2. 2 Your data is anywhere but not in your control Security breaches are recurrent – Weakest link: hardware, software, technicians, … You may trust the science of cryptography

3. 3 + CRYPTOGRAPHY “Applied Crypto” – system constructions – practical & efficient “Foundation” – formal definitions – formal security proof I. Privacy Enhancing Technologies II. Searchable Encryption III. Cloud Crypto. IV. Lattice- Based Crypto Projects I, III, IV are ongoing FYPs in ’13-’14 Projects I-III have both research and implementation elements Project IV requires a good foundation in Mathematics

4. 4 Confid- entiality Integrity (/ Auth.) Info. Security Availab- ility

5. 5 Encryption supposes to hide as much info of the plaintext as possible You may want your mobile devices only download encrypted e-mails marked with the keyword “urgent” from the server. You don’t want the server to know what are the keywords associated with each email.

6. 6 Download all data, then decrypt – O(N) communication – N: number of documents Build a local index, then download – O(N) local storage Ideally, O(n) complexity (at least at client side) – n: number of matching documents (n << N)

7. 7 = Enc( ) = “work, blah blah …” Keyword ( ) = [“work”] = [“work”] = Enc(“work …”)

8. 8 Encryption of the same plaintext always lead to the same ciphertext – Not the most secure, but allows efficient indexing Order-preserving encryption – the relative order of plaintexts is preserved in ciphertexts

9. 9 Is “absolute-”authentication always good? Right balance of privacy and accountability Electronic Payments – Octopus, electronic toll pricing, Bitcoin, etc – Do you worry about leaking your spending pattern? – Merchants & Bank also have their concerns Double-spending, money laundry, etc.

10. 10 Everyone can write on different topics Writers & reviewers can be anonymous Multiple posts are unlinkable Even in places with restricted freedom of speech, user will not be identified (and punished)

11. 11 Easy! Use pseudonyms – Service provider (SP) knows your nym and IP – profile a user uniquely by sophisticated data mining Easy! Use anonymous network, e.g., Tor What if user repeatedly violating copyright, posting advertisement, using abusive language? So exit-nodes of Tor are blocked Crypto-solutions, e.g., MS U-Prove, IBM Idemix

12. 12 A system must be serving the info when it is needed. How can cryptography help to ensure availability? E.g., consider cloud storage again, how can I ensure that the cloud service provider is really storing my file? At least, I can provide (cryptographic) evidence when it fails to do so.

13. 13 The cloud may not want to store the same copy of the file from different users twice. Check a message digest like hash(file)? You can then transfer this short hash to your friend => Instant sharing! Again, we need cryptographic technique

14. 14 Symmetric key encryption: dk = ek Public key encryption: (dk, ek) is a valid key pair Identity-based encryption: dk ID can decrypt Enc f ID’ (m) when f ID’ (ID)=1, i.e., ID = ID’ Key-Policy ABE: dk f decrypt Enc A () when f(A)=1 Ciphertext-Policy: dk A decrypt Enc f () Functional encryption: dk g dec Enc f () if R(f, g)=1

15. 15 Big data You may not have the computational resource or the expertise to analyze the big data Outsource it to the cloud! What if the computation is sensitive? – Filing tax, DNA-related computation, etc What if the cloud computed wrongly? – Wrong decision in investment

16. 16 A lattice is a set of points in the n-dimensional Euclidean space R n with a strong periodicity. Intractable mathematical problems are leveraged to construct cryptographic systems. Shortest Vector Problem: Given a basis of a lattice, find the shortest vector in the lattice.

17. 17 Fully Homomorphic Encryption – It was open until 2009 Multi-linear pairing – The first construction was born in May last year! – Bi-linear pairing already solved many problems in this decade, e.g.: – public-key searchable encryption – functional encryption

18. 18 familiarity with proofs designing systems (basic) probability and number theory You don’t need to know number theory but you are expected to pick it up under my advice open-minded cryptanalysis (black-hat) Email: smchow@ie.cuhk.edu.hksmchow@ie.cuhk.edu.hk We can setup meetings for further discussion