs with blockchain technology, sensitive data can be processed securely within the secure enclave, maintaining privacy without sacrificing the benefits of decentralization. TEEs allow for:
+
+- **Secure Computation**: Performing computations on encrypted data without exposing it.
+- **Private Transactions**: Keeping user balances and transaction details confidential.
+- **Enhanced Security**: Protecting private keys and sensitive operations from being compromised.
+
+### Use Cases in Blockchain
+
+#### Secure Transactions in Cryptocurrency
+
+TEEs enable users to keep their private keys encrypted while allowing transactions to be signed within the secure enclave. This ensures that even if the device or operating system is compromised, the private key remains protected.
+
+##### Code Example
+
+```solidity
+pragma solidity ^0.8.0;
+
+contract SecureTransaction {
+    address public owner;
+    bytes32 private encryptedPrivateKey;
+    
+    constructor(bytes32 _encryptedKey) {
+        owner = msg.sender;
+        encryptedPrivateKey = _encryptedKey;
+    }
+
+    function executeTransaction(address to, uint256 amount) public {
+        require(msg.sender == owner, "Not authorized");
+        // Decrypt the private key inside a TEE and sign the transaction securely
+        // Send the transaction to the blockchain without exposing the private key
+    }
+}
+```
+
+Storing the encrypted key on-chain ensures that it is accessible in a decentralized manner to any authorized off-chain TEE services.
+It eliminates single point of Failure: Relying solely on a specific TEE instance introduces centralization and creates potential single points of failure.