RSA Modulus (n)
n = p × q
• Product of two large primes
• 2048-bit integer
• Publicly shared component
• 2048-bit integer
• Publicly shared component
Public Exponent (e)
e = 65537
• Standard choice
• Must be coprime to φ(n)
• Used for encryption
• Must be coprime to φ(n)
• Used for encryption
Why e = 65537?
Fermat Number:
65537 = 2¹⁶ + 1 (F₄)
65537 = 2¹⁶ + 1 (F₄)
Binary Form:
Only two 1-bits
Only two 1-bits
Prime Number:
Passes all primality tests
Passes all primality tests
Efficiency:
Fast modular exponentiation
Fast modular exponentiation
65537 in binary:
100000000000000001
Only 2 ones → Fast computation!
Encryption Formula
C = M^e mod n
Where: C = ciphertext, M = message, e = 65537, n = modulus
Interactive Demo
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