Spatial Encryption. March 17, Adam Barth, Dan Boneh, Mike Hamburg

Transcription

1 Adam Barth Dan Boneh Mike Hamburg March 17, 2008

2 Traditional Public-Key Infrastructure CA Alice Bob

3 Traditional Public-Key Infrastructure CA PK Bob, proof of identity Alice Bob

4 Traditional Public-Key Infrastructure CA PK Bob, proof of identity S CA (PK Bob ) Alice Bob

5 Traditional Public-Key Infrastructure CA PK Bob, proof of identity S CA (PK Bob ) PK Bob, S CA (PK Bob ) Alice Bob

6 Traditional Public-Key Infrastructure CA PK Bob, proof of identity S CA (PK Bob ) Alice PK Bob, S CA (PK Bob ) E PKBob (m) Bob

7 Traditional Public-Key Infrastructure CA PK Bob, proof of identity S CA (PK Bob ) Alice PK Bob, S CA (PK Bob ) E PKBob (m) Bob But for , Bob is offline!

8 Identity-Based Encryption Public key can be any string Private key given by trusted authority

9 Identity-Based Encryption Public key can be any string Private key given by trusted authority PKG Alice Bob

10 Identity-Based Encryption Public key can be any string Private key given by trusted authority PKG proof of identity Alice Bob

11 Identity-Based Encryption Public key can be any string Private key given by trusted authority PKG proof of identity SK Alice Bob

12 Identity-Based Encryption Public key can be any string Private key given by trusted authority PKG proof of identity SK Alice E bob@microsoft.com (m) Bob

13 Problems using IBE for Sending to multiple recipients Lots of ciphertext Solved by broadcast IBE

14 Problems using IBE for Sending to multiple recipients Lots of ciphertext Solved by broadcast IBE Multiple trusted authorities

15 Encryption Wishlist Send to multiple recipients Trust in multiple authorities Short ciphertexts Short public keys Short private keys No central authority Hierarchical delegation

16 Encryption Wishlist Send to multiple recipients " Trust in multiple authorities " Short ciphertexts "(2 group elements) Short public keys "(random oracle model) Short private keys %O(max recipient list) No central authority % Hierarchical delegation "

17 A new primitive Identities are points in a vector space Keys for any hyperplane Can decrypt at any point in the hyperplane Delegate from plane to line to point

18 Our implementation Encryption, decryption are efficient Ciphertext is short Master public key is long but random Proportional to dimension of vs Short in the random oracle model Private keys are long Proportional to dimension of vs

19 for Vector space is polynomials SK Auth : polys w/root at Auth SK Auth, Bob : polys w/roots at Auth, Bob Alice encrypts her message to (x voltage)(x thawte) (x bob@...) (x zak@...)

20 Hierarchical IBE W for /path/to/data/ is (path, to, data,,..., )

21 Hierarchical IBE W for /path/to/data/ is (path, to, data,,..., )... or... W is (x /path)(x /path/to)(x /path/to/data) Q(x) Enables broadcast HIBE Enables delegation for encryption

22 Nitty-Gritty Based on Boneh-Boyen-Goh H-IBE Uses bilinear pairings Selective-ID secure in the standard model

23 Summary A new crypto primitive Generalization of H-IBE Enables efficient encryption Enables broadcast H-IBE

24 The End Questions?