Security and Privacy for Cloud Computing Refik Molva
Cloud Computing � Outsourcing � Storage � Computation � High availability � No maintenance � Decreased Costs � Elasticity & Flexibility Security and Privacy for Cloud Computing - R. Molva Slide 2
Security & Privacy Challenges Outsourcing - Potentially untrusted Service Provider - Data storage and computations ⇒ New requirements (PoR, verifiability, . . .) ⇒ Crypto schemes dealing with untrusted partners � PIR � Secure multi-party computation � Computing with encrypted functions � Verifiability: proof of data possession, proof of execution Security and Privacy for Cloud Computing - R. Molva Slide 3
Security & Privacy Challenges Large scale - Data - Computations ⇒ Severely asymmetric scenarios � Customer (verifier) << Service Provider (prover) � “Quantum leap”: classical schemes don’t work, need for new approaches � Example: integrity – customer cannot even keep a hash value per data split ⇒ Joint Crypto & Cloud schemes Security and Privacy for Cloud Computing - R. Molva Slide 4
Security & Privacy Solutions � Privacy � Privacy preserving word search � Multi-user searchable encryption � Integrity � Proof of Retrievability � Message-locked PoR � Verifiability � Verifiable computation � Proof composition Security and Privacy for Cloud Computing - R. Molva Slide 5
Privacy preserving word search Outsourced Backup Service Find Blocks including W � several years’ corporate data � regularly stored in the Cloud � Privacy � Encryption by the customer � Query: only a small portion needs to be restored � How to find it without downloading the entire DB? Requirement for a new solution � to search words in an encrypted DB � with privacy Security and Privacy for Cloud Computing - R. Molva Slide 6
Privacy preserving word search � Existing solutions not scalable � Encrypted keyword search algorithms � Private information retrieval (PIR) � PRISM: Privacy preserving search in MapReduce � Data and query privacy � Idea: PIR on intermediate data maps � Advantage: parallelism with MapReduce Security and Privacy for Cloud Computing - R. Molva Slide 7
PRISM - Upload [PETS’12] File w 0 , w 1 , . . . . w n-1 WordEncrypt E(w 0 ) , E(w 1 ) , . . . . E(w n-1 ) User Upload Cloud E(w i ) , . . . E(w j ) E(w k ) , . . . E(w l ) E(w m ) , . . . E(w n ) E(w u ) , . . . E(w v ) Mapper hash(E(w i )) X,Y, b X Binary Map Y b Security and Privacy for Cloud Computing - R. Molva Slide 8
PRISM – Word Search Query for word w hash(E(w)) X,Y, b PIR query for (X,Y) User Cloud Mapper Binary Map PIR(X,Y) x PIR(X,Y) x PIR(X,Y) x PIR(X,Y) x ∑ homomorphic Reducer User E(result) Security and Privacy for Cloud Computing - R. Molva Slide 9
Multi-user Searchable Encryption (MUSE) Multiple Readers Multiple Writers Security and Privacy for Cloud Computing - R. Molva Slide 10 10
SotA - Access pattern leakage [PETS’17] � Iterative Testing Each encrypted keyword is tested separately in all documents - Similarities between documents & position of the keyword revealed - Collusion (CSP, User) ⇒ Privacy Breach Security and Privacy for Cloud Computing - R. Molva Slide 11
MUSE: Multi-User Searchable Encryption [ISC’15] No collusion between Proxy and CSP Security and Privacy for Cloud Computing - R. Molva Slide 12 12
Cloud Security Research � Privacy � Privacy preserving word search � Multi-user searchable encryption � Integrity � Proof of Retrievability � Message-locked PoR � Verifiability � Verifiable computation � Proof composition Security and Privacy for Cloud Computing - R. Molva Slide 13
Proof of Retrievability � Motivating scenario: outsourced storage Is my data still there? � Requirements � Integrity check by Client � No data stored at Client � No bulk data transfer � Proof of Retrievability (POR) Security and Privacy for Cloud Computing - R. Molva Slide 14
Proof of Retrievability – Related Work � Related work [Deswarte et. al, Filho et. al, ...] � Deterministic � Verification of the entire data ⇒ costly � Probabilistic [Ateniese et. al, Shacham et.al, Juels et al, ...] � Tags for each block + random verification ⇒ cost of homomorphic ops � randomly located sentinels => limited # of verifications � StealthGuard [ESORICS’14] � privacy preserving search of watchdogs � Unbounded # of queries Security and Privacy for Cloud Computing - R. Molva Slide 15
