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PORs: Proofs of Retrievability for Large Files Ari Juels RSA Laboratories Burt Kaliski © 2007 RSA Laboratories EMC Innovation Network

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The Subprime Mortgage Debacle Banks issued dubious mortgages to customers Banks packed mortgages as securities and sold them They “outsourced” risk But risk came home to roost… –E.g. Bank of America’s Q3 ’07 earnings dropped 32% The moral: Risk is passed around in complex, difficult-to-trace ways…

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Storage-as-a-Service (SaaS) MegArchive Corp. Seattle, USA Alice MiniFile Inc. Bangalore, India Bob Liverpool, UK Peer-to-peer network My Wedding Photos ! One day, Alice’s machine crashes, so she contacts MegArchive…

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Other financially motivated service degradation MegArchive moves Alice’s file to a slow disk array –File is there, but retrieval is unacceptably slow MegArchive uses cheap storage that degrades over time MegArchive throws away a portion of Alice’s file to save space –Most users don’t retrieve their backup files anyway

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PORs: Proofs of Retrievability Alice would like to ensure that her file F is retrievable –She may also want to ensure compliance with a Service-Level Agreement (SLA) The simple approach: Alice periodically downloads F This is resource-intensive! What about spot-checking instead?

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Spot checking: Preparation Alice F Archive f2f2 f1f1 f3f3 f1f1 f2f2 f3f3

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Spot checking: Verification Alice F f1f1 f2f2 f3f3 Archive f2f2 f3f3 ~ ~ f1f1 ~~ = ?

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Spot checking: Verification Alice F f1f1 f2f2 f3f3 Archive f2f2 f3f3 ~ ~ f1f1 ~~ X

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Spot checking Alice f1f1 f2f2 f3f3 Archive f2f2 f3f3 F ~ ~ f1f1 ~~ Pros: Alice needn’t download all of F Can detect large erasure / corruption Cons: Alice must store chunks of F Can’t detect small erasure / corruption

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MAC refinement: Preparation Alice Archive f2f2 f1f1 f3f3 k MAC k [f 1 ] c1c1 c2c2 c3c3 F

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MAC refinement: Preparation Alice F Archive f2f2 f1f1 f3f3 k c2c2 MAC k [f 1 ] c1c1 c3c3

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MAC refinement: Preparation Alice F Archive f2f2 f1f1 f3f3 k c2c2 c1c1 c3c3

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MAC refinement: Verification Alice F Archive f2f2 f3f3 k c2c2 c1c1 c3c3 Pros: Alice needn’t store any of F Can detect large erasure / corruption Cons: Can’t detect small erasure / corruption F ~ f1f1

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Error correcting code F Archive parity bits * decoder F With ECC to encode F → F*, big error in F* induces small error in F In effect, we can amplify errors in stored file

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ECC + MAC [loosely like LIBBI ’03, NR ’06] Alice F Archive f2f2 f1f1 f3f3 k c2c2 c1c1 c3c3 parity bits f4f4 c4c4 F*F* Pros: Alice needn’t store any of F—only key k Alice can detect even small corruption in F (= large corruption in F * )

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ECC + MAC: Verification Alice F Archive f2f2 f1f1 f3f3 k c2c2 c1c1 c3c3 parity bits f4f4 c4c4 F*F* Example: ECC corrects up to 10% corruption Alice checks 30 positions Each check detects corruption with probability ≥.9 Alice detects insurmountable corruption with prob. ≥ > 95%

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A challenge Applying such an ECC to all of F is impractical Instead, we can stripe the ECC We’ll need many stripes for efficiency But then a clever adversarial archive can corrupt selectively…

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Selective corruption F Archive c2c2 c1c1 c3c3 c4c4 F*F* Adversary corrupts just one stripe S File is now irretrievable! Unless Alice checks S, she does not detect corruption If S is tiny fraction of file, adversary escapes detection with high probability

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Solution: Hide ECC stripes F Archive c2c2 c1c1 c3c3 c4c4 F*F* Do secret, randomized partitioning of F into stripes –E.g. use secret key to generate pseudorandom permutation and then choose stripes sequentially Encrypt and permute parity bits –In paper, we permute and encrypt F too, but not strictly necessary F itself is untouched, i.e., intact within F * ! But adversary does not know where stripes are, so Adversary cannot feasibly target a stripe!

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Another challenge: How do we formally define a POR? Adversary may respond correctly to challenges, but deny service on retrieval! No global solution: Pattern / number of requests betrays nature of request A practical approach to definition: 1.Assume memoryless adversary, e.g., software that can be rewound/reset 2.Ensure that challenge interface is identical to retrieval interface, i.e., formal extraction model –Limit distinction to pattern / number of requests

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Yet another challenge: Bandwidth As Alice makes many checks, she fetches many file pieces f i Can we reduce bandwidth? One approach: MAC on server side –For i th check, generate one-time MACing key k i = g(k) –Let archive compute and return m’ i = MAC k [f i ] and E[m i ] –Alice checks that m’ i = m i –To preserve extraction interface, Alice must also request and check a (small) piece of f i i

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Another bandwidth-limiting approach: Sentinels F Insert hidden, random sentinel blocks into encryption of F Idea: Check sentinel blocks instead of file blocks Theoretically interesting because POR independent of F! –Compare with proof of knowledge… Interesting in practical sense because sentinels can be combined –Archive can XOR sentinels before sending –Allows for, e.g., hierarchical POR (In paper, we permute F too, but not strictly necessary)

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Further / related research Implementation –F may be too large to fit in main memory –Quantifying QoS guarantees File updates: PORs break! –Efficient fix? Extended models –E.g., publicly verifiable Algebraic approaches –Burns et al., CCS ’07 (next talk!) and other previous work [E.g., FB ’06]

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