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 Hash function: H(m) = c Variable-length messages, fixed-length checksum Examples: MD5, SHA-1 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) 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

c =enc(m, K) m=dec(c, K) 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) Symmetric Encryption (Secret-key Encryption) Encryption and decryption use the same key secret key Examples: DES, AES 9 ciphertext plaintext

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

Asymmetric Encryption (Public-key Encryption) Properties: 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 By definition of public-key encryption

Using Public-key Crypto Key generation –Creates the 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 the public key –Much slower than symmetric-key encryption 14 Challenge: how to ensure the correct public key is used?

Using Public Key to Establish a Shared Secret AliceBob C=E(PK B, s) s PK B s=D(SK B, C) Pick a random secret s

Digital Signature Based on public-key crypto. Signing: sig= Sign(m, K priv ) Verification: Verify(sig, K pub, 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 18 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

Exercise after class Set up public-key based authentication using SSH Play with the various crypto primitives using OpenSSL ( –The command-line tool documentation can be found at ml ml –Openssl should be installed at most Unix systems. 19