November  2019, 13(4): 733-757. doi: 10.3934/amc.2019043

The secure link prediction problem

1. 

Cryptology and Security Research Unit, Indian Statistical Institute, Kolkata, India

2. 

R C Bose Centre for Cryptology and Security, Indian Statistical Institute, Kolkata, India

* Corresponding author

Received  October 2018 Revised  January 2019 Published  June 2019

Link Prediction is an important and well-studied problem for social networks. Given a snapshot of a graph, the link prediction problem predicts which new interactions between members are most likely to occur in the near future. As networks grow in size, data owners are forced to store the data in remote cloud servers which reveals sensitive information about the network. The graphs are therefore stored in encrypted form.

We study the link prediction problem on encrypted graphs. To the best of our knowledge, this secure link prediction problem has not been studied before. We use the number of common neighbors for prediction. We present three algorithms for the secure link prediction problem. We design prototypes of the schemes and formally prove their security. We execute our algorithms in real-life datasets.

Citation: Laltu Sardar, Sushmita Ruj. The secure link prediction problem. Advances in Mathematics of Communications, 2019, 13 (4) : 733-757. doi: 10.3934/amc.2019043
References:
[1]

https://www.cryptopp.com/benchmarks.html.Google Scholar

[2]

G. Asharov, Y. Lindell, T. Schneider and M. Zohner, More efficient oblivious transfer and extensions for faster secure computation, in 2013 ACM SIGSAC Conference on Computer and Communications Security, CCS'13, Berlin, Germany, November 4-8, 2013, 2013, 535–548. doi: 10.1145/2508859.2516738. Google Scholar

[3]

L. Backstrom, C. Dwork and J. M. Kleinberg, Wherefore art thou r3579x: anonymized social networks, hidden patterns, and structural steganography, WWW '07 Proceedings of the 16th international conference on World Wide Web, (2007), 181–190. doi: 10.1145/1242572.1242598. Google Scholar

[4]

D. Boneh, E. Goh and K. Nissim, Evaluating 2-dnf formulas on ciphertexts, in Theory of Cryptography, Second Theory of Cryptography Conference, TCC 2005, Cambridge, MA, USA, February 10-12, 2005, Proceedings, 3378 (2005), 325–341. doi: 10.1007/978-3-540-30576-7_18. Google Scholar

[5]

C. Bösch, A. Peter, B. Leenders, H. W. Lim, Q. Tang, H. Wang, P. H. Hartel and W. Jonker, Distributed searchable symmetric encryption, in 2014 Twelfth Annual International Conference on Privacy, Security and Trust, Toronto, ON, Canada, July 23-24, 2014, 2014, 330–337.Google Scholar

[6]

M. Chase and S. Kamara, Structured encryption and controlled disclosure, in Advances in Cryptology - ASIACRYPT 2010 - 16th International Conference on the Theory and Application of Cryptology and Information Security, Singapore, December 5-9, 2010. Proceedings, 6417 (2010), 577–594. doi: 10.1007/978-3-642-17373-8_33. Google Scholar

[7]

V. Kolesnikov, A. Sadeghi and T. Schneider, Improved garbled circuit building blocks and applications to auctions and computing minima, in Cryptology and Network Security, 8th International Conference, CANS 2009, Kanazawa, Japan, December 12-14, 2009. Proceedings, 2009, 1–20.Google Scholar

[8]

V. Kolesnikov and T. Schneider, Improved garbled circuit: Free XOR gates and applications, in Automata, Languages and Programming, 35th International Colloquium, ICALP 2008, Reykjavik, Iceland, July 7-11, 2008, Proceedings, Part II - Track B: Logic, Semantics, and Theory of Programming & Track C: Security and Cryptography Foundations, 5126 (2008), 486–498. doi: 10.1007/978-3-540-70583-3_40. Google Scholar

[9]

J. Leskovec and A. Krevl, SNAP Datasets: Stanford large network dataset collection, http://snap.stanford.edu/data, 2014.Google Scholar

[10]

D. Liben-Nowell and J. M. Kleinberg, The link prediction problem for social networks, in Proceedings of the 2003 ACM CIKM International Conference on Information and Knowledge Management, New Orleans, Louisiana, USA, November 2-8, 2003, 2003, 556–559. doi: 10.1145/956863.956972. Google Scholar

