RSA Calculator
Generate RSA keys and perform encryption/decryption using the RSA cryptographic algorithm
RSA Key Generation
Common values: 3, 17, 65537. Must be coprime with λ(N)
Generated RSA Keys
Calculated Values
N = p × q = —
λ(N) = lcm(p-1, q-1) = —
Private exponent d = —
Key Components
Public Key: (N=—, e=65537)
Private Key: (N=—, d=—)
⚠️ Invalid parameters
Encryption & Decryption
Encryption
Encrypted Message
C = —
Formula: C = Me mod N
Decryption
Decrypted Message
M = —
Formula: M = Cd mod N
RSA Algorithm Steps
1
Choose Primes
Select two prime numbers p and q
2
Calculate N
N = p × q (modulus)
3
Find λ(N)
λ(N) = lcm(p-1, q-1)
4
Choose e
Public exponent coprime to λ(N)
5
Calculate d
Private exponent: d ≡ e⁻¹ (mod λ(N))
Example Calculation
Given:
p = 89, q = 67
e = 17
Results:
N = 89 × 67 = 5,963
λ(N) = lcm(88, 66) = 264
d = 233
Encryption Example:
Message: M = 1415
Encrypted: C = 1415¹⁷ mod 5963 = 1032
Encrypted: C = 1415¹⁷ mod 5963 = 1032
Security Notes
⚠️
Use large prime numbers in practice (1024+ bits)
⚠️
This calculator is for educational purposes only
ℹ️
RSA security relies on difficulty of factoring large numbers
✓
Modern RSA uses 2048-bit or 4096-bit keys
Understanding the RSA Algorithm
What is RSA?
RSA (Rivest-Shamir-Adleman) is an asymmetric cryptographic algorithm published in 1977. It uses a pair of mathematically related keys: a public key for encryption and a private key for decryption.
Key Components
- •N: Modulus (product of two primes)
- •e: Public exponent (encryption key)
- •d: Private exponent (decryption key)
- •λ(N): Carmichael function of N
Mathematical Foundation
Key Generation:
1. Choose primes p, q
2. N = p × q
3. λ(N) = lcm(p-1, q-1)
4. Choose e: gcd(e, λ(N)) = 1
5. d ≡ e⁻¹ (mod λ(N))
Encryption/Decryption:
Encrypt: C ≡ M^e (mod N)
Decrypt: M ≡ C^d (mod N)
Security Considerations
Strengths
- • Mathematically proven security
- • Based on prime factorization difficulty
- • Widely adopted and tested
- • Enables digital signatures
Considerations
- • Requires large key sizes (2048+ bits)
- • Vulnerable to quantum computers
- • Padding schemes needed for security
- • Slower than symmetric encryption