Storage Systems Autumn 2009

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1 Storage Systems Autumn 2009 Chapter 5: Securely Auditing André Brinkmann

2 Sources Different Publications Slides from Randal Burns, Johns Hopkins University, USA

3 Awkward for large data What s wrong with LOCKSS Needs too many copies to get safety guarantees Expensive for servers to read entire files when checking Inappropriate for data with privacy constraints This mandates long-term secrets Transfer trust from data owner to storage

4 Archival Data on Untrusted Stores Data owner (client) transfers data to a third-party outsourced store (server) that retains it contractually Large amounts of data that are accessed infrequently or never Long contractual lifetimes..decades Subject to data loss Device failures Administration errors (migration, backup and restore) Financial motivation for storage service providers to cheat Sell long-term storage and discard the data Present multiple copies as a single copy (collusion) Conceal data loss incidents to preserve reputation Data loss incidents in archives are a silent failure To the data owner (client)

5 Archival Introspection Data owners (clients) periodically check that servers continue to store the exact data that were originally stored Actually can only verify that they can produce it Clients do not possess the data (that s the point of outsourcing) Insufficient to verify data on read Too late to repair damaged data Some data are never read, yet must be retained Using such a construct for introspection requires the client to read/retrieve all of its data from the server Topic of lots of recent work

6 Storing a File Outsourced storage Client metadata O(1) Server storage O(n)

7 Verifying Server Possession Size of client metadata Network complexity of the protocol Server computation and I/O complexity

8 Size of client metadata Solution Constraints O(1) for any size file conforms with storage outsourcing Network complexity of the protocol O(1) so that it scales to large archives Server computation and I/O complexity Should be O(1) or O(log n) Otherwise, server must iterate over all data in its archive periodically We hold that clients need to be able to verify that a server has retained file data without retrieving the data from the server and without having the server access the entire file.

9 Related Concepts Replica maintenance (Oceanstore, LOCKSS) Mutual assurance among storage sites In client/server framework, client transfers trust to storage system

10 Algebraic Signatures Algebraic signatures have the property sig a (x y) = sig a (x) sig a (y) For m/n redundancy encoded data, e.g. RS codes or any other code computed using xor as well as Galois fields the signature of the parity block equals the parity of the signatures of the corresponding data blocks. T. S. J. Schwarz and E. L. Miller. Store, forget, and check: Using algebraic signatures to check remotely administered storage. In Proceedings of ICDCS, 2006.

11 Algebraic Signatures Spread erasure coded data across multiple sites Query sites and use algebraic property to cross check Several tricks to get it right Blinding by pseudo-random stream Randomized m/n linearen codes

12 Properties of Algebraic Signatures The algebraic signatures construct: Is very fast (when compared with public key methods) Not known to be secure Does not meet performance goals O(n) server I/O and computational complexity O(n) network complexity

13 Sentinel Blocks A. Juels and B. S. Kaliski. PORs: Proofs of Retrievability for Large Files. IACR eprint archive, #2007/243, 2007.

14 Properties of Sentinel Blocks Encrypt a file and add sentinel blocks at random offsets Sentinel data are generated by keyed pseudo-random function Storage site cannot differentiate sentinels from data blocks Randomly challenge storage site for sentinels Gain probabilistic guarantee that data have not been deleted Cannot delete substantial portions of file without deleting sentinels w.h.p. Limited number of challenges; each challenge reveals sentinels Consumes sentinel blocks over time Meets all other performance requirements O(1) I/O and computation complexity at server O(1) network complexity (xor sentinel data blocks prior to return)

15 Intuition: RSA Signature PDP Create an RSA signature over the entire file Use power property of exponentiation to create a challenge without revealing the file s signature Exponential number of different challenges D. L. G. Filho and P. S. L. M. Baretto. Demonstrating data possession and uncheatable data transfer. IACR eprint archive, #2006/150, 2006

16 Properties of RSA Signature PDP Secure proof of possession -- within RSA security assumption Good stuff -- ideal network and client protocol O(1) client metadata O(1) network complexity Slow (really slow) Server must access the entire file to generate proof Server must exponentiate entire file (this is the big deal) 20 secs/mb with 1024 bit keys on a 3GHz processor So, not a solution for storage applications

17 G. Ateniese, R. Burns, et al.: Provable Data Possession at Untrusted Stores Provable Data Possession

18 Provable Data Possession

19 Verifying the Challenge Response Server responds with Client computes and verifies that

20 Some PDP Observations Two part signature (homomorphic verifiable tags) Allows for composition Verifies any random subset of blocks Exponential number of unique challenges Different challenge for every value of Provably secure KEA-1 assumption Privacy preserving Can be, current implementation reveals some information about b i

21 Meets the solution constraints Properties of PDP Size of client metadata = O(1) for any size file Network complexity of the protocol = O(1) Server computation = O(1) (# of exponentiations) Server I/O complexity = O(c) = O(1) Only requires a single exponentiation at server Probabilistic proof of possession Based on spot checking/sampling blocks

22 Performance of PDP

23 Preparing the file Exponentation for every block of the file One time task Can choose the block size (pre-process vs. check tradeoff) What s the downside?

24 Conclusions Public Key cryptography has a place in storage systems As long as we don t encrypt/sign all the data on demand I/O complexity at the server is the limiting factor Mandates probabilistic/sampling approaches If you can t stand the pre-processing costs Maybe can use Schwarz-Miller But, places more demands on the server(s)

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