Public Key Encryption and the RSA Algorithm Computer Networking- A top-Down Approach Featuring the Internet James F Kurose and Keith W Ross, Second Edition, Pearson Publication Chapter 7- page 642 – 647
Goal To understand what public key encryption is doing to achieve security. To focus on the working principle of public key encryption using RSA algorithm
Objective The student will be able to apply the technique followed in public key encryption method
Private-Key Cryptography traditional private/secret/single key cryptography uses only one key . Key is shared by both sender and receiver and needs to be known in advance. if the key is disclosed communications are compromised. This is also referred to as symmetric key approach.
Possibility of secret key in advance In internet communicating parties never meet or converse except over the network. Is it possible for communication to take place without having secret key in advance? Answer is YES.
Public-Key Cryptography uses two keys – a public key and a private key asymmetric since sender do not know private key of receiver uses clever application of number theory concepts to function complements rather than replaces private key cryptography
Diagram to understand PKE
Public Key Encryption public-key/two-key/asymmetric cryptography involves the use of two keys: a public-key, which may be known by anybody, and can be used to encrypt messages a private-key, known only to the recipient, used to decrypt messages is asymmetric because those who encrypt messages cannot decrypt messages
Bob communicating with Alice
Why PK Cryptography? developed to address two key issues: key distribution – how to have secure communications in general without having to trust a KDC with your key digital signatures – how to verify a message comes intact from the claimed sender public key invention is due to Whitfield Diffie & Martin Hellman at Stanford U. in 1976
Applications can classify uses into 3 categories: encryption/decryption (provide secrecy) digital signatures (provide authentication) key exchange (of session keys)
RSA Ron Rivest, Adi Shamir & Leonard Adleman of MIT in 1977. best known & widely used public-key scheme
Two interrelated components of RSA The choice of the public key and the private key The encryption and decryption algorithm
Steps to generate public and private Keys Choose two large prime numbers, p and q. Compute n = pq and z = (p – 1)(q – 1). 3. Choose a number, e, less than n, that has no common factors (other than 1) with z. 4. Find a number, d, such that ed – 1 is exactly divisible (that is, with no remainder) by z. We choose d such that ed mod z = 1 5. The public key that Bob makes available to the world, KB+, is the pair of numbers (n, e); his private key, KB–, is the pair of numbers (n, d).
Encryption and Decryption steps
Pros and Cons of RSA The security of RSA relies on the fact that there are no known algorithms for quickly factoring a number, in this case the public value n, into the primes p and q. It is not known whether or not there exist fast algorithms for factoring a number, hence the security of RSA is not guaranteed. If one knew p and q, then given the public value e, one could easily compute the secret key, d.
Things to ponder The application of PKC Limitation of Public key cryptography KDC Digital signature Example to solve with integer numbers Example to solve with text Alert points
General Instruction for evaluation Students will follow the team members formed for problem solving Each team will be assigned a task on the spot in the classroom based on this ppt.
End of RSA FLIPPED CLASSROOM SESSION Click here to view the movie