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Mathematics of Cryptography
Undergraduate
Definition
Cryptography uses mathematical techniques for secure communication. It's based on number theory, algebra, and complexity theory.
Formulas
c = m^e mod n, m = c^d mod n
RSA encryption/decryption
ed ≡ 1 ±odφ(n)
RSA key relationship
Examples
Example 1
Encrypt m=5 using RSA with p=3, q=11, e=3.
Applications
Internet Security
HTTPS, TLS
E-commerce
Payment security
Blockchain
Digital signatures
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