RSA Key Generator
Public Key:
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Private Key:
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Encrypted Message:
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Decrypted Message:
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Understanding RSA Cryptography
RSA Algorithm Fundamentals
RSA is a public-key cryptosystem used for secure data transmission.
Key Generation:
- Choose two prime numbers p and q
- Calculate n = p × q
- Calculate φ(n) = (p-1)(q-1)
- Choose e where 1 < e < φ(n) and gcd(e,φ(n)) = 1
- Calculate d where d × e ≡ 1 (mod φ(n))
Public Key: (n,e)
Private Key: (n,d)
Mathematical Principles
- Prime Numbers: Foundation of RSA security
- Modular Arithmetic: Core operations
- Euler's Totient Function: Key generation
- Extended Euclidean Algorithm: Finding d
- Chinese Remainder Theorem: Optimization
- Fermat's Little Theorem: Primality testing
- Integer Factorization: Security basis
- Number Theory: Mathematical foundation
Security Features
Key Length
Determines security level
Prime Generation
Critical for security
Padding Schemes
Prevents attacks
Side-Channel Defense
Protects against timing attacks
Advanced Topics
- Quantum Resistance: Post-quantum considerations
- Key Distribution: Certificate authorities
- Digital Signatures: Message authentication
- Performance Optimization: CRT implementation
- Security Proofs: Mathematical guarantees
- Attack Vectors: Known vulnerabilities
- Implementation Security: Best practices
- Key Management: Lifecycle handling