Information and network security 32 principles of public key cryptosystems
- 1. Information and Network Security:32 Principles of Public-Key Cryptosystems Prof Neeraj Bhargava Vaibhav Khanna Department of Computer Science School of Engineering and Systems Sciences Maharshi Dayanand Saraswati University Ajmer
- 4. Principles of Public-Key Cryptosystems • Stallings Figure “Public-Key Cryptosystems: Secrecy and Authentication” illustrates the essential elements of a public-key encryption scheme. • Note that public-key schemes can be used for either secrecy or authentication, or both (as shown here). There is some source A that produces a message in plaintext X The M elements of X are letters in some finite alphabet. • The message is intended for destination B. B generates a related pair of keys: a public key, PUb, and a private key, PRb. PRb is known only to B, whereas PUb is publicly available and therefore accessible by A. • With the message X and the encryption key PUb as input, A forms the ciphertext Y = E(PUb, X) The intended receiver, in possession of the matching private key, is able to invert the transformation: X = D(PRb, Y) An adversary, observing Y and having access to PUb, but not having access to PRb or X, must attempt to recover X and/or PRb.
- 5. Principles of Public-Key Cryptosystems • This provides confidentiality. Can also use a public-key encryption to provide authentication: Y = E(PRa, X); X = D(PUa, Y) To provide both the authentication function and confidentiality have a double use of the public- key scheme (as shown here): Z = E(PUb, E(PRa, X)) X = D(PUa, D(PRb, Z)) • In this case, separate key pairs are used for each of these purposes. The receiver owns and creates secrecy keys, sender owns and creates authentication keys. • In practice typically DO NOT do this, because of the computational cost of public-key schemes. Rather encrypt a session key which is then used with a block cipher to encrypt the actual message, and separately sign a hash of the message as a digital signature - this will be discussed more later.
- 6. Public-Key Applications • can classify uses into 3 categories: • encryption/decryption (provide secrecy) • digital signatures (provide authentication) • key exchange (of session keys) • some algorithms are suitable for all uses, others are specific to one
- 7. • Public-key systems are characterized by the use of a cryptographic type of algorithm with two keys. • Depending on the application, the sender uses either the sender’s private key or the receiver’s public key, or both, to perform some type of cryptographic function. • In broad terms, we can classify the use of public-key cryptosystems into the three categories: • • Encryption/decryption: The sender encrypts a message with the recipient’s public key.
- 8. • Digital signature: The sender “signs” a message with its private key, either to the whole message or to a small block of data that is a function of the message. • • Key exchange: Two sides cooperate to exchange a session key. Several different approaches are possible, involving the private key(s) of one or both parties. • Some algorithms are suitable for all three applications, whereas others can be used only for one or two of these applications.
- 9. Public-Key Requirements • Public-Key algorithms rely on two keys where: • it is computationally infeasible to find decryption key knowing only algorithm & encryption key • it is computationally easy to en/decrypt messages when the relevant (en/decrypt) key is known • either of the two related keys can be used for encryption, with the other used for decryption (for some algorithms) • these are formidable requirements which only a few algorithms have satisfied
- 10. Public-Key Requirements • need a trapdoor one-way function • one-way function has • Y = f(X) easy • X = f–1(Y) infeasible • a trap-door one-way function has • Y = fk(X) easy, if k and X are known • X = fk –1(Y) easy, if k and Y are known • X = fk –1(Y) infeasible, if Y known but k not known • a practical public-key scheme depends on a suitable trap-door one-way function
- 11. Security of Public Key Schemes like private key schemes brute force exhaustive search attack is always theoretically possible but keys used are too large (>512bits) security relies on a large enough difference in difficulty between easy (en/decrypt) and hard (cryptanalyse) problems more generally the hard problem is known, but is made hard enough to be impractical to break requires the use of very large numbers hence is slow compared to private key schemes
- 12. Assignment • Explain the Principles of Public-Key Cryptosystems.