an efficient and probabilistic secure bit …rlu1/slide/20140523ximengliu.pdfoutline main references...

OutlineMain References

IntroductionProblem Statement

PreliminariesThe proposal scheme

An Efficient and Probabilistic SecureBit-Decomposition

Reporter:Ximeng LiuSupervisor: Rongxing Lu

School of EEE, NTUhttp://www.ntu.edu.sg/home/rxlu/seminars.htm

May 22, 2014

http://www.ntu.edu.sg/home/rxlu/seminars.htm An Efficient and Probabilistic Secure Bit-Decomposition




1 Main References

2 Introduction

3 Problem Statement

4 Preliminaries

5 The proposal scheme





Main References

Samanthula B K K, Chun H, Jiang W. An efficient andprobabilistic secure bit-decomposition[C]//Proceedings of the 8thACM SIGSAC symposium on Information, computer andcommunications security. ACM, 2013: 541-546.





Introduction

Statistical data analysis is an essential task in many data miningand business intelligence applications. However, when the datacome from multiple parties and where user privacy is a big concern,we need to perform the data analysis task in a privacypreservingmanner. The data analysis task becomes even more challengingwhen the data is in encrypted form which is quite common inoutsourced databases.





secure bit-decomposition (SBD)

SBD acts as an important primitive in various secure multi-partycomputation (MPC) protocols such as secure comparison, publicmodulo and private exponentiation on encrypted integers.





Problem Statement

We consider two semi-honest (also referred to ashonest-but-curious) parties Alice and Bob. We assume that Alicegenerates a Paillier public/secret key pair (pk; sk) and broadcaststhe public key pk to Bob.





k-Nearest Neighbor algorithm

Let < E ;D > be the encryption and decryption functionsassociated with the public/secret key pair (pk, sk). Without loss ofgenerality, assume that Bob holds the Paillier encrypted valueE (x), where 0 ≤ x < 2m (here m is referred to as the domain sizeof x in bits).





Problem Statement

We explicitly assume that x is not known to Alice and Bob.Suppose (x0, · · · , xm−1) denotes the binary representation of xwhere x0 and xm−1 are the least and most significant bitsrespectively. The goal of this paper is to convert encryption of xinto the encryptions of the individual bits of x without disclosingany information regarding x to both Alice and Bob.





More formally, we define the SBD protocol as follows:

SBD(E (x)) =< E (x0), · · · ,E (xm−1) >

At the end of the SBD protocol, the values E (x0), · · · ,E (xm−1)are known only to Bob and nothing is revealed to Alice. Note thatsince SBD protocol is used as a sub-routine in many secureapplications, leaking either the value of x or any of the bit values(xi ’s) to either Alice or Bob may not be allowed.





Preliminaries

Our protocol uses standard binary conversion algorithm as abaseline. Let x be an integer such that 0 ≤ x < 2m. The overallsteps involved in the standard binary conversion method arehighlighted in Algorithm 1. Briefly, we first divide x by 2. Theremainder 0 or 1 (i.e., x mod 2) will be the bit in question andthen x is replaced by the quotient (denoted by q0, whereq0 = b x2c). This process is repeated until m iterations.





Standard Binary Conversion Method

Figure: Security model





Paillier Cryptosystem

Paillier cryptosystem exhibits the following properties:a. Homomorphic Addition: E (y + z) = E (y) ∗ E (z) mod N2;b. Homomorphic Multiplication: E (z ∗ y) = E (y)z mod N2;





SBD protocol






Encrypted LSB protocol






Secure Verification of Result(SVR)






Thank youRongxing’s Homepage:

http://www.ntu.edu.sg/home/rxlu/index.htmPPT available @: http://www.ntu.edu.sg/home/rxlu/seminars.htm

Ximeng’s Homepage:http://www.nbnix.com/


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