November  2018, 1(4): 311-330. doi: 10.3934/mfc.2018015

Cryptographic algorithms for privacy-preserving online applications

1. 

Computer Science Department, Bowling Green State University, Bowling Green, Ohio 43401, USA

2. 

Computer Science Department, George Washington University, 2121 I St NW, Washington, DC 20052, USA

3. 

School of Big Data and Software Engineering, Chongqing University, Chongqing, China

* Corresponding author: Chunqiang Hu

Received  August 2018 Revised  September 2018 Published  December 2018

Privacy in online applications has drawn tremendous attention in recent years. With the development of cloud-based applications, protecting users' privacy while guaranteeing the expected service from the server has become a significant issue. This paper surveyed the most popular cryptographic algorithms in privacy-preserving online applications to provide a tutorial-like introduction to researchers in this area. Specifically, this paper focuses on introduction to homomorphic encryption, secret sharing, secure multi-party computation and zero-knowledge proof.

Citation: Ruinian Li, Yinhao Xiao, Cheng Zhang, Tianyi Song, Chunqiang Hu. Cryptographic algorithms for privacy-preserving online applications. Mathematical Foundations of Computing, 2018, 1 (4) : 311-330. doi: 10.3934/mfc.2018015
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A. Ben-David, N. Nisan and B. Pinkas, Fairplaymp: A system for secure multi-party computation, in Proceedings of the 15th ACM Conference on Computer and Communications Security, ACM, 2008, 257-266. doi: 10.1145/1455770.1455804. Google Scholar

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[10]

J. Benaloh and J. Leichter, Generalized secret sharing and monotone functions, in Proceedings on Advances in Cryptology, Springer-Verlag New York, Inc., 403 (1990), 27-35. doi: 10.1007/0-387-34799-2_3. Google Scholar

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[12]

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[13]

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[15]

Z. Brakerski and V. Vaikuntanathan, Fully homomorphic encryption from ring-lwe and security for key dependent messages, in Annual Cryptology Conference, Springer, 2011, 505-524. doi: 10.1007/978-3-642-22792-9_29. Google Scholar

[16]

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[17]

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[18]

N. BusomR. PetrlicF. SebéC. Sorge and M. Valls, Efficient smart metering based on homomorphic encryption, Computer Communications, 82 (2016), 95-101. doi: 10.1016/j.comcom.2015.08.016. Google Scholar

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Z. CaiZ. HeX. Guan and Y. Li, Collective data-sanitization for preventing sensitive information inference attacks in social networks, IEEE Transactions on Dependable and Secure Computing, 15 (2018), 577-590. doi: 10.1109/TDSC.2016.2613521. Google Scholar

[20]

Z. Cai and X. Zheng, A private and efficient mechanism for data uploading in smart cyber-physical systems, IEEE Transactions on Network Science and Engineering, (2018), 1-1. doi: 10.1109/TNSE.2018.2830307. Google Scholar

[21]

J.-S. Coron, D. Naccache and M. Tibouchi, Public key compression and modulus switching for fully homomorphic encryption over the integers, in Annual International Conference on the Theory and Applications of Cryptographic Techniques, Springer, 7237 (2012), 446-464. doi: 10.1007/978-3-642-29011-4_27. Google Scholar

[22]

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I. Damgård, V. Pastro, N. Smart and S. Zakarias, Multiparty computation from somewhat homomorphic encryption, in Advances in Cryptology-CRYPTO 2012, Springer, 7417 (2012), 643-662. doi: 10.1007/978-3-642-32009-5_38. Google Scholar

[24]

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[25]

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[26]

B. Ewanick, Zero knowledge proof, Google Scholar.Google Scholar

[27]

J. Fan and F. Vercauteren, Somewhat practical fully homomorphic encryption, IACR Cryptology ePrint Archive, 2012 (2012), 144. Google Scholar

[28]