Proof of Retrievability - StealthGuard E n c r w w y p w t Security and Privacy for Cloud Computing - R. Molva Slide 16
Proof of Retrievability – StealthGuard Word Search Query (PRISM) w 1 w 2 w 3 w 4 w n Yes/No Yes/No Yes/No Yes/No Yes/No Missing word Missing data split Security and Privacy for Cloud Computing - R. Molva Slide 17
How many watchdogs to check? or how to detect lack of Setup by Client retrievability? Adversary Model: Error-correction Bernoulli processes � _ ��� ⇒ Error-correction � � � ���, � ��� , �� Retrievability: � ��� � � � Permutation File not retrievable: � ��� � � � � � ���, � � � Detection: Encryption Watchdog insertion W W W W Security and Privacy for Cloud Computing - R. Molva Slide 18
The Integration Problem Cloud Operations Data reduction Availability Computation efficiency Multi-tenancy Low performance or Severe conflict Security & Privacy Data confidentiality Data Integrity Privacy preserving processing Verifiability Security and Privacy for Cloud Computing - R. Molva Slide 19
Conflict between PoR & deduplication � PoR → User specific encoding � Deduplication → Keep a unique copy in storage PoR PoR No Deduplication Security and Privacy for Cloud Computing - R. Molva Slide 20
Message-locked PoR - Idea � PoR setup (Tags and Watchdogs) � PoR can be represented by � �, � � Derive � from file content Convergent Encryption ( K= H(F) ) suffers from dictionary attacks ⇒ Secure Message-Locked Key Generation Security and Privacy for Cloud Computing - R. Molva Slide 21
Message-locked PoR [CCSW’16] � Secure Message-Locked Key Generation � � � ' � � � '( ) � �' Key Server * KS � � ← % & � '( ∗ �, � ← " # � '() � ' Data F Key Server � � ') Owner KS + � Message-locked PoR = PoR using ,- � �, � � StealthGuard – watchdogs � Private Compact PoR - tags [Shacham et al 2008] Security and Privacy for Cloud Computing - R. Molva Slide 22
Cloud Security Research � Privacy � Privacy preserving word search � De-duplication on encrypted data � Integrity � Proof of Retrievability � Verifiability � Verifiable computation � Proof composition Security and Privacy for Cloud Computing - R. Molva Slide 23
Verifiable Computation Setup Problem Generation Computation Verification � ., � . � ? � Compute � . 1 � � . , 0 Compute Proof 0 Verify ., 1, 0 R1: Cost(Verify) ≪ Cost(Compute) R2: Public delegatability [Parno et al. 2012] Anyone can submit a computation request R3: Public verifiability [Parno et al. 2012] Anyone can verify a computation result Security and Privacy for Cloud Computing - R. Molva Slide 24
Verifiability for 3 Operations � ., � . � ? � , 1 � � . , 0 Compute � . and 0 Verify ., 1, 0 High-Degree Large Matrix Conjunctive Polynomial Evaluation Multiplication Keyword Search � � 3 � 4 5 6 3 6 ∈ 8 9 :3; �B� � >. . with @ � > 6A ∈ 8 9 Search(.) 6<= . � . C , . D , … , . � ⟙ ∈ 8 9 � . . ∈ 8 9 Keywords G � HI C , I D , … , I � J 1 � 1 C , 1 D , … , 1 � ⟙ � >. ∈ 8 9 � 1 � � . ∈ 8 9 1 ID of files � 6 such that G ⊂ � 6 Security and Privacy for Cloud Computing - R. Molva Slide 25
[AsiaCCS 2016] Verifiable Polynomial Evaluation – Idea Euclidean Division of Polynomials � � LM N O ��, L� �M, O� ., � . � ? ��, L� 1, 0 Compute 1 � � . 0 � L�.� Verify 1 � 0 M . N O . ? M, O small degree Security and Privacy for Cloud Computing - R. Molva Slide 26
[AsiaCCS 2016] Verifiable Matrix Multiplication – Idea Auxiliary Matrices P � Q> N O O pseudo-random �>, P� ., >. � ? O �>, P� 1, 0 Compute 1 � >. Verify 0 � P. 0 � Q1 N O. ? Projection R ∙ 0 � R ∙ Q1 N R ∙ O. Security and Privacy for Cloud Computing - R. Molva Slide 27
Cloud Security Research � Privacy � Privacy preserving word search � De-duplication on encrypted data � Integrity � Proof of Retrievability � Verifiability � Verifiable computation � Proof composition Security and Privacy for Cloud Computing - R. Molva Slide 28
Proof Composition Problem Verifiability of general program P(x) purpose programs 5 ≔ � . ] ≔ M 5 - Efficient methods for handling ⁞ sequence of operations Pinocchio [Parno et al] ^ ≔ _ 1 - Efficient schemes for a single very complex operation Example: - No technique achieving both program NN2(x) 5 ≔ > C . . x purposes ] ≔ bcde 5 c ≔ M 2 . b Security and Privacy for Cloud Computing - R. Molva Slide 29
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