On the Practical Feasibility of Secure Distributed Computing A Case Study

1. On the Practical Feasibility of Secure Distributed ComputingA Case Study Gregory Neven, Frank Piessens, Bart De Decker Dept. of Computer Science, K.U.Leuven Celestijnenlaan 200A, B-3001 Heverlee, Belgium

2. Secure Distributed Computing • Given • n different participants P1…Pn • each participant Pi has a secret input xi • some function f • How to • compute y = f(x1,…, xn) • without Pi being able to learn anything more about xj(i j) than what is implied by the function result itself Introduction Secure Distributed Computing Case Study: Secret Query Database Conclusion

3. Secure Distributed Computing(cont) • Practical applications • Second price auctions • Voting • Privacy for mobile code • Secret Query Database • Query a database while preserving privacy of query • Example Alice sells records from database of CV’s Bob doesn’t want just any CV doesn’t want to reveal his selection criteria Introduction Secure Distributed Computing Case Study: Secret Query Database Conclusion

4. Overview • Secure Distributed Computing • Trivial solution • Protocol (by Abadi & Feigenbaum) • Other protocols • Case study: Secret Query Database • Implementation • Assessment • Conclusion

5. x1 y y xn y x2 Trivial Solution • Using a Trusted Third Party (TTP) y = f(x1,…,xn) Introduction Secure Distributed Computing Case Study: Secret Query Database Conclusion

6. Outline of the Protocol • Two participants • Alice knows secret data x = x1x2… • Bob knows secret function f (as a boolean circuit) • Compute y = f(x) without compromising their secrets • Outline Introduction Secure Distributed Computing Case Study: Secret Query Database Conclusion Alice Bob f x = x1x2… En(y1), En(y2), … y y

7. Encryption Scheme • Probabilistic encryption • one plaintext  many possible ciphertexts • secure for small message spaces • disadvantage: huge data blowup • Homomorphic encryption scheme • E(x) op E(y) = E(xop’y) • Properties: Introduction Secure Distributed Computing Case Study: Secret Query Database Conclusion

8. ? Evaluation of the Circuit • NOT-gate • XOR-gate • AND-gate Introduction Secure Distributed Computing Case Study: Secret Query Database Conclusion No interaction with Alice!

9. Evaluation of the Circuit (cont) Alice Bob Introduction Secure Distributed Computing Case Study: Secret Query Database Conclusion ? Choose random c1, c2 Decryption  d1, d2 !  communication overhead 

10. Other SDC Protocols • Goldreich, Micali and Wigderson (1987) • Two-party • Based on symmetric encryption and oblivious transfer • Sander and Tschudin (1998) • Two-party • Autonomous protocol • Based on dual-homomorphic encryption schemes • Polynomial evaluation only Introduction Secure Distributed Computing Case Study: Secret Query Database Conclusion

11. Other SDC Protocols (cont) • Chaum, Damgard and van de Graaf (1988) • Multi-party • Based on blindable bit commitments • Franklin and Haber (1996) • Multi-party • Based on group-oriented cryptography Introduction Secure Distributed Computing Case Study: Secret Query Database Conclusion

12. Secret Query Database • Problem statement • Query DB while preserving privacy of query • Example • Alice sells records from database of CV’s = secret data x • Bob doesn’t want just any CV doesn’t want to reveal his selection criteria = secret function Q( ) Introduction Secure Distributed Computing Case Study: Secret Query Database Conclusion

13. Implementation Alice Bob Introduction Secure Distributed Computing Case Study: Secret Query Database Conclusion n, En(x1), En(x2),… n = pq record x query Q evaluation En(Q(x)) Decrypt Q(x) En(Q(x)) x Q(x) = 1 ?

14. Security Trade-Off • Security parameter: |n| • Each record different n 512 bits • Huge data blowup! • 1 plaintext bit  512 encrypted bits • Encrypted records reusable • p and q are never revealed • Same encryption used for multiple session  Edited on CD-ROM Introduction Secure Distributed Computing Case Study: Secret Query Database Conclusion

15. Assessment • Typical values • |record x| = 500 bytes • |database| = 1000 records • |query Q| = 1000 gates • |n| = 512 bits (security parameter) • Communication complexity Introduction Secure Distributed Computing Case Study: Secret Query Database Conclusion

16. Conclusion • High overhead, but • increasing bandwidth of the Internet • trade-off communication  security • trade-off communication  query complexity • mobile agent technology • SDC is ready for practical applications Introduction Secure Distributed Computing Case Study: Secret Query Database Conclusion

17. Quadratic Residuosity • Suppose • p and q primes congruent to 3 mod 4 • n = pq • a is a quadratic residue (QR) mod n iff • Quadratic Residuosity Assumption (QRA): Is a a QR mod n or not? • easy if p and q are known • hard if p and q are unknown

18. Some Properties • Inversion If a is a QR mod n, then is a QNR mod n (and vice versa) • Multiplication mod n a  b

19.  Efficiency Improvement If c2 = 0  b1  c2 = 0  En(b1  c2) = En(0) If c2 = 1  b1  c2 = b1  En(b1  c2) = En(b1) Alice Bob ? Choose random c1, c2 Decryption  d1, d2 !