1. Anonymity-preserving Public-Key Encryption Markulf Kohlweiss Ueli Maurer, Cristina Onete, Björn Tackmann, and Daniele Venturi PETS 2013

2. PETS 2013 | Markulf Kohlweiss | Anonymity-preserving PKE | Slide 2 Context: Encryption and Anonymity  Public-key encryption  Short but eventful history, late 70s, 80s.  Security usually defined using Games: IND-CPA, IND-CCA, …  Anonymity  Shorter eventful history, early 90s.  Anonymity is arguably a more high-level property  What if used together?  Key privacy, robust encryption, formal analysis of onions  Games prone to require iterations to find “right” notion

3. PETS 2013 | Markulf Kohlweiss | Anonymity-preserving PKE | Slide 3 What is Anonymous Encryption? [PH08] Sender AnonymityReceiver Anonymity Anonymity not created, but preserved

4. PETS 2013 | Markulf Kohlweiss | Anonymity-preserving PKE | Slide 4 Our contribution

5. PETS 2013 | Markulf Kohlweiss | Anonymity-preserving PKE | Slide 5 Chosen Ciphertext Attack Security (IND-CCA) Challenger Dec Bit b d = b? m 0, m 1 Enc(m b ) bit d c Dec(c) pk

6. PETS 2013 | Markulf Kohlweiss | Anonymity-preserving PKE | Slide 6 Key Privacy (IK-CCA) [BBDP01] Challenger Dec 1 Bit b d = b? m Enc(pk b; m) bit d c Dec 1 (c) Dec 0 c Dec 0 (c) pk 0, pk 1

7. PETS 2013 | Markulf Kohlweiss | Anonymity-preserving PKE | Slide 7 Weak Robustness (WROB) [ABN10] Challenger c  Enc(pk i, m) m, i, j Dec c,i Dec i (c) ≠ Dec(sk j, c) ? ┴ pk 1,..., pk n

8. PETS 2013 | Markulf Kohlweiss | Anonymity-preserving PKE | Slide 8 Constructive Cryptography [MR11]  Resources (existing/assumed, desired):  Available to everyone, including adversary/simulator through interfaces  Converters:  Transform existing into desired resources  Two interfaces, inner and outer  Protocol: composition of many converters, one for each user  Security:  Correctness: without Eve the protocol works correctly  Security: when Simulator connected, no-one can distinguish between assumed and desired worlds.

9. PETS 2013 | Markulf Kohlweiss | Anonymity-preserving PKE | Slide 9 Confidential Receiver-Anonymous Channel

10. PETS 2013 | Markulf Kohlweiss | Anonymity-preserving PKE | Slide 10

11. PETS 2013 | Markulf Kohlweiss | Anonymity-preserving PKE | Slide 11 Constructing the Channel from Broadcast BnBn B2B2 B1B1 … n x (pk i ) m m m m ┴ Existing Resources

12. PETS 2013 | Markulf Kohlweiss | Anonymity-preserving PKE | Slide 12 Constructing the Channel from Broadcast … n x (pk i ) Converters Encryption scheme that is:  IND-CCA  IK-CCA  WROB m* m*, j … m m Existing Resources BnBn BjBj B1B1

13. PETS 2013 | Markulf Kohlweiss | Anonymity-preserving PKE | Slide 13 Simulation (intuition) B1B1 … (c, i) c … … BjBj BiBi BnBn B1B1 … (m, i) … … BjBj BiBi BnBn  Key-Generation: generate n keypairs (for each B i ), one separate (sk, pk)  Ciphertext generation: get |m|, encrypt 0 |m| under pk to get c c c m, i Existing world Desired world D |m|

14. PETS 2013 | Markulf Kohlweiss | Anonymity-preserving PKE | Slide 14 Simulation (intuition) B1B1 … (c, i) c … … c* (c*, j) BjBj BiBi BnBn … (m, i) … (m*, j) … m*  Ciphertext delivery: deliver c* to B j : (c*, j) if c* not seen before decrypt under sk j and inject message m* into network Dec(c*) m* Existing world Desired world |m| D B1B1 BjBj BiBi BnBn

15. PETS 2013 | Markulf Kohlweiss | Anonymity-preserving PKE | Slide 15 Simulation (intuition) B1B1 … (c, i) c … … c (c, i*) BjBj BiBi BnBn … (m, i) |m| … … m If i = i* (H, i*) H m  Ciphertext delivery: deliver c to B j : (c, i*) if c seen before deliver corresponding msg. to correct receiver Intuition: this is where we need WROB – wrong receiver outputs error m=Dec(c) m Assumed world Desired world D B1B1 BjBj BiBi BnBn Trial Delivery

16. PETS 2013 | Markulf Kohlweiss | Anonymity-preserving PKE | Slide 16 (More) Results in a Nutshell  WROB sufficient  SROB leads to a tighter reduction  WROB necessary  without WROB, achieve anonymity with erroneous transmission  Impossibility: SROB does not construct better resource  Constructive aspects:  Model network with single sender, many receivers  PK settings: use uni-directional authenticated channels  Trial deliveries prevent better anonymity

17. PETS 2013 | Markulf Kohlweiss | Anonymity-preserving PKE | Slide 17 Results in Picture Game-based analysisConstructive result IND-CCA IK-CCA SROB IND-CCA IK-CCA WROB

18. PETS 2013 | Markulf Kohlweiss | Anonymity-preserving PKE | Slide 18 Strong Robustness (SROB) Challenger c, i, j Dec c,i Dec i (c) both ┴ ≠ Dec(sk i, c) ┴ ≠ Dec(sk j, c) pk 1,..., pk n

19. PETS 2013 | Markulf Kohlweiss | Anonymity-preserving PKE | Slide 19