Remote Data Integrity Checking for Public Clouds

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1 IBM Student Workshop for Frontiers of Cloud Computing 01 Remote Data Integrity Checking for Public Clouds Bo (Irvine) Chen Department of Computer Science New Jersey Institute of Technology joint work with Reza Curtmola (NJIT) Giuseppe Ateniese (JHU) Randal Burns (JHU)

2 Outsource Data to the Cloud Cloud computing/storage brings a lot of benefits: Good elasticity, low cost, easy management, high reliability, etc. People can choose to outsource their data to the cloud to enjoy the benefits However? How can the data owners have confidence that their data have not been tampered with over time Security is one of the largest barriers that stop people from using the cloud How can I make sure that my data are OK all the time???

3 Remote Data Checking (RDC) Remote Data Checking (RDC) is a mechanism used by the data owner (auditor) to check the integrity of data stored at a third party, such as a Cloud Storage Provider (CSP) CSP is not trusted A general RDC scheme contains two phases: Setup and Challenge phase Setup Client may now delete the file Challenge challenge proof of possession 3

4 Provable Data Possession (PDP) Ateniese et al. propose an efficient RDC scheme, Provable Data Possession (PDP) [AB+07, AB+11] PDP is efficient due to the adoption of adopts spot checking technique, in which the client (auditor) randomly samples a certain number of blocks for checking (rather than check the whole outsourced data) PDP shows that if the adversary corrupts 1% of the data, by randomly sampling 460 blocks, the client can detect the corruption with 99% probability The auditor challenges a server for a random set of blocks b1 b b3 b4 b5 b6 b7 b8 b9 bn client Spot checking technique 4

5 Vulnerability of Spot Checking Spot checking technique, however, is vulnerable to small corruption attack Small corruption can be as small as 1 bit very difficult to detect small corruptions by spot checking The adversary only corrupts a few blocks among the file 5

6 Preliminary Solutions for Small Corruption Attack An (n, k) Error Correcting Code (ECC): k data symbols are encoded into n symbols, such that any k out of n symbols can be used to recover the original k data symbols. It can correct up to d=n-k erasures 1 3 k 1 d k data symbols d=n-k parity symbols Small corruption problem is usually addressed by integrating ECCs with Remote Data Checking (Robustness) Robustness can guarantee that small errors which cannot be detected can be recovered How to integrate ECC code to address small corruption attack? 6

7 Preliminary Solutions for Small Corruption Attack (cont.) Full-file encoding encoded file F 9 file F (1, 9) ECC code parity p F is the input of RDC file F 1 st attempt: Expensive encoding, because the code must be as large as the file 7

8 Preliminary Solutions for Small Corruption Attack (cont.) Chunk-based encoding encoded file F file F chunk encode parity p F is the input of RDC (4, 3) ECC for each chunk nd attempt: Cheap encoding (the chunk is small) Cannot address small corruption parity p problem

9 πr scheme πr scheme can address the small corruption problem [CBK08, AB+11, BJO09] Must hide the association between symbols and the corresponding constraint groups The server should not know which symbols are in the same constraint group original file F constraint group F is randomly permuted parity P A (4, 3) error correcting code is applied on every chunk encoded file F P is randomly permuted and encrypted 8 9 F is the input of RDC πr scheme 9

10 Dynamic Setting We have provided solutions to address the small corruption problem for static data Static data: Once the data have been stored in the server, it will never be updated What if the data needs to be updated? Update operations: Insert, delete, modify, append Challenge: Under an adversarial setting, there is a fundamental tension between dynamic updates and the encoding required for small corruption attack file parity untrusted cloud server 10

11 R-DPDP: Robust Dynamic Provable Data Possession Bo Chen and Reza Curtmola, Robust Dynamic Provable Data Possession, ICDCS-SPCC 01, June 01. Bo Chen and Reza Curtmola, Robust Dynamic Remote Data Checking for Public Clouds, The 35th IEEE Sarnoff Symposium (Student Posters), May

