Public and private keys are fundamental components of asymmetric cryptography. This system enables secure communication, data encryption, and digital signatures. Below is a detailed breakdown of their functionality:
1. Key Pair Generation
The process begins with generating a mathematically linked key pair:
- Public Key: Shared openly with others
- Private Key: Kept secret by the owner
RSA Algorithm Example
- Select two large prime numbers (p and q)
- Calculate the modulus (n = p × q)
- Choose a public exponent (e), often 65537
- Compute the private exponent (d) using modular arithmetic
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2. Encryption and Decryption Process
Public Key Encryption
- Scenario: Alice wants to send Bob an encrypted message
Steps:
- Alice obtains Bob's public key
- Encrypts plaintext into ciphertext using the public key
- Sends the encrypted message
| Component | Description |
|---|---|
| Plaintext | Original readable message |
| Ciphertext | Encrypted unreadable data |
| Public Key | Lockbox for encryption |
Private Key Decryption
- Only Bob's private key can decrypt messages encrypted with his public key
- The mathematical relationship between keys enables secure reversal of encryption
3. Digital Signatures and Verification
Creating Signatures
- Generate a file hash (digital fingerprint)
- Encrypt the hash with the sender's private key
- Attach this encrypted hash (signature) to the document
Signature Verification
- Receiver decrypts signature using sender's public key
- Generates a fresh hash of received document
- Compares decrypted hash with newly created hash
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FAQ Section
Q: Can public keys decrypt messages?
A: No - only the corresponding private key can decrypt messages encrypted with its paired public key.
Q: Why are two primes used in RSA?
A: Multiplying large primes creates a modulus that's computationally infeasible to factor, ensuring security.
Q: How are keys securely stored?
A: Hardware security modules (HSMs) or encrypted key vaults protect private keys from unauthorized access.
Q: What happens if a private key is lost?
A: Encrypted data becomes irrecoverable - emphasizing the need for secure backup solutions.
Security Considerations
The system's strength relies on:
- Computational difficulty of prime factorization (RSA)
- Elliptic curve discrete logarithm problem (ECC)
- Key length adequacy (2048-bit RSA or 256-bit ECC minimum)
This cryptographic framework enables secure:
- Email communication (PGP)
- Website connections (SSL/TLS)
- Blockchain transactions
- Digital identity verification