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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show all references

References:
[1]

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[2]

Zero-knowledge proof, 2018, https://en.wikipedia.org/wiki/Zero-knowledge_proof.

[3]

A. Acar, H. Aksu, A. S. Uluagac and M. Conti, A survey on homomorphic encryption schemes: Theory and implementation, ACM Computing Surveys (CSUR), 51 (2018), Article No. 79. doi: 10.1145/3214303.

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A. AlhothailyA. AlrawaisT. SongB. Lin and X. Cheng, Quickcash: Secure transfer payment systems, Sensors, 17 (2017), 1376. doi: 10.3390/s17061376.

[5]

A. AlhothailyC. HuA. AlrawaisT. SongX. Cheng and D. Chen, A secure and practical authentication scheme using personal devices, IEEE Access, 5 (2017), 11677-11687. doi: 10.1109/ACCESS.2017.2717862.

[6]

M. Andrychowicz, S. Dziembowski, D. Malinowski and L. Mazurek, Secure multiparty computations on bitcoin, in Security and Privacy (SP), 2014 IEEE Symposium on, IEEE, 2014, 443-458. doi: 10.1109/SP.2014.35.

[7]

F. ArmknechtC. BoydC. CarrK. GjøsteenX. JäschkeC. A. Reuter and M. Strand, A guide to fully homomorphic encryption, IACR Cryptology ePrint Archive, 2015 (2015), 1192.

[8]

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.

[9]

J. Benaloh, Dense probabilistic encryption, in Proceedings of the Workshop on Selected Areas of Cryptography, 1994, 120-128.

[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.

[11]

M. Bertilsson and I. Ingemarsson, A construction of practical secret sharing schemes using linear block codes, in International Workshop on the Theory and Application of Cryptographic Techniques, Springer, 1992, 67-79. doi: 10.1007/3-540-57220-1_53.

[12]

G. R. Blakley et al., Safeguarding cryptographic keys, in Proceedings of the National Computer Conference, 48 (1979), 313-317.

[13]

M. Blum, P. Feldman and S. Micali, Non-interactive zero-knowledge and its applications, in Proceedings of the Twentieth Annual ACM Symposium on Theory of Computing, ACM, 1988, 103-112. doi: 10.1145/62212.62222.

[14]

D. Bogdanov, S. Laur and J. Willemson, Sharemind: A framework for fast privacy-preserving computations, in European Symposium on Research in Computer Security, Springer, 2008, 192-206.

[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.

[16]

Z. Brakerski and V. Vaikuntanathan, Efficient fully homomorphic encryption from (standard) lwe, SIAM Journal on Computing, 43 (2014), 831-871. doi: 10.1137/120868669.

[17]

E. F. Brickell, Some ideal secret sharing schemes, in Workshop on the Theory and Application of of Cryptographic Techniques, Springer, 434 (1990), 468-475. doi: 10.1007/3-540-46885-4_45.

[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.

[19]

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.

[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.

[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.

[22]

I. Damgård, M. Geisler, M. Krøigaard and J. B. Nielsen, Asynchronous multiparty computation: Theory and implementation, in International Workshop on Public Key Cryptography, Springer, 5443 (2009), 160-179. doi: 10.1007/978-3-642-00468-1_10.

[23]

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.

[24]

I. Damgard and M. Jurik, A generalisation, a simplification and some applications of Paillier’s probabilistic public-key system, in Proceedings of the 4th International Workshop on Practice and Theory in Public Key Cryptosystems, 2001, 119-136.

[25]

T. ElGamal, A public key cryptosystem and a signature scheme based on discrete logarithms, IEEE Transactions on Information Theory, 31 (1985), 469-472. doi: 10.1109/TIT.1985.1057074.

[26]

B. Ewanick, Zero knowledge proof, Google Scholar.

[27]

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

[28]

P. Feldman, A practical scheme for non-interactive verifiable secret sharing, in Foundations of Computer Science, 1987., 28th Annual Symposium on, IEEE, 1987, 427-438. doi: 10.1109/SFCS.1987.4.

[29]

C. Fontaine and F. Galand, A survey of homomorphic encryption for nonspecialists, EURASIP Journal on Information Security, 2007 (2007), 15.

[30]

C. Gentry, Fully homomorphic encryption using ideal lattices, Proceedings of the 41st Annual Acm Symposium on Symposium on Theory of Computing-stoc'09, (2009), 169-178.

[31]

C. Gentry and S. Halevi, Fully homomorphic encryption without squashing using depth-3 arithmetic circuits, in Foundations of Computer Science (FOCS), 2011 IEEE 52nd Annual Symposium on, IEEE, 2011, 107-116. doi: 10.1109/FOCS.2011.94.

[32]

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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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