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Asymmetric Cryptography - Coggle Diagram

- - - - recipient's public key
      - secure exchange
  - - - RSA
        
        Public Key
        
        Modulus N = p x q, encryption exponent e, together from public key (N, e)
        
        Private Key
        
        Prime factors p and q
        
        Security
        
        N is factored, private key can be derived and RSA is compromised
      - N = p x q, p and q are prime
    - - Diffie-Hellman Key Exchange (DH)
        
        shared secret over inscure channel
      - g^x = y (mod p), find x
        
        g is known base (generator)
        
        p is a known prime (finite field)
        
        y is a known result
        
        x is the unknown exponent
      - Digital Signature Algorithm (DSA)
        
        Signing and verifying messages securely
    - - Q = xP, find x
      - y^2 = x^3 + ax + b, where 4a^3 + 27b^2 not equal 0
      - Elliptic curve points (x,y), plus the point at infinity, supporting point addition
      - add points repeatly (scalar multiplication), hard to figure out how many times you added.
      - strong security with much smaller keys
      - Elliptic Curve Diffie-Hellman (ECDH)
      - Elliptic Curve Digital Signature Algorithm (ECDSA)
        
        Digital signatures used in cryptocurrencies (Bitcoin)
- - - - public key (n,e)
        
        Ciphertext C = P^e (mod n), e is the public exponent
        
        1 < e < (p-1) x (q-1), e and (p-1) x (q-1) are coprime
      - private key (n,d)
        
        Plaintext P = C^d (mod n), d is the private exponent
        
        d x e = 1 (mod (p-1) x (q-1)), d is the modular inverse of e (mod (p-1) x (q-1))
- - - - secure protocols to setup encryption keys with/wo insecure channels
      - authenticating key
      - conf
      - confidenticality with symmetric keys through public key cryptosystems (RSA, ECC, EIGamal)