Asymmetric-Key Cryptography

I. Overview link

%%{init: { 'theme': 'base', 'themeVariables': { 'edgeLabelBackground': '#fff' }}}%%
flowchart LR
    A["Symmetric keys\nrequire pre-sharing"] -- "Using a public/private key pair" --> B["Key distribution\nproblem solved"]
    style A fill:#f9f9f9,stroke:#333,stroke-width:3px
    style B fill:#e1f5fe,stroke:#01579b,stroke-width:3px

Definition: A cryptographic scheme that uses a pair of keys — a public key and a private key — generated from a hard mathematical problem such as integer factorization or the discrete logarithm problem.

Features:
( Easy Key Distribution ) The public key can be distributed openly, making key management far simpler than with symmetric-key cryptography
( Confidentiality and Non-repudiation ) Alongside confidentiality through data encryption, it provides non-repudiation via digital signatures
( Computational Complexity ) Because it relies on complex operations grounded in hard mathematical problems, it is relatively slower than symmetric-key cryptography

II. Mechanism & Components link

A. Confidentiality and Authentication (Digital Signature) Process link

graph TD
    subgraph "Confidentiality"
        A1["Sender"] -->|"Encrypt with recipient's public key"| B1["Ciphertext"]
        B1 -->|"Decrypt with recipient's private key"| C1["Recipient (confidentiality achieved)"]
    end

    subgraph "Authentication & Non-repudiation"
        A2["Sender"] -->|"Encrypt with sender's private key"| B2["Digital signature"]
        B2 -->|"Decrypt with sender's public key"| C2["Verification (identity confirmed)"]
    end

Detailed mechanism:

• Confidentiality: Encrypted with the recipient’s public key → only decryptable with the recipient’s private key
• Authentication and non-repudiation: Encrypted (signed) with the sender’s private key → anyone can decrypt (verify) it with the sender’s public key

B. Major Algorithms and Their Mathematical Hard Problems link

III. Advanced Topics & Comparison link