Cryptography subject gor lectures 111.ppt
- 1. CS5204 – Operating Systems 1 Cryptographic Security
- 2. CS 5204 – Operating Systems 2 Cryptographic Security Security Considerations Goals: • privacy/confidentiality - information not disclosed to unauthorized entities • integrity - information not altered deliberately or accidentally • authentication - validation of identity of source of information • non-repudiation - source of information can be objectively established Factors: • reliance on unknown, vulnerable intermediaries (e.g., Internet routers) • parties may have no personal or organizational relationship (e.g., e-commerce) • use of automated surrogates (e.g., agents) Threats: • replay of messages • interference (inserting bogus messages) • corrupting messages
- 3. CS 5204 – Operating Systems 3 Cryptographic Security Cryptography Encryption key Decryption key public information E CA M D C M’ Ke M Kd Forms of attack: ciphertext only known plaintext chosen plaintext
- 4. CS 5204 – Operating Systems 4 Cryptographic Security Forms of Cryptosystems • Private Key (symmetric) : A single key is used for both encryption and decryption. Key distribution problem a secure channel is needed to transmit the key before secure communication can take place over an unsecure channel. • Public Key (asymmetric): The encryption procedure (key) is public while the decryption procedure (key) is private. Requirements: 1. For every message M, D(E(M)) = M 2. E and D can be efficiently applied to M 3. It is impractical to derive D from E.
- 5. CS 5204 – Operating Systems 5 Cryptographic Security Combining Public/Private Key Systems (1) (2) A B Public key encryption is more expensive than symmetric key encryption For efficiency, combine the two approaches (1) Use public key encryption for authentication; once authenticated, transfer a shared secret symmetric key (2) Use symmetric key for encrypting subsequent data transmissions
- 6. CS 5204 – Operating Systems 6 Cryptographic Security Secure Communication - Public Key System M M ? User X User Y User Z DY(C) EY(M) C EY is the public key for user Y DY is the secret key for user Y
- 7. CS 5204 – Operating Systems 7 Cryptographic Security Rivest Shamir Adelman (RSA) Method M M User X User Y Me mod n Cd mod n Encryption Key for user Y Decryption Key for user Y C (e, n) (d, n)
- 8. CS 5204 – Operating Systems 8 Cryptographic Security RSA Method 1. Choose two large (100 digit) prime numbers, p and q,and set n = p x q 2. Choose any large integer, d, so that: GCD( d, ((p 1)x(q 1)) = 1 3. Find e so that: e x d = 1 (modulo (p 1)x(q 1)) Example: 1. p = 5, q = 11 and n = 55. (p 1)x(q 1) = 4 x 10 = 40 2. A valid d is 23 since GCD(40, 23) = 1 3. Then e = 7 since: 23 x 7 = 161 modulo 40 = 1
- 9. CS 5204 – Operating Systems 9 Cryptographic Security (Large) Document Integrity File/ message hash process digest Digest properties: • fixed-length, condensation of the source • efficient to compute • irreversible - computationally infeasible for the original source to be reconstructed from the digest • unique - difficult to find two different sources that map to the same digest (collision resistance) Also know as: fingerprint Examples: MD5 (128 bits), SHA-1 (160 bits)
- 10. CS 5204 – Operating Systems 10 Cryptographic Security (Large)Document Integrity file hash process digest file encrypt with sender’s private key digital envelope
- 11. CS 5204 – Operating Systems 11 Cryptographic Security Guaranteeing Integrity hash process file digest decrypt with sender’s public key file digital envelope digest compare
- 12. CS 5204 – Operating Systems 12 Cryptographic Security Digital Signatures (Public Key) Requirements: unforgable and unique receiver: knows that a message came from the sender (authenticity) sender: cannot deny authorship( non-repudiation) message integrity sender & receiver: message contents preserved (integrity) (e.g., cannot cut and paste a signature into a message) Public Key System: sender, A: (EA : public, DA : private) receiver, B: (EB : public, DB : private) sender(A) C= EB (DA (M)) > receiver(B) receiver(B) M = EA (DB (C)) > M
- 13. CS 5204 – Operating Systems 13 Cryptographic Security Secure Communication (Public Key) B A Handshaking IA, IB are “nonces” nonces can be included in each subsequent message PKB: public key of B; PKA: public key of A; EPKA (IA, IB) EPKB, (IA, A) EPKB (IB)