Chapter 3 - Public-Key Cryptography & Authentication Network Security Faisal Ahmad Khan faisal.khan@buitms.edu.pk Office: 01, SS Block, BUITEMS

Authentication Requirements - must be able to verify that: 1. Message came from the apparent source or author, 2. Contents have not been altered, 3. Sometimes, it was sent at a certain time or sequence. Sometimes we would like to provide authentication without encryption (public statements do not need privacy). Still, authentication requires that the sender know something that the forger does not ( a secret key). Conventional encryption can be used, but the sender must share the secret key with the receivers (and keep it secret from others). 2

The MAC algorithm is a “cryptographic hash” algorithm. Key MAC2 The MAC algorithm is a “cryptographic hash” algorithm. Key 3

Cryptographic (or Secure) Hash Function, H(x) (note: 3 main properties are underlined) Can be applied to a block of data “x” of any size (length) an produces a fixed-length output (e.g., 512 bytes), H(x). H(x) is relatively easy to compute. It is computationally infeasible to get x from H(x). For a given H(x), it is computationally infeasible to find y != x such that H(y) = H(x) (collision resistance). [You can not change a given message and get same hash] It is computationally infeasible to find a pair x,y such that H(y) = H(x) (collision resistance). [You can not find any two messages in a generated bunch that have the same hash] 4

encryption (digital signature) Hash Key (a) Using secret-key encryption x x Encrypt Decrypt (b) Using public-key encryption (digital signature) 5

Secret Value is added by both parties to message before the “hash,” function is used to get the Message Integrity Check (MIC). It is removed before transmission. MIC MIC It is critical that a forger can not compose a different message that would produce the same MIC value. 6

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SHA-1 8 Secure Hash Algorithm 1 -> 160-bit "hash” So new standards: SHA-256, SHA-512, … , SHA-3 8

Public-Key Cryptography (Public-Private Key) plaintext (data file or message) encryption by key-1 decryption by key-1 ciphertext (stored or transmitted safely) decryption by key-2 encryption by key-2 plaintext (original data or message) 9

Encryption using a Public-Key System Bob Alice 10

Authentication using a Public-Key System Bob Alice 11

RSA (Rivest, Shamir, and Adleman) Key length is variable, 2048 bits recommended (2011). The plaintext block ("m") must be less than the key length. Key Generation • Choose two large prime numbers, p and q (secret) • n = pq, Ø(n) = (p-1)(q-1) • Find a number, e, that is relatively prime* to Ø(n) • The public key is e and n : (e,n) *no common factors • Find d, the multiplicative inverse to e mod Ø(n) (by “Number Theory”: d * e mod Ø(n) = 1) The private key is d and n (d,n), public key is (e,n) Encryption: c = m^e mod n ("m" is message) Decryption: m = c^d mod n ("c" is ciphertext) 12

(the plaintext message) Does RSA Work? (Does D(E(m))=m) c = E(m) =(m ^ e) mod n (the ciphertext) D(c) = (c ^ d) mod n (decryption of c) = m^(e*d) mod n = m^(e*d mod Ø(n)) mod n (Number Theory) = m^(1) mod n = m (the plaintext message) 13

Is RSA Secure? To factor a 512-bit number (to find p and q from n) with the best known technique would take 500,000 MIPs-years • In 500 years on a 1000 MIP/s CPU, an eavesdropper can encrypt a list of all possible 512-bit messages (using the Public Key), and compare the corresponding ciphertext to the transmitted ciphertext. • If the message is your password, make sure you picked a good one (not in any dictionary). • A defense is to add random bits to the message. MIPs - Millions of Instructions per second. 14

Diffie-Hellman Technique Mutual Secret Keys or Public (but not Private) Keys Global Public Elements: q (large prime) and a (a < q) User A’s Key: Select secret Xa (Xa < q) A’s public info is Ya = a^Xa mod q User B’s Key: Select secret Xb (Xb < q) B’s public info is Yb = a^Xb mod q Joint Key = Yb ^Xa mod q (A’s calculation) Ya ^ Xb mod q (B’s calculation) a^(Xa*Xb) mod q (in both cases) No one else knows either Xa or Xb, so they can not find out K since Ya * Yb mod q = a^(Xa + Xb) mod q 15

Diffie-Hellman used for a Public-Key System for Encryption (can not sign messages) + a and q YB + message encrypted with “ K” B has to send “ YB” with message so A can decrypt it. (YA, a,q are A’s Public Key) “Trudie” does not know Xa: Can not read message. Different correspondents (B's) will select different XB's and generate different "public" keys (K's).Must tell A the YB. 16

Raw “Certificate” has user name, public key, expiration date, ... CA Secure Area Generate hash code of Raw Certificate Raw Cert. MIC Hash Encrypt hash code with CA’s private key to form CA’s signature Signed Cert. Signed Certificate Recipient can verify signature using CA’s public key. Certificate Authority generates the “signature” that is added to raw “Certificate” 17

Browsers Come With a CA Cert Database You can add additional certificates from sites you trust. 18

The GT CA Certificate 19