Privacy Preserving Multiset Union with ElGamal Encryption

The privacy preserving multiset union (PPMU) protocol allows a set of parties, each with a multiset, to collaboratively compute a multiset union secretly, meaning that any information other than union is not revealed. We propose an efficient PPMU protocol, using multiplicative homomorphic property of ElGamal encryption over Fq[x]/f(x) where q is a prime and f(x) is an irreducible polynomial over Fq. The protocol involves a constant number of rounds and improves the computation and communication complexities of the scheme proposed by Kissner and Song. We also prove the security of the protocol in the random oracle model.

[1]  Nigel P. Smart,et al.  A comparison of different finite fields for use in elliptic curve cryptosystems , 2000 .

[2]  Hugo Krawczyk,et al.  Secure Distributed Key Generation for Discrete-Log Based Cryptosystems , 1999, Journal of Cryptology.

[3]  Tad Hogg,et al.  Enhancing privacy and trust in electronic communities , 1999, EC '99.

[4]  Vitaly Shmatikov,et al.  Privacy-Preserving Graph Algorithms in the Semi-honest Model , 2005, ASIACRYPT.

[5]  Yvo Desmedt,et al.  Threshold Cryptosystems , 1989, CRYPTO.

[6]  Chris Clifton,et al.  Privacy-preserving distributed mining of association rules on horizontally partitioned data , 2004, IEEE Transactions on Knowledge and Data Engineering.

[7]  Dawn Xiaodong Song,et al.  Privacy-Preserving Set Operations , 2005, CRYPTO.

[8]  Taher El Gamal.  A public key cryptosystem and a signature scheme based on discrete logarithms , 1984, IEEE Trans. Inf. Theory.

[9]  D. Song,et al.  Private and threshold set-intersection , 2004 .

[10]  Benny Pinkas,et al.  Efficient Private Matching and Set Intersection , 2004, EUROCRYPT.

[11]  Christof Paar,et al.  Optimal Extension Fields for Fast Arithmetic in Public-Key Algorithms , 1998, CRYPTO.

[12]  Lifang Gu,et al.  Privacy-preserving data linkage protocols , 2004, WPES '04.

[13]  Jacques Stern,et al.  Sharing Decryption in the Context of Voting or Lotteries , 2000, Financial Cryptography.

[14]  Pascal Paillier,et al.  Public-Key Cryptosystems Based on Composite Degree Residuosity Classes , 1999, EUROCRYPT.

[15]  Victor Shoup,et al.  A computational introduction to number theory and algebra , 2005 .

[16]  Torben P. Pedersen.  A Threshold Cryptosystem without a Trusted Party (Extended Abstract) , 1991, EUROCRYPT.

[17]  Alexandre V. Evfimievski,et al.  Limiting privacy breaches in privacy preserving data mining , 2003, PODS.

[18]  Oded Goldreich.  Foundations of Cryptography: Volume 1 , 2006 .

[19]  T. Elgamal.  A public key cryptosystem and a signature scheme based on discrete logarithms , 1984, CRYPTO 1984.