Footprint Scheduling @ Financial Cryptography 2016, Barbados, Feb 2016

Transcript

1. Footprint Scheduling for dining-cryptographer networks peter@cryptojedi.org Moritz Neikes Peter Schwabe Anna Krasnova anna@mechanical-mind.org moritz@post-apocalyptic-crypto.org Radboud Universiteit Nijmegen 1/67
2. Vimbodia Great Kingdom of Emacston 2/67
3. Vimbodia Great Kingdom of Emacston 3/67
4. https://xkcd.com/378/ 4/67
5. Vimbodia Great Kingdom of Emacston 5/67
6. Vimbodia Great Kingdom of Emacston $#@&*! 6/67
7. Problem Many users Unstable connections even against very strong adversaries Anonymous communication 7/67
8. DC networks (Chaum, 1988) 8/67
9. Charlie Alice Bob 9/67
10. Charlie Alice Bob 0 1 1 10/67
11. Charlie Alice Bob 0 1 1 key 11/67
12. Charlie Alice Bob 0 1 1 0 1=1 0 1=1 1 1=0 0 1 1 12/67
13. Charlie Alice Bob 0 1 1 0 1=1 0 1=1 1 1=0 0 1 1 0 1=0 1 result 13/67
14. Charlie Alice Bob 0 1 1 0 1=1 0 1=1 1 1=0 0 0 1 sending 14/67
15. Charlie Alice Bob 0 1 1 0 1=1 0 1=1 1 1=0 0 0 1 0 0=1 1 sending 15/67
16. More Bits 16/67
17. Charlie Alice Bob 100110 100110 111110 100110 001010 100110 110100 110100 001010 111110 101100 010010 000000 111110 101100 010010 100110 001010 101100 110100 100110 010010 17/67
18. Charlie Alice Bob 100110 100110 100110 001010 100110 110100 110100 001010 111110 101100 111000 001011 011111 011111 101100 111000 100110 001010 101100 110100 100110 010010 18/67
19. Charlie Alice Bob 100110 100110 100110 001010 100110 110100 110100 001010 111110 101100 111000 001011 011111 011111 101100 111000 100110 001010 101100 110100 100110 010010 collision 19/67
20. Multiple senders Collision Corruption Retransmission Wasted traffic Inefficient Collisions 20/67
21. BAD Multiple senders Collision Corruption Retransmission Wasted traffic Inefficient Collisions 21/67
22. WORSE More users More collisions More corruption More wasted traffic Collisions 22/67
23. Unconditional anonymity Collisions Recap Arbitrary messages Many participants High traffic load DC networks: 23/67
24. Scheduling 24/67
25. 000000 001000 100000 schedule 101000 000000 000000 000000 000000 000000 000000 1 6 5 4 3 2 slot reserve 25/67
26. Collisions during reservation? 000000 001000 001000 000000 Detectable Undetectable 001000 001000 001000 001000 26/67
27. Collisions during reservation? 000000 001000 001000 000000 Detectable Undetectable 001000 001000 001000 001000 not enough :( 27/67
28. Tree-like collision resolution with superposed receiving Andreas Pfitzmann, 1990 28/67
29. Existing algorithms scales disconnect hides # senders message collisions Pfitzmann # senders breaks no none 29/67
30. 000000 001000 100000 schedule 101000 000000 000000 000000 000000 000000 000000 1 6 5 4 3 2 slot reserve 30/67
31. Existing algorithms scales disconnect hides # senders message collisions Pfitzmann # senders breaks no none Chaum # users unaffected no trade-off 31/67
32. Vimbodia Great Kingdom of Emacston :( 32/67
33. Collisions during reservation? 000000 001000 001000 000000 Detectable Undetectable 001000 001000 001000 001000 More slots! More bits! Footprint scheduling 33/67
34. Footprint scheduling More bits per slot 2 bits for now More choices Flip left / right / both bit(s) detect more collisions 34/67
35. Alice: Bob: Charlie: 10 11 01 footprint 35/67
36. 00.11.00 01.00.00 00.10.00 01.01.00 Alice: Bob: Charlie: 10 11 01 footprint 3 slots 36/67
37. 00.11.00 01.00.00 00.10.00 01.01.00 Alice: Bob: Charlie: 10 11 01 taken free 37/67
38. 00.11.00 01.00.00 00.10.00 01.01.00 Alice: Bob: Charlie: 10 11 01 taken free DEDUCE REUSE RECYCLE 38/67
39. 00.00.11 11.00.00 00.00.01 11.00.10 01.01.00 Alice: Bob: Charlie: 01 11 11 previously II. 39/67
40. 00.10.00 01.00.00 00.00.10 11.00.10 01.01.00 01.10.10 Alice: Bob: Charlie: 10 10 01 previously III. 40/67
