1 19 -101 Cryptography Basic Concepts

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1 19 -101 Cryptography: Basic Concepts • • Plaintext: message text M to be protected Ciphertext: encrypted plaintext C Key: A secret shared by sender and recipient Encryption: a mathematical transformation E of a plaintext into a cipher text using key K – E(plaintext, K) = ciphertext – E(M, K) = C • Decryption: recovery of the plaintext from the ciphertext – D(C, K) = M • Key concept: – encryption should be computationally easy – decryption should be computationally easy if you have the key K and very difficult without K • Work factor: – a measure of the time to recover M from C in the absence of K c 1995 -98 Peha and Sirbu

3 19 -101 Early Encryption Caesar code All letters increased by the same amount. E(POLICY) = P O L I C Y + 2 = RQNKEA One-to-one mapping for all letters ABCDEFGHIJKLMNOPQRSTUVWXYZ YMZKDBSQIHEAGRNWTFCJLVXUOP Add a different number to each letter. E(CODE) = C O D E +25 +23 +4 +1 = B L H F c 1995 -98 Peha and Sirbu

4 19 -101 Public Key Encryption • A user creates two keys SK and PK which are mathematically related. • The public key, PK, is made widely available. – C = E(M, SK) • A user’s private key SK is not divulged to anyone • To send a message to a user, you encrypt it with his public key – C = E(M, PK) • Only the recipient has the private key which can decrypt the message – M = D(C, SK) c 1995 -98 Peha and Sirbu

6 19 -101 Public Key Encryption using RSA • Choose large prime numbers p, q. • Choose e, d such that e*d mod (p-1)(q-1) = 1. – e relatively prime to (p-1)(q-1) • Encode: C = E(M) = Me mod (pq) e d • Decode: M = E(C) = Cd mod (pq) • Public: e and p*q • Private: d • To find d from e and pq, you must factor p*q, to find (p-1)(q-1). – finding prime factors is a hard problem. • Encryption and Decryption are commutative” – E(D(M) = D(E(M) c 1995 -98 Peha and Sirbu

8 19 -101 Using Public Keys for Signatures • Given a Message M, computer a Message Digest, H(M) • Encrypt H(M) using the Private key of the sender – D(H(M)) • Send M, D(H(M)) • The recipient uses sender’s public key to verify signature • If E(D(H(M))) matches H(M) computed on the received message, then: – the message must have been signed by the sender, * only the sender knows D – it has not been altered. * infeasible to create an altered message which computes to the same H(M) c 1995 -98 Peha and Sirbu

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