[11]

Y. Lindell and B. Pinkas, A proof of security of yao's protocol for two-party computation, J. Cryptology, 22 (2009), 161-188. doi: 10.1007/s00145-008-9036-8. Google Scholar

[12]

C. LiuL. Zhu and J. Chen, Graph encryption for top-k nearest keyword search queries on cloud, T-SUSC, 2 (2017), 371-381. doi: 10.1109/TSUSC.2017.2704163. Google Scholar

[13] A. MenezesP. C. van Oorschot and S. A. Vanstone, Handbook of Applied Cryptography, CRC Press, Boca Raton, FL, 1997.
[14]

X. Meng, S. Kamara, K. Nissim and G. Kollios, GRECS: graph encryption for approximate shortest distance queries, in Proceedings of the 22nd ACM SIGSAC Conference on Computer and Communications Security, Denver, CO, USA, October 12-6, 2015, 2015, 504–517. doi: 10.1145/2810103.2813672. Google Scholar

[15]

M. Naor and B. Pinkas, Efficient oblivious transfer protocols, in Proceedings of the Twelfth Annual Symposium on Discrete Algorithms, January 7-9, 2001, Washington, DC, USA., 2001, 448–457. Google Scholar

[16]

K. Nayak, X. S. Wang, S. Ioannidis, U. Weinsberg, N. Taft and E. Shi, Graphsc: Parallel secure computation made easy, in 2015 IEEE Symposium on Security and Privacy, SP 2015, San Jose, CA, USA, May 17-21, 2015, 2015, 377–394. doi: 10.1109/SP.2015.30. Google Scholar

[17]

PBC Library, The Pairing-based Cryptography Library, https://crypto.stanford.edu/pbc/.Google Scholar

[18]

L. Sardar and S. Ruj, Prototypes of secure link prediction schemes, GitHub repository, https://github.com/sardarlaltu/SecureLinkPrediction.Google Scholar

[19]

M. Shen, B. Ma, L. Zhu, R. Mijumbi, X. Du and J. Hu, Cloud-based approximate constrained shortest distance queries over encrypted graphs with privacy protection, IEEE Trans. Information Forensics and Security, 13 (2018), 940–953. doi: 10.1109/TIFS.2017.2774451. Google Scholar

[20]

D. X. Song, D. A. Wagner and A. Perrig, Practical techniques for searches on encrypted data, in 2000 IEEE Symposium on Security and Privacy, Berkeley, California, USA, May 14-17, 2000, 2000, 44–55.Google Scholar

[21]

E. Stefanov, M. van Dijk, E. Shi, C. W. Fletcher, L. Ren, X. Yu and S. Devadas, Path ORAM: An extremely simple oblivious RAM protocol, J. ACM, 65 (2018), Art. 18, 26 pp. doi: 10.1145/3177872. Google Scholar

[22]

Q. Wang, K. Ren, M. Du, Q. Li and A. Mohaisen, Secgdb: Graph encryption for exact shortest distance queries with efficient updates, in Financial Cryptography and Data Security - FC 2017, Sliema, Malta, April 3-7, 2017, Revised Selected Papers, 10322 (2017), 79–97. Google Scholar

[23]

A. C. Yao, Protocols for secure computations (extended abstract), in 23rd Annual Symposium on Foundations of Computer Science, Chicago, Illinois, USA, 3-5 November 1982, 1982, 160–164. Google Scholar

[24]

Y. Zheng, B. Wang, W. Lou and Y. T. Hou, Privacy-preserving link prediction in decentralized online social networks, in Computer Security - ESORICS 2015 - Vienna, Austria, September 21-25, 2015, Proceedings, Part II, 9327 (2015), 61–80. doi: 10.1007/978-3-319-24177-7_4. Google Scholar

show all references

References:
[1]

https://www.cryptopp.com/benchmarks.html.Google Scholar

[2]

G. Asharov, Y. Lindell, T. Schneider and M. Zohner, More efficient oblivious transfer and extensions for faster secure computation, in 2013 ACM SIGSAC Conference on Computer and Communications Security, CCS'13, Berlin, Germany, November 4-8, 2013, 2013, 535–548. doi: 10.1145/2508859.2516738. Google Scholar