41. 00.10.00 01.00.00 00.00.10 11.00.10 01.01.00 01.10.10 Alice: Bob: Charlie: 10 10 01 previously III. converged! 41/67
42. 00.10.00 01.00.00 00.00.10 11.00.10 01.01.00 01.10.10 Alice: Bob: Charlie: 10 10 01 previously III. converged! 01.10.10 000000 000000 000000 1 3 2 42/67
43. Footprint scheduling Iterate Discuss for rounds bits per slot 2 slots s # users s r 43/67
44. 100110 START PICK FREE SLOT COLLISION? TOSS COIN FREE SLOT? 100110 BACK OFF NO YES MOVE YES STAY NO PICK FOOTPRINT 44/67
45. 100110 START PICK FREE SLOT COLLISION? TOSS COIN FREE SLOT? 100110 BACK OFF NO YES MOVE YES STAY NO PICK FOOTPRINT 45/67
46. 100110 START PICK FREE SLOT COLLISION? TOSS COIN FREE SLOT? 100110 BACK OFF NO YES MOVE YES STAY NO PICK FOOTPRINT 46/67
47. 100110 START PICK FREE SLOT COLLISION? TOSS COIN FREE SLOT? 100110 BACK OFF NO YES MOVE YES STAY NO PICK FOOTPRINT 47/67
48. 100110 START PICK FREE SLOT COLLISION? TOSS COIN FREE SLOT? 100110 BACK OFF NO YES MOVE YES STAY NO PICK FOOTPRINT 48/67
49. 100110 START PICK FREE SLOT COLLISION? TOSS COIN FREE SLOT? 100110 BACK OFF NO YES MOVE YES STAY NO PICK FOOTPRINT 49/67
50. 100110 START PICK FREE SLOT COLLISION? TOSS COIN FREE SLOT? 100110 BACK OFF NO YES MOVE YES STAY NO PICK FOOTPRINT 50/67
51. 100110 START PICK FREE SLOT COLLISION? TOSS COIN FREE SLOT? 100110 BACK OFF NO YES MOVE YES STAY NO PICK FOOTPRINT 51/67
52. 100110 START PICK FREE SLOT COLLISION? TOSS COIN FREE SLOT? 100110 BACK OFF NO YES MOVE YES STAY NO PICK FOOTPRINT 52/67
53. 100110 START PICK FREE SLOT COLLISION? TOSS COIN FREE SLOT? 100110 BACK OFF NO YES MOVE YES STAY NO PICK FOOTPRINT 53/67
54. 00.10.00 00.00.00 00.00.10 11.00.10 01.01.00 00.10.10 Alice: Bob: Charlie: 10 10 01 Disconnects previously free 54/67
55. Interleaving Header: 1 2 3 4 scheduling message cycle 1 2 Payload: 42B 8B 55/67
56. Interleaving Header: Payload: 42B 8B 1 2 3 4 scheduling message cycle 1 2 56/67
57. Disruptors random checks discard schedule commit to PRNG seed 1 2 2 2 commit check? 57/67
58. Vimbodia Great Kingdom of Emacston : ) 58/67
59. Existing algorithms scales disconnect hides # senders message collisions Pfitzmann # senders breaks no none Chaum # users unaffected no trade-off Footprint Scheduling # senders unaffected passive none* 59/67
60. Existing algorithms scales disconnect hides # senders message collisions Pfitzmann # senders breaks no none Chaum # users unaffected no trade-off Footprint Scheduling # senders unaffected passive none* peter@cryptojedi.org anna@mechanical-mind.org moritz@post-apocalyptic-crypto.org 60/67
61. Traditional alg. Bit-map protocols Tokens (slotted) ALOHA CSMA Carrier Sense Multiple Access Collision resolution Collision-free doesn't scale inefficient no anonymity 61/67
62. Alice Bob Charlie 100110 100110 100110 001010 100110 110100 Fred George 100110 110111 100110 011001 100110 101110 62/67
63. Alice Bob Charlie 100110 100110 100110 001010 100110 110100 Fred George 100110 011001 100110 101110 63/67
64. Pfitzmann's algorithm http://dud.inf.tu-dresden.de/sirene/publ/Pfit_88_0.pdf By design no undetectable collisions Andreas Pfitzmann, 1990 _6.pdf ... Cleverly utilizes collisions Scales with # senders Breaks on disconnect >11 min to complete based on latency between major US cities 10,000 users 64/67
65. Optimization • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • 6 9 12 15 2 4 6 8 # Bits per slot Required rounds # Slots 8 16 32 64 128 65/67
66. Optimization 0 5 10 0 2500 5000 7500 10000 # Participants Required rounds # Slots 8 16 32 64 128 66/67
67. • • • • • • • • • • • • • • • • • • • • • • • • • • 4.0 4.5 5.0 5.5 6.0 100 500 1000 2000 5000 10000 # Participants Data (log) Algorithm Chaum Footprint Pfitzmann 67/67