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Figure 1.  General Online Application Architecture
Figure 2.  Blakley's Secret Share Scheme [1]
Figure 3.  Garbled Circuits Overview
Figure 4.  Garbled Circuits Mappings
Figure 5.  A ZKP Example [2]
Figure 6.  An Online Auction Scheme Model
Table 1.  Comparison of Homomorphic Schemes
SchemeAdditive-Homo Multi-Homo Full-Homo
GM(Goldwasser) and Micali 1982 [34] $\surd$
Exponential Elgamal [44] $\surd$
Benaloh 1994 [9] $\surd$
NS (Naccache and Stern) 1998 [62] $\surd$
OU (Okamoto and Uchiyama) 1998 [64] $\surd$
Paillier 1999 [65] $\surd$
DJ (Damgad and Jurik) 2001 [24] $\surd$
KTX (Kawachi, Tanaka and Xagawa)[46] 2007 $\surd$
RSA 1978 [73] $\surd$
Elgamal 1985 [25] $\surd$
Gentry 2009 [30] $\surd$
GH(Gentry and Halevi)[31] 2011 $\surd$
>Coron 2011 [21] $\surd$
BGV (Brakerski, Gentry and Vaikuntanathan)2011 [82] $\surd$
LTV (Lopez-Alt, Tromer and Vaikuntanathan)2012 [57] $\surd$
JFV(Junfeng Fan, Frederik and Vercauteren) 2012 [27] $\surd$
GSW (Gentry-Sahai-Waters) 2013 [32] $\surd$
Gorti's EHC (Enhanced homomorphic Cryptosystem) 2013 [70] $\surd$
SchemeAdditive-Homo Multi-Homo Full-Homo
GM(Goldwasser) and Micali 1982 [34] $\surd$
Exponential Elgamal [44] $\surd$
Benaloh 1994 [9] $\surd$
NS (Naccache and Stern) 1998 [62] $\surd$
OU (Okamoto and Uchiyama) 1998 [64] $\surd$
Paillier 1999 [65] $\surd$
DJ (Damgad and Jurik) 2001 [24] $\surd$
KTX (Kawachi, Tanaka and Xagawa)[46] 2007 $\surd$
RSA 1978 [73] $\surd$
Elgamal 1985 [25] $\surd$
Gentry 2009 [30] $\surd$
GH(Gentry and Halevi)[31] 2011 $\surd$
>Coron 2011 [21] $\surd$
BGV (Brakerski, Gentry and Vaikuntanathan)2011 [82] $\surd$
LTV (Lopez-Alt, Tromer and Vaikuntanathan)2012 [57] $\surd$
JFV(Junfeng Fan, Frederik and Vercauteren) 2012 [27] $\surd$
GSW (Gentry-Sahai-Waters) 2013 [32] $\surd$
Gorti's EHC (Enhanced homomorphic Cryptosystem) 2013 [70] $\surd$
Table 2.  Multi-party Computation Implementations
SchemeFeature Party
FairPlay [58] Boolean Circuits Two-Party
SPDZ [23] Arithmetic Circuits Two-Party
MASCOT [47] Arithmetic Circuits Two-Party
Tasty [40] Boolean & Arithmetic Circuits Two-Party
Sharemind [14] Boolean Circuits Three-Party
FairPlayMP [8] Boolean Circuits Two or More
VIFF [22] Arithmetic Circuits Two or More
SchemeFeature Party
FairPlay [58] Boolean Circuits Two-Party
SPDZ [23] Arithmetic Circuits Two-Party
MASCOT [47] Arithmetic Circuits Two-Party
Tasty [40] Boolean & Arithmetic Circuits Two-Party
Sharemind [14] Boolean Circuits Three-Party
FairPlayMP [8] Boolean Circuits Two or More
VIFF [22] Arithmetic Circuits Two or More
Table 3.  Recent Hot Research Topics that in Privacy-Aware Computing
Homomorphic Encryption Secret Sharing/MPC Zero-knowledge Proof
Electronic Voting $\surd$ $\surd$ $\surd$
Online Auction $\surd$ $\surd$ $\surd$
Smart Grid $\surd$ $\surd$ $\surd$
Gene Testing $\surd$ $\surd$
Social network $\surd$ $\surd$ $\surd$
Blockchain $\surd$ $\surd$ $\surd$
Homomorphic Encryption Secret Sharing/MPC Zero-knowledge Proof
Electronic Voting $\surd$ $\surd$ $\surd$
Online Auction $\surd$ $\surd$ $\surd$
Smart Grid $\surd$ $\surd$ $\surd$
Gene Testing $\surd$ $\surd$
Social network $\surd$ $\surd$ $\surd$
Blockchain $\surd$ $\surd$ $\surd$
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