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A Quick Tour of Cryptographic Primitives

18739A: Foundations of Security and Privacy. A Quick Tour of Cryptographic Primitives. Anupam Datta CMU Fall 2009. Basic Cryptographic Concepts. Encryption scheme (symmetric and public key) Signature scheme Message authentication code Hash function

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A Quick Tour of Cryptographic Primitives

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  1. 18739A: Foundations of Security and Privacy A Quick Tour of Cryptographic Primitives Anupam Datta CMU Fall 2009

  2. Basic Cryptographic Concepts • Encryption scheme (symmetric and public key) • Signature scheme • Message authentication code • Hash function • A network protocol like SSL is built using these primitives

  3. Symmetric Encryption Scheme • Key generation algorithm • Produces a key that is used for encryption and decryption • Algorithm to encrypt a message • Algorithm to decrypt a ciphertext • Correctness: • Decrypting a ciphertext obtained by encrypting message m with the corresponding key k returns m dec(enc(m,k),k) = m • (Symbolic) Security: • A ciphertext cannot be decrypted without access to the key Can you think of a stronger security property?

  4. Public-Key Encryption Scheme • Key generation algorithm • Produces private decryption & public encryption key pair • Algorithm to encrypt a message • Algorithm to decrypt a ciphertext • Correctness: • Decrypting a ciphertext obtained by encrypting message m with the corresponding encrytion key returns m dec(enc(m, pk(A)), sk(A)) = m • (Symbolic) Security: • A ciphertext cannot be decrypted without access to the private decryption key Why would you want public key encryption?

  5. Signature Scheme • Key generation algorithm • Produces private signing & public verification key pair • Algorithm to sign data • Algorithm to verify signature • Correctness: • Message signed with a signing key verifies with the corresponding verification key verify(m,sign(m,sk(A)), pk(A)) = ok • Security: • A signature cannot be produced without access to the private signing key Can you think of a scenario where you may not want non-repudiation?

  6. Message Authentication Code (MAC) • Key generation algorithm • Produces a key • Algorithm to mac a message • Algorithm to verify a mac on a message • Correctness: • Message mac-ed with key verifies with the same key verify(k, m, mac(k,m)) = ok • Security: • A MAC cannot be produced without access to the key Similar to signature, but uses symmetric key What property does a signature have, but a MAC does not?

  7. Hash Functions • Key generation algorithm • Produces a key • Algorithm to hash a message m, given a key k to a fixed length output hash(k, m) • Security (Collision resistance) Given hash function hash: X  Y and key k, cannot find a collision, i.e. x, x’  X s.t. x ≠ x’ and hash(k,x) = hash(k,x’) What is the difference between a MAC and a hash function?

  8. Cryptographic Constructions • Signature scheme • DSS, RSA-FDH,… • Hash function • SHA-1, MD5,… • Message Authentication Code (MAC) • HMAC, CBC-MAC, NBAC… • Encryption scheme • Asymmetric (public key): RSA, Diffie-Hellman, El Gamal,… (distinct keys for encryption and decryption) • Symmetric: DES, 3DES, AES, RC4,… (same key for encryption and decryption) • Want to know more? • 18-733: Applied Cryptography Later: Peeking inside the RSA encryption scheme

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