Privacy preserving cloud computing Issues and solutions

The cloud computing is getting more and more popular, however, because of it’s nature, the privacy of cloud computing users is compromised due to the data out sourcing. Today, we are going to talk about a particular cloud computing scenario called Associate Rules Mining over a transaction database, discuss its privacy issues and how people resolve them. Overview

A little background Support The k-anonymity concept A privacy preserving requirement that only allow k as the smallest number of entries that can be traced in a database using possible identifiers. In another word, no unique entry will be identified in the database if it is in k- anonymity(Example) The EIgamal Crypto System A variant of Diffie Hellman Crypto System (Example) The Plaintext Equality Test In short, a method to test the equality of two pieces of plain text given their Elgamal encryptions without disclosing two pieces of plain text. Association rules mining: In short, to find out what items are bought together frequently by performing a data mining algorithm in a transaction database. a transaction record in database will look like: {ID:###, amount:**, item0:milk, item1 beer, …} And a rule will look like: {milk, egg} -> {bread} Support Calculated as sp(n) = number of times n appears in set S ÷ number of items in S A little background

A little more background Apriori algorithm Apriori is an algorithm for frequent item set mining and association rule learning over transactional databases. And it works as follows: Input transactions set T, threshold e: Initialize a pairs set S Initialize a pairs set R K <- 1 While True: Go over the T and generate all unique item pairs with k items in the pair into S If S is empty break For each pair p calculate the support SP(p) = number of p appeared in T / number of item in T Remove pairs with SP(p) < e from S Add all remaining pairs in S to R K <- k + 1 Return R A little more background

A Little more background Elgamal Crypto We are going to describle it in a classic Alice and Bob scenario Alice Bob Choose his big prime 𝜌 and 𝛼 Generate private key 𝐾 𝑝𝑟 = 𝑑 Generate public key 𝐾 𝑝𝑢𝑏 =𝛽= 𝑎 𝑑 mod 𝑝 (𝛽, 𝜌, 𝛼) Choose her 𝑖 Generate her 𝐾 𝑡𝑚𝑝 = 𝛼 𝑖 𝑚𝑜𝑑 𝑝 Generate her 𝐾 𝑚𝑎𝑠𝑘 = 𝛽 𝑖 𝑚𝑜𝑑 𝑝 Generate her encrypted text 𝑦=𝑥× 𝐾 𝑚𝑎𝑠𝑘 𝑚𝑜𝑑 𝑝 𝑦, 𝐾 𝑡𝑚𝑝 → 𝐾 𝑚𝑎𝑠𝑘 = 𝐾 𝑡𝑚𝑝 𝑑 mod p, 𝑥=𝑦× 𝐾 𝑚𝑎𝑠𝑘 −1 A Little more background

Consider the scene: Associated Rules Mining over transactions database What privacy issue might occur? User data transaction data is out sourced to a curious cloud database server. Assume the mining service is performed by a third provider, the third mining provider might be interested in the transaction data. The internet service provider might be interested in the mined rules when they are transferred to data owners. Privacy Issues

A privacy preserving schema for Associated Rules Mining in transaction servers proposed by[1] provides a solution. Step 1: Transactions data encrypted and uploaded to DB using Elgamal Crypto Sytem by client Step 2: Because the Elgamal Crypto can some times encrypt two same item(text) into different encryptions, Plaintext Equality Test are performed by DB to eliminate the different encryptions for the same item, after this, all encryptions in DB are unique. Step 3: DB performs Apriori on data stored and return rules to client in encrypted form. No server S# are used? Because it’s not the final solution, recall the threshold e In Apriori and the support of the rules, they will be known by the DB. In another word, the DB is not completely blind to the client data. Fig 1 proposed system architecture (refer to [1]) Solutions [1] Yi, X., Rao, F.Y., Bertino, E. and Bouguettaya, A., 2015, April. Privacy-preserving association rule mining in cloud computing. In Proceedings of the 10th ACM symposium on information, computer and communications security (pp. 439-450). ACM.

Solutions How to hide the supports of rules ? Add noise to data stored in DB to add noise we need to construct a table of items that could be included in a transaction which the DM servers S# can refer to create a transaction noise. Algorithm: Item Dictionary Anonymization[1] Purpose: create an items table and achieve K-anonymity to all servers Input: {a1, a2, a3, …, ay}(all items included in all transactions) Output: {c1, c2,, …, cy} (a encrypted items table) for i in 1…y{ DB server looks up the ai from input; DB computes encryption c using public key given by client from ai } for j in 1 to n{ server Sj mixies c1, c2, …, cy by re-encryption and random shuffling. server Sj forwards the result to Sj+1 server Return (c1, c2, …, cy); Solutions [1] Yi, X., Rao, F.Y., Bertino, E. and Bouguettaya, A., 2015, April. Privacy-preserving association rule mining in cloud computing. In Proceedings of the 10th ACM symposium on information, computer and communications security (pp. 439-450). ACM.

Solutions How to hide the supports of rules ? Add noise to data stored in DB After the item table created we can now use the DM servers S# to create noise transactions, for maximum anonymity we also need to anonymize the whole transaction data set. Algorithm: Same Item Identification and replacement[1] Purpose: replace old encryptions using the encryptions in item table This algorithm basically iterate through all the items in all the transactions and replace the old encryptions with the new one in the newly created item table. Algorithm: Transaction Anonymization[1] Purpose: achieve K-anonymity for all transactions to all servers. Basically this algorithm will use two loops to re-encrypt and shuffle all the transactions, for each transaction additional encryption for each item and shuffling are applied. Solutions [1] Yi, X., Rao, F.Y., Bertino, E. and Bouguettaya, A., 2015, April. Privacy-preserving association rule mining in cloud computing. In Proceedings of the 10th ACM symposium on information, computer and communications security (pp. 439-450). ACM.

Solutions Finally, we are in the process of data mining! What is different now? The transactions in DB now has a lot of noise, thus the DB can not get real support(sp) for each item or item set. All the transaction records are perfectly mixed and achieved maximum anonymity to all servers. All items have unique encryptions The next step is to perform normal Apriori algorithm in the DB by DMs and return encrypted rules to the client. Because all the items are encrypted twice, the client will have to decrypt all the rules twice. Solutions

The proposed method may have a big security issue, because it is stated in paper that the DMs (Server Sj) need to look at the original item set to create the item encryption table to add noise. The proposed method will have to go over the whole transaction dataset twice to create the whole ready-for-mining data set, and the method encrypts each item twice. It is not very computationally efficient. Finally, the proposed method needs to use auxiliary servers to perform the tasks in the adding noise phase and the mining phase, this can potentially increase risk of privacy leaks and it increases the expense considering the client is using this service because of limited budget. Comments

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