# Hey! Cross Check on Computation in Cloud

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2 TABLE I COMPARISON OF DIFFERENT DATA AUDITING TECHNIQUES WITH SINGLE TPA Properties Sebe et al [1] Wang et al [2] Wang et al [4][3] HAIL [5] Hao et al [6] Primitives Asymmetric-key Merkle Hash Tree, Bilinear Map, Homomorphic MAC, cryptography Bilinear MAC, Verifiable Integrity protected (RSA Modules) Map Homomorphic Tags ECC Authenticator Type of guarantee Probabilistic Probabilistic Probabilistic Probabilistic Deterministic Public Verifiability No Yes Yes Yes Yes With the Help of TPA No Yes Yes Yes Yes Data dynamics Yes Yes No Yes Yes Privacy preserving - No Yes Yes Yes Support for Sampling No Yes Yes Yes Yes Probability of Detection [1-(1 p) c ] [1-(1 p) c ] [1-(1 p) c s ] [1-(1 p) c s ] [1-(1 p) c s ] 1. The Probabilistic guarantee of data integrity is achieved by using the probabilistic checking method. It is called probabilistic because the blocks are randomly selected, the detection probability will be high if the server deletes a fraction of all the blocks. 2. The deterministic guarantee of data integrity is achieved by checking the integrity of all data blocks. 3. A third party auditor has certain special expertise and technical capabilities, which the clients do not have. 4. n is the block number, c is the sampling block number, s is the numbers of sectors in blocks, p and P k is the probability of block corruption in a cloud server and k-th cloud server in a multi-cloud P = P k. application onto the Cloud which will severely affect the customer. 5. Loss of physical control: Cloud customers have their data and program outsourced to cloud servers. As a result, owners lose direct control on the data sets and programs. Loss of physical control means that customers are unable to resist certain attacks and accidents. For example, data or software may be altered, lost, or even deleted; in addition, it is difficult and impractical to ensure data/computation integrity and confidentiality with traditional methods. 6. Data Location: In cloud environment data location is transparent from customer. The customer doesn t know where his own data s are located and the Vendor does not reveal where all the data s are stored. The data won t even be in the same country of the customer, it might be located anywhere in the world. It might raise SLA and Legal issue. 7. Cross-VM attack via Side Channels: Cross-VM attack exploits the nature of multi-tenancy, which enables that VMs belonging to different customers may co-reside on the same physical machine. We concentrate on the data integrity verification which is one of the biggest concerns with cloud data storage at untrusted servers because it may be possible that cloud user or /and cloud provider may be malicious. It is also an interesting problem that how cloud users and cloud providers have trusted to each other for storing the data and how privacy of the cloud users must be maintained. One solution of this problem is to perform encryption and decryption operations but it involves with computational and operational overheads. Another solution of this problem is to perform data auditing that is a periodic event to evaluate security, data integrity, privacy preservation and computational accuracy. II. LITERATURE SURVEY ON DATA AUDITING In cloud scenario, the users might have limited computation capability, network bandwidth, battery power and communication resources. So, they are not capable to perform auditing. Thus, on the behalf of cloud customer, a third party may be responsible for this data auditing task. The schemes ([1], [2], [4], [3], [5], [6]) assigns auditing work to only a single TPA (Third Party Auditor).Table 1 shows the comparative analysis of these data auditing schemes that has single TPA. Demerits of Data Auditing Techniques With Single TPA None of these scheme support TPA for cross check for the computation accuracy and data integrity verification. In these schemes, TPA cannot able to handle SLA and Legal issues for data possession and prone to singlepoint failure. 285

4 International Conference on Cloud, Big Data and Trust 2013, Nov 13-15, RGPV Fig. 1. Proposed Model performs computation over these data content and the output of computation stored for verification say Result Computation for Cross Check Part-2: TPA group performs computation operation on encrypted data blocks that responded in Step 3 with the homomorphic property of our scheme and then output of the computation operation is decrypted by TPA. We called the output of decryption operation Result Cross Check and Verify: TPA matches this Result-2 with Result-1. TPA replies to cloud user the result of this cross check. IV. CRYPTOGRAPHIC TOOL: PAILLIER CRYPTOSYSTEM We used a variant of paillier cryptography system in which Group Z N and Z N are utilized such that Z N Z N is isomor-phic to Z N 2. A. Key-Generation Algorithm 1) An entity chooses two distinct odd prime numbers p and q of the same length. 2) Calculate N = pq and Euler s totient function on N is (N) = [(p-1)(q-1)]. 3) Assure that a) gcd(n; (N)) =