12 Cauchy Reed-Solomon Codes Cauchy Reed-Solomon codes are a type of RS codes (Error Correcting Code) which are efficient in encoding/decoding [PX06] and have some useful properties: When modifying/appending a symbol, we only need the parity symbols and a data symbol to update the codeword efficiently data symbol modify P P parity symbol P = _ + neglect coding coefficients P 3 3 append P P 5 P P = + 5 Update a (5, 4) Cauchy RS code Insert/delete one symbol requires a number of symbols linear to the code size Inefficient 1

13 VLCG We propose VLCG (Variable Length Constraint Group) scheme based on two insights: To encode the file initially, we assign symbols to constraint groups based on the value of the symbols o o To insert/delete/modify/append a symbol does not affect the entire file (only affect one constraint group) Constraint groups may have different sizes To leverage the properties of Cauchy RS codes, we convert all the update operations into append and modify operations o o o Insertion operation is converted into append operation Deletion operation is converted into modify operation A modification is equivalent to a deletion plus an insertion 13

14 VLCG (cont.) file F initial file encoding h K ( ) hk(.) is a PRF keyed with key K constraint group parity P insert a symbol P h K ( ) delete a symbol P h K ( 5 ) 14

15 RDC-NC: Remote Data Checking for Network Coding-based Distributed Storage Systems Bo Chen, Reza Curtmola, Giuseppe Ateniese, and Randal Burns, Remote Data Checking for Network Coding-based Distributed Storage Systems, ACM CCSW '10, October

16 Beyond Single-server RDC Single-server RDC (PDP, R-DPDP) is only one facet of maintaining the health of data (prevention) We really want to ensure long-term data reliability Remote data checking for distributed storage systems Data is stored redundantly at multiple servers Replication Erasure coding Network coding S1 S Sn client 16

17 Reliability in Distributed Storage Systems Traditional approaches to store data redundantly at multiple servers: Replication Erasure Coding Reduced storage overhead Large bandwidth overhead for repair (entire file is retrieved) repair repair S 1 F S F S 1 c 1 F MB S S 3 F F new replica created F b 1 1MB b 1MB S S 3 c c 3 S c 3 new coded block created Replication Any blocks are enough to recover original file (3,) Erasure coding 17

18 Reliability based on Network Coding Network Coding (Regenerating Code): A new coding method that sacrifices some storage overhead for repair bandwidth [DGW+07, DGW+10] Compute coded blocks as linear combinations of original blocks Repair bandwidth is optimal (retrieve x bits to repair x bits) random coding coefficient F 0.66MB 0.66MB 0.66MB b 1 b b 3 S 1 S b 1 b b 3 b 1 +b b 1 +b b 1 +b +b S b 1 +3b +b 3 3b 1 +4b +b 3 new coded blocks created b 1 +b 3 S 3 b +b 3 Network coding (n=3, k=) 18

19 The Need for Remote Data Integrity Checking What if storage servers (cloud servers) are not trusted? Client must ensure storage servers don t misbehave Client periodically checks integrity of outsourced data stored in each server (challenge phase) Client takes action (repair) upon detecting corruption at one of the storage servers (repair phase) 19

20 Adversarial Model Mobile adversary that can behave arbitrarily (Byzantine behavior) The adversary can corrupt at most n-k out of the n servers within any given time interval (an epoch) 0

21 Localize faulty servers Challenges Lack of fixed file layout (makes it difficult to maintain constant storage on client) Erasure coding has fixed file layout (a new, repaired block is identical to the original block) Additional attacks. Replay attack, pollution attack, etc. The newly generated blocks in repair are not necessarily equal to the original corrupted blocks (replay attack) The untrusted servers are responsible for generating the blocks in repair phase (pollution attack) 1

22 Integrity Check for Each Server Can single server solutions (PDP[AB+07, AB+11], PoR [JK07, SW08]) be used? No! Collusion of servers (server can reuse each other s data and meta-data to answer the challenge) Our solution still uses metadata for integrity checks (allows to easily localize faulty servers) Meta-data is customized per server per block: Assign a logical ID to coded blocks (server_index block_index) and embed IDs and coding coefficients into meta-data Tackle the problem of collusion of servers Provide integrity for every block in every server

