2 Server PIR with subpolynomial communication Zeev Dvir
2 -Server PIR with sub-polynomial communication Zeev Dvir Princeton University Joint work with Sivakanth Gopi
![Private Information Retrieval [CKGS 98] User Server](http://slidetodoc.com/presentation_image_h/05dc0ca1f0b9bf3dd57f839a85b5f3d7/image-2.jpg "Private Information Retrieval [CKGS 98] User Server")
Private Information Retrieval [CKGS 98] User Server
![Private Information Retrieval [CKGS 98] Server User](http://slidetodoc.com/presentation_image_h/05dc0ca1f0b9bf3dd57f839a85b5f3d7/image-3.jpg "Private Information Retrieval [CKGS 98] Server User")
Private Information Retrieval [CKGS 98] Server User
![Private Information Retrieval [CKGS 98] Two broad types of protocols: Single Server + Cryptographic](http://slidetodoc.com/presentation_image_h/05dc0ca1f0b9bf3dd57f839a85b5f3d7/image-4.jpg "Private Information Retrieval [CKGS 98] Two broad types of protocols: Single Server + Cryptographic")
Private Information Retrieval [CKGS 98] Two broad types of protocols: Single Server + Cryptographic assumptions [This talk] Multiple non-communicating servers. Information theoretic privacy.
![Private Information Retrieval [CKGS 98] Focus of this talk: 2 -Server PIR (hardest) Server](http://slidetodoc.com/presentation_image_h/05dc0ca1f0b9bf3dd57f839a85b5f3d7/image-5.jpg "Private Information Retrieval [CKGS 98] Focus of this talk: 2 -Server PIR (hardest) Server")
Private Information Retrieval [CKGS 98] Focus of this talk: 2 -Server PIR (hardest) Server 1 Server 2
![Private Information Retrieval [CKGS 98] Focus of this talk: 2 -Server PIR (hardest) Server](http://slidetodoc.com/presentation_image_h/05dc0ca1f0b9bf3dd57f839a85b5f3d7/image-6.jpg "Private Information Retrieval [CKGS 98] Focus of this talk: 2 -Server PIR (hardest) Server")
Private Information Retrieval [CKGS 98] Focus of this talk: 2 -Server PIR (hardest) Server 1 Server 2 Simplest: One round most protocols) * User sends one message to each server * Each server answers
![Private Information Retrieval [CKGS 98] Focus of this talk: 2 -Server PIR (hardest) Server](http://slidetodoc.com/presentation_image_h/05dc0ca1f0b9bf3dd57f839a85b5f3d7/image-7.jpg "Private Information Retrieval [CKGS 98] Focus of this talk: 2 -Server PIR (hardest) Server")
Private Information Retrieval [CKGS 98] Focus of this talk: 2 -Server PIR (hardest) Server 1 Server 2 Cost: Total number of bits sent (user + server)
![Upper bounds: # Servers Cost Ref method [CGKS 95 , BI 01, WY 05]](http://slidetodoc.com/presentation_image_h/05dc0ca1f0b9bf3dd57f839a85b5f3d7/image-8.jpg "Upper bounds: # Servers Cost Ref method [CGKS 95 , BI 01, WY 05]")
Upper bounds: # Servers Cost Ref method [CGKS 95 , BI 01, WY 05] [CGKS 95] Low degree polynomials +Composition [Amb 97] [BIKR 02] [Yek 08, Efr 09] Matching-Vector Families [This work] MV codes viewed as polynomials [DGY 10]
![Lower bounds * It satisfies the weaker notion (defined in [RY 05]) of employing](http://slidetodoc.com/presentation_image_h/05dc0ca1f0b9bf3dd57f839a85b5f3d7/image-9.jpg "Lower bounds * It satisfies the weaker notion (defined in [RY 05]) of employing")
Lower bounds * It satisfies the weaker notion (defined in [RY 05]) of employing a group-based secret sharing scheme.
Talk Outline • • Overview of existing constructions The new protocol PIR and LDCs Future directions
![A 6 -Server scheme [Yek 08, Efr 09, DGY 10]](http://slidetodoc.com/presentation_image_h/05dc0ca1f0b9bf3dd57f839a85b5f3d7/image-11.jpg "A 6 -Server scheme [Yek 08, Efr 09, DGY 10]")
A 6 -Server scheme [Yek 08, Efr 09, DGY 10]
![A 6 -Server scheme [Yek 08, Efr 09, DGY 10]](http://slidetodoc.com/presentation_image_h/05dc0ca1f0b9bf3dd57f839a85b5f3d7/image-12.jpg "A 6 -Server scheme [Yek 08, Efr 09, DGY 10]")
A 6 -Server scheme [Yek 08, Efr 09, DGY 10]
![A 6 -Server scheme [Yek 08, Efr 09, DGY 10] mod 6](http://slidetodoc.com/presentation_image_h/05dc0ca1f0b9bf3dd57f839a85b5f3d7/image-13.jpg "A 6 -Server scheme [Yek 08, Efr 09, DGY 10] mod 6")
A 6 -Server scheme [Yek 08, Efr 09, DGY 10] mod 6
![A 6 -Server scheme [Yek 08, Efr 09, DGY 10]](http://slidetodoc.com/presentation_image_h/05dc0ca1f0b9bf3dd57f839a85b5f3d7/image-14.jpg "A 6 -Server scheme [Yek 08, Efr 09, DGY 10]")
A 6 -Server scheme [Yek 08, Efr 09, DGY 10]
![A 6 -Server scheme [Yek 08, Efr 09, DGY 10]](http://slidetodoc.com/presentation_image_h/05dc0ca1f0b9bf3dd57f839a85b5f3d7/image-15.jpg "A 6 -Server scheme [Yek 08, Efr 09, DGY 10]")
A 6 -Server scheme [Yek 08, Efr 09, DGY 10]
Talk Outline • • Overview of existing constructions The new protocol PIR and LDCs Future directions
High level idea
Case study: Restriction to `real’ lines Single (random) point sent to server!
`Nicer’ derivatives Same for partial derivatives:
Interlude: `Nicer’ derivatives But let’s pretend for a second that it is mod 6…
“Pretend” mod 6
Removing the `pretend mod 6’ :
Matrix notation
Matrix notation
A 2 -Server scheme
Variations:
Talk Outline • • Overview of existing constructions The new protocol PIR and LDCs Future directions
![Locally Decodable Codes [KT 00] Decoder](http://slidetodoc.com/presentation_image_h/05dc0ca1f0b9bf3dd57f839a85b5f3d7/image-31.jpg "Locally Decodable Codes [KT 00] Decoder")
Locally Decodable Codes [KT 00] Decoder
Locally Decodable Codes Decoder
Talk Outline • • Overview of existing constructions The new protocol PIR and LDCs Future directions
Future work (? ) Can we reduce the communication further by taking more derivatives?
Future work (? )
THANK YOU !!
Talk Outline
- Slides: 37