5 b) For any integer a > 0, we have ( 1 + N ) a = ( 1 + an ) mod N 2. As a consequence, the order of ( 1+N ) in Z 2 N is N. That is, ( l + N ) N = 1 mod N 2 and ( 1 + N ) a 6= 1 mod N 2 for any 1 < a < N. 4) Selects a random r Z N such that gcd(l ( r N mod N 2 ), N) = 1, where L(x) = (x 1)=N. 5) The public key of our system is ( N ) and private key is ( N, (N) ). B. Encryption Algorithm Let m Z N be a plain-text to be encrypted and r Z N be a random number. With the definition of isomorphism, The cipher-text is given by function f that mapped into Z N X Z N! Z N 2 : c = E(mmodN; rmodn) = f(m; r) = [(1+N) m :r N modn 2 ] where c Z N 2. C. Decryption Algorithm The user efficiently use its private key ( N, (N) ) 1) Set c^ := [c (n) mod N 2 ] where c is cipher-text. 2) Set m^ : = ( c^ - 1) / N. (Note that all this is carried out over the integers.) 3) After decryption plain-text is given by m : = [ m^. (N) 1 mod N 2 ] D. Utilization of Homomorphic Property Z N 1) Update Operation: On any m1,m2 Z N and r1, r2 E(m1; r1):e(m2; r2) = E(m1 + m2; r1r2)modn 2 We use this property for dynamic updating of data and for computing Addition of two plain-text without retrieving plaintexts. 2) Append Operation: On any m1,m2 Z N and r1, r2 Z N E m2 (m1; r1) = E(m1m2; r1 m2 )modn 2 E. Self Binding Property: With the self binding property, any cipher-text can be changed to another cipher-text without affecting the plain-text. [E(m1; r1):r 2 N ]modn 2 = E(m1; r1r2) We utilize this property for making the job of adversary very difficult to predict the plain-text. REFERENCES [1] F. Sebe, J. Domingo-Ferrer, A. Martinez-Balleste, Y. Deswarte, and J.- J. Quisquater. Efficient Remote Data Possession Checking in Critical Information Infrastructures. IEEE Trans. Knowledge and Data Eng,vol. 20, no. 8, pages , Aug [2] Q. Wang, C. Wang, J. Li, K. Ren, and W. Lou. Enabling Public Verifiability and Data Dynamics for Storage Security in Cloud Computing,. Proc. 14th European Conf. Research in Computer Security (ESORICS), IEEE, [3] C. Wang, S.S.-M. Chow, Q. Wang, K. Ren, and W. Lou Privacy- Preserving Public Auditing for Secure Cloud Storage. In Cryptology eprint Archive, Report 2009/579, [4] C. Wang, Q. Wang, K. Ren, and W. Lou Privacy-Preserving Public Auditing for Data Storage Security in Cloud Computing. In Proc. IEEE INFOCOM, IEEE, [5] K.D. Bowers, A. Juels, and A. Oprea HAIL: A high-availability and integrity layer for cloud storage,, Proc. 16th ACM conference On Computer and communications security,, pages , [6] Zhuo Hao, Sheng Zhong and Nenghai Yu. A Privacy-Preserving Remote Data Integrity Checking Protocol with Data Dynamics and Public Verifiability, IEEE Transection on Knowledge and Data Engineering, VOL. 23, NO. 9, September [7] Pascal Paillier Public-Key Cryptosystems Based on Composite Degree Residuosity Classes, Published in J. Stern, Ed., Advances in Cryptology EUROCRYPT 99, vol of Lecture Notes in Computer Science, pp , Springer-Verlag, [8] Pascal Paillier and David Pointcheval. Efficient Public-Key Cryptosystems Provably Secure Against Active Adversaries, Advances in Cryptology Proceedings of ASIACRYPT, Springer-Verlag, LNCS 1716, pages ,1999. [9] Dan Boneh and Hovav Shacham. CryptoBytes, RSA Laboratories, Volume 5, No. 1 Winter/Spring 2002 [10] Dario Catalano, Rosario Gennaro, Nick Howgrave-Graham and Phong Q. Nguyen. Paillier s cryptosystem revisited, published in Proceeding CCS 01 Proceedings of the 8th ACM conference on Computer and Communications Security Pages , 2001 We use this property for dynamic appending of data and for computing multiplication of two plain-text without retrieving plain-texts. 288

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