23 Replay Attack By replaying intentionally, the adversary can corrupt the whole system Replay attack is specific for random network coding-based distributed storage systems (reduce the linear independency of blocks, eventually corrupt the whole system) Difficult to detect and maintain constant client storage (3, ) network coding, original file contains 3 blocks (b1, b, b3) The original data is unrecoverable b 1 b 1 3b 1 +3b 3 3b +3b 3 S 1 S 1 S 1 S 1 b +b 3 b +b 3 3b +3b 3 3b 1 +3b 3 b 3 b 3 b 3 b 3 S b 1 +b S b 1 +b S b 1 +b Replay without being detected S b 1 +b b 1 +b 3 b 1 +b +b 3 S 3 S 3 b +b 3 b 1 +b S 3 b 1 +b +b 3 b 1 +b 3 b 1 +b S 3 b +b 3 S 3 b 1 +b 3 b +b 3 epoch1 epoch epoch3 epoch4 3

24 Replay Attack (cont.) Our solution for replay attack We encrypt the coding coefficients (under the assumption that the original file should not be public) We prove that by encrypting the coefficients, a malicious server s ability to execute a harmful replay attack becomes negligible The server cannot do better than randomly select blocks for replay attack Please refer to the paper for the detailed proof 4

25 Inconsistency between Challenge Phase and Repair Phase Malicious servers can pretend to be good in challenge phase, but behave maliciously in repair Corrupt data (pollution attack) Do not use the random coefficients to generate the new block (entropy attack) 5

26 Inconsistency between Challenge Phase and Repair Phase (cont.) Our solution Repair tag which supports aggregation Client picks the random coefficients and enforces servers to use Client checks if servers use correctly coded blocks Client checks if servers use coding coefficients provided by client repair tag server side Repair client side 0.66MB 0.66MB 0.66MB b 1 b b 3 S 1 S b 1 b b 3 b 1 +b b 1 +b 3 1 b 1 +b 1 1*(b 1 +b )+1*b 3 = t 1 b 1 +b +b 3 t 1 t 1 T t T = (t 1 ) 1 ( t ) 1 S b 1 +3b +b 3 3b 1 +4b +b 3 new coded block created S 3 b +b 3 proof that coded block is correctly computed 6

27 References [AB+07] G. Ateniese, R. Burns, R. Curtmola, J. Herring, L. Kissner, Z. Peterson, and D. Song, Provable data possession at untrusted stores, in Proc. of ACM CCS, 007. [AB+11] G. Ateniese, R. Burns, R. Curtmola, J. Herring, O. Khan, L. Kissner, Z. Peterson, and D. Song, Remote Data Checking Using Provable Data Possession, ACM Transactions on Information and System Security (TISSEC), May 011. [CBK08] R. Curtmola, O. Khan, and R. Burns, Robust remote data checking, in Proc. of ACM StorageSS, 008. [BJO09] K. D. Bowers, A. Juels, and A. Oprea, Proofs of retrievability: Theory and implementation, in Proc. of CCSW, 009. [PX06] J. S. Plank and L. Xu, Optimizing Cauchy Reed-Solomon codes for faulttolerant network storage applications, IEEE NCA 006. [DGW+07] A. G. Dimakis, B. Godfrey, M. J. Wainwright, and K. Ramchandran, Network coding for distributed storage systems, In INFOCOM, 007. [DGW+10] A. G. Dimakis, P. B. Godfrey, Y. Wu, M. O. Wainwright, and K. Ramchandran, Network coding for distributed storage systems, IEEE Transactions on Information Theory, 010. [JK07] A. Juels and B. S. Kaliski, PORs: Proofs of retrievability for large files, In Proc. of ACM CCS, 007. [SW08] H. Shacham and B. Waters, Compact proofs of retrievability, in Proc. of Asiacrypt,

28 Conclusion Remote Data Checking (RDC) allows the data owners to check the integrity of the data outsourced to the public clouds We propose Robust Dynamic Provable Data Possession (R-DPDP), to address the small corruption problem for dynamic RDC We propose RDC-NC, a novel remote data checking scheme for network coding-based distributed storage systems Thank you! 8

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