Basic Cryptography 1 What is cryptography Cryptography is

Basic Cryptography 1

What is cryptography? • Cryptography is a mathematical method of protecting information – Cryptography is part of, but not equal to, security – Predated modern computing • In modern computing, crypto is used to remediate deficiencies in the cyber space. 2

Cryptographic Primitives • In this course, we do not study the math part of crypto; rather, we use cryptography primitives as “black boxes. ” – Need to understand the fundamental properties of the crypto primitives • Four primitives: – Cryptographic hash – Symmetric encryption – Asymmetric encryption – Digital signatures 3

Using the crypto primitives • Build security protocols – e. g. SSL/TLS • Build more complex security systems using the primitives – e. g. PKI 4

Cryptographic Hash function: H(m) = c Variable-length messages, fixed-length checksum Properties: 1. Given m, easy to compute H(m) 2. Given c, hard to find m (preimage resistance) 3. Given m, hard to find another m’ s. t. H(m’) = H(m) (second-preimage resistance) 4. Hard to find m and m’ s. t. H(m) = H(m’) (collision resistance) Examples: MD 5, SHA-1 5

Applications of Hash Function • Provides integrity guarantee – If the message content is changed, the hash will be different. • Hide information – Knowing the hash does not reveal the input message. • N. B. Hash is NOT encryption! 6

A simple application • A Commitment Scheme – We are having an online “sealed first-price auction” – Everyone submits a bid in a chat-room – There is no trusted third party – Bids may be submitted at different times • Requirements: – The bids need to be secret before opening – The bids need to be binding after opening – Use cryptographic hash function to implement such a scheme 7

Using Salt with Hash • A salt is a message that is typically concatenated to the Hash function’s input. – Used to increase the input space of the hash – Increase the difficulty of brute-force attacks 8

Symmetric Encryption (Secret-key Encryption) ciphertext plaintext c =enc(m, K) m=dec(c, K) secret key Encryption and decryption use the same key Properties: 1. Given ciphertext, hard to infer plaintext (ciphertext only attack) 2. Ciphertext and plaintext known, hard to infer key (known-plaintext attack) 3. Access to encryption oracle, hard to infer key (chosen-plaintext attack) 4. Access to decryption oracle, hard to infer key (chosen-ciphertext attack) Examples: DES, AES 9

The key management problem • Every pair of communicating parties need to establish a shared key • Leads to keys for N parties • Typically requires a key-management/key agreement scheme to be used in practice 10

Diffie-Hellman Key Agreement (1976) Alice Bob

Asymmetric Encryption (Public-key Encryption) Every party has a pair of keys: <Kpub , Kpriv> Public key: announce to everyone Private key: known to the owner only Encryption and decryption use two different keys: c = enc(m, Kpub) m = dec(c, Kpriv) It is hard to infer private key from the public key Examples: RSA, El-Gamal 12

Asymmetric Encryption (Public-key Encryption) Properties: By definition of public-key encryption 1. Given ciphertext, hard to infer plaintext (ciphertext only attack) 2. Ciphertext and plaintext known, hard to infer private key (known-plaintext attack) 3. Encryption oracle given, hard to infer private key (chosen-plaintext attack) 4. Decryption oracle given, hard to infer private key (chosen-ciphertext attack) 13

Using Public-key Crypto • Key generation – Creates the <public, private> key pair – Typically involves pseudo-random number generation • Encryption using public-key crypto – Does not need to share keys – Does not need a secure channel to transmit Challenge: how to ensure the public key correct public key is used? – Much slower than symmetric-key encryption 14

Using Public Key to Establish a Shared Secret PKB C=E(PKB , s) Alice Pick a random secret s Bob s s=D(SKB, C)

Digital Signature Based on public-key crypto. Signing: sig= Sign(m, Kpriv) Verification: Verify(sig, Kpub, m) = True Properties: 1. Verification of the validity of a digital signature needs only the public key. 2. Only the owner of the corresponding private key can produce a valid signature Examples: RSA, DSA, El-Gamal 16

Applications of Digital Signature • Ensuring data authenticity – Sender signs the message, receiver verifies the signature • Providing non-repudiation – Digital signature serves as proof that the message is generated by the private-key holder 17

Message Authentication Code Hash with a shared key. tag= MAC(m, K) Properties: 1. Only the holder of the key K can generate a valid MAC tag. Examples: HMAC 18

Exercise after class • Set up public-key based authentication using SSH • Play with the various crypto primitives using Open. SSL (http: //www. openssl. org/) – The command-line tool documentation can be found at http: //www. openssl. org/docs/apps/openssl. ht ml – Openssl should be installed at most Unix systems. 19