Wk 12 Cryptography and Network

Wk 12 Cryptography and Network

1. Homomorphic and Functional Encryption

   • Homomorphic: Computing on Encrypted Data
     • FULLY HOMOMORPHIC ENCRYPTION “Anything you can do on plain text data, FHE can do on encrypted data” (fully = any function F) (additive = only additions) (multiplicative = only multiplications) (somewhat/partially = circuits of small depth)
       • MULTIPLICATIVE HOMOMORPHISM: El Gamal Encryption
       • ADDITIVE HOMOMORPHISM: Goldwasser Micali Encryption
       • OTHER SCHEMES: Additively Homomorphic: – Paillier – Damgard-Jurik (both addition of large numbers) • Additions + a single Multiplication: – Boneh-Goh-Nissim (based on gap groups) – Gentry-Halevi-Vaikuntanathan (based on lattices) • HE with Large ciphertext blowup: – Sander-Young-Yung
       • LEARNING WITH ERRORS (LWE)
       • HOMOMORPHIC OPERATIONS: Homomorphic addition: C1 + C2 Homomorphic multiplication*: C1C2
       • APPLICATIONS: ─ Encrypted machine learning (SVMs, decision trees) ─ Encrypted AES and stream cipher computations ─ Encrypted VoIP Interactive Methods: Secure Computation
       • Functional Encryption: A method of releasing partial information about the encrypted data to third parties. But a controlled form of partial information.

2. Multi Party Computation and Distributing Trust

   • Goal: Compute arbitrary functions g(x,y) without revealing x or y to each other
     • Applications of MPC: Electronic Election, Auctions, E-commerce applications, Medical Research, Risk Prediction for Global Economy, Data Mining
       • Intersection without revealing individual Lists
   • Key Tool: Secret Sharing
     • Secret Sharing Using Polynomials
   • Distributing Trust and Power: Don’t store keys in 1 place: Don’t do Computation in 1 place Key escrow Cloud Application: remote storage and computation
     • DISTRIBUTE INFORMATION AND POWER
   • Two Party Computation: Two Party computation: certified mail, PIR, secret exchange
     • APPLICATIONS Certified e-mail Secret Exchange Private Information Retrieval

3. Security problems

   • Trusting users try to communicate
     • Use Cryptography.
       • Use Transport Layer Security (TLS)
         • Use a Cartificate issues by a Cert Auth.
   • One user attacks another
     • Untrustworthy users
       • Most communication on the Internet is among parties that do not trust each other and with good reason.
   • The network itself is attacked.
     • One part of the network attacks another
   • Denial of service attacks.
     • Use many computers to send unwanted traffic toward a host or region of the network, thus overwhelming it.

4. Public-Key Cryptography

   • RSA
   • El Gamal
   • Semantic Security
   • Digital Signatures
   • Elliptic Curvatures