Public Key & Management

Public Key & Management

1. Also known as Asymmetric encryption. It uses 2 diff keys one for encryption and other for description.

   • Key Pair -- Public available for all & Private secret key
   • Components -- Plaintext, Encryption Algorithm, Public & Private Key, Ciphertext, Decryption Algorithm

2. RSA Algorithm

   • Plaintext & Ciphertext are integers between 0 & n-1 for some value of n
     • 1. Encryption/decryption 2. Digital Signature 3. Key distribution
   • WORKING -- 3 Steps
     • 1. Key Generation
       • 1. Select p, q such that both are prime number & p != q 2. Calculate n = p * q  3. Calculate  φ(n) = (p-1)*(q-1) 4. Select integer e, gcd(φ(n),e) = 1 & 1<e<φ(n) 5. Calculate d, d*e(mod φ(n)) = 1  6. Public Key PU = {e,n} 7. Private Key PR = {d,n}
       • 2. Encryption
         • Plaintext - M Ciphertext -- C = M^e mod n
         • 3. Decryption
           • Ciphertext - C Plaintext M` = C^d mod n 
     • Factoring Problem
   • 1. Stream Cipher 2. p and q should be prime 3.Ф(n) = (p-1)(q-1)

3. KEY DISTRIBUTION

   • 1. Public Announcements
     • BROADCAST
   • 2. Publicly Available Directory
     • TRUSTED ENTITY MAINTAINING KEYS
   • 3. Public Key authority
     • AUTHORITY DISTRIBUTING THE KEYS IN A SECURED WAY BY USING TIMESTAMP
   • 4. Public Key Certificates
     • CERTIFICATE AUTHORITY -- DIGITAL CERTIFICATES
     • Public Key Certificate

4. DIGITAL SIGNATURE

   • Digital Signature FLow
   • Verify the Authenticity & maintain integrity. Its divided into 2 parts -- Signing & Verification
     • 1. Authentication -- Confidentiality 2. Integrity -- Same message Sender/Receiver 3. Non Repudiation -- Sender cannot falsely claim that they haven't signed it
   • WORKING
     • Message -- Message Digest -- Encrypted using private key of the sender
       • Receiver decrypts using public key of the sender -- Compare Message Digest -- Verify Signature
   • DIGITAL SIGNATURE ALGORITHM
     • 1. KEY GENERATION
       • p : prime number  q : prime divisor of (p-1) g : h(p-1)/q  Private Key : x -- random interger with 0<x<q Public Key : y = g^x mod p Pre-message Secret Number : k-- random integer 0<k<q 
       • 2. SIGNING
         • r = (g^k mod p) mod q s = [k -1 (H(M) + xr)] mod q  Signature = (r,s)  
         • 3. VERIFIACTION