The Problem We'reSolving
• Symmetric cryptography requires shared
secret keys
• How do two parties securely share a key over
insecure channel?
• Analogy: Sending a locked box without sharing
the key first
• Birth of asymmetric cryptography in 1970s
3.
Public Key Cryptography
Fundamentals
•Two mathematically related keys: Public &
Private
• Public key: freely distributed, used for
encryption
• Private key: kept secret, used for decryption
• Based on one-way mathematical functions
• Encryption/Decryption flow → Diagram
RSA Algorithm -The Pioneer
• RSA (1977) – Rivest, Shamir, Adleman
• Mathematical foundation: product of large
primes
• Key Generation: choose p, q → n = p×q;
choose e, compute d
• Security basis: factoring large numbers is hard
• Still widely used, but requires 2048+ bit keys
6.
Elliptic Curve Cryptography(ECC)
• More efficient alternative to RSA
• Mathematical foundation: elliptic curves over
finite fields
• Smaller keys, same security (256-bit ECC ≈
3072-bit RSA)
• Popular curves: secp256r1, Curve25519
• Applications: Mobile, IoT, cryptocurrencies
7.
Diffie-Hellman Key Exchange
•Purpose: Establish shared secret over insecure
channel
• Mathematical basis: Discrete logarithm
problem
• Steps: Agree on parameters → exchange
public values → compute secret
• Analogy: Color mixing example
• Modern variants: ECDH
8.
Post-Quantum Cryptography
• Quantumthreat: could break RSA/ECC
• Timeline: 10–30 years
• New problems: lattice-based, hash-based,
code-based cryptography
• NIST standardization in progress