[3]

L. Backstrom, C. Dwork and J. M. Kleinberg, Wherefore art thou r3579x: anonymized social networks, hidden patterns, and structural steganography, WWW '07 Proceedings of the 16th international conference on World Wide Web, (2007), 181–190. doi: 10.1145/1242572.1242598. Google Scholar

[4]

D. Boneh, E. Goh and K. Nissim, Evaluating 2-dnf formulas on ciphertexts, in Theory of Cryptography, Second Theory of Cryptography Conference, TCC 2005, Cambridge, MA, USA, February 10-12, 2005, Proceedings, 3378 (2005), 325–341. doi: 10.1007/978-3-540-30576-7_18. Google Scholar

[5]

C. Bösch, A. Peter, B. Leenders, H. W. Lim, Q. Tang, H. Wang, P. H. Hartel and W. Jonker, Distributed searchable symmetric encryption, in 2014 Twelfth Annual International Conference on Privacy, Security and Trust, Toronto, ON, Canada, July 23-24, 2014, 2014, 330–337.Google Scholar

[6]

M. Chase and S. Kamara, Structured encryption and controlled disclosure, in Advances in Cryptology - ASIACRYPT 2010 - 16th International Conference on the Theory and Application of Cryptology and Information Security, Singapore, December 5-9, 2010. Proceedings, 6417 (2010), 577–594. doi: 10.1007/978-3-642-17373-8_33. Google Scholar

[7]

V. Kolesnikov, A. Sadeghi and T. Schneider, Improved garbled circuit building blocks and applications to auctions and computing minima, in Cryptology and Network Security, 8th International Conference, CANS 2009, Kanazawa, Japan, December 12-14, 2009. Proceedings, 2009, 1–20.Google Scholar

[8]

V. Kolesnikov and T. Schneider, Improved garbled circuit: Free XOR gates and applications, in Automata, Languages and Programming, 35th International Colloquium, ICALP 2008, Reykjavik, Iceland, July 7-11, 2008, Proceedings, Part II - Track B: Logic, Semantics, and Theory of Programming & Track C: Security and Cryptography Foundations, 5126 (2008), 486–498. doi: 10.1007/978-3-540-70583-3_40. Google Scholar

[9]

J. Leskovec and A. Krevl, SNAP Datasets: Stanford large network dataset collection, http://snap.stanford.edu/data, 2014.Google Scholar

[10]

D. Liben-Nowell and J. M. Kleinberg, The link prediction problem for social networks, in Proceedings of the 2003 ACM CIKM International Conference on Information and Knowledge Management, New Orleans, Louisiana, USA, November 2-8, 2003, 2003, 556–559. doi: 10.1145/956863.956972. Google Scholar

[11]

Y. Lindell and B. Pinkas, A proof of security of yao's protocol for two-party computation, J. Cryptology, 22 (2009), 161-188. doi: 10.1007/s00145-008-9036-8. Google Scholar

[12]

C. LiuL. Zhu and J. Chen, Graph encryption for top-k nearest keyword search queries on cloud, T-SUSC, 2 (2017), 371-381. doi: 10.1109/TSUSC.2017.2704163. Google Scholar

[13] A. MenezesP. C. van Oorschot and S. A. Vanstone, Handbook of Applied Cryptography, CRC Press, Boca Raton, FL, 1997.
[14]

X. Meng, S. Kamara, K. Nissim and G. Kollios, GRECS: graph encryption for approximate shortest distance queries, in Proceedings of the 22nd ACM SIGSAC Conference on Computer and Communications Security, Denver, CO, USA, October 12-6, 2015, 2015, 504–517. doi: 10.1145/2810103.2813672. Google Scholar

[15]

M. Naor and B. Pinkas, Efficient oblivious transfer protocols, in Proceedings of the Twelfth Annual Symposium on Discrete Algorithms, January 7-9, 2001, Washington, DC, USA., 2001, 448–457. Google Scholar

[16]

K. Nayak, X. S. Wang, S. Ioannidis, U. Weinsberg, N. Taft and E. Shi, Graphsc: Parallel secure computation made easy, in 2015 IEEE Symposium on Security and Privacy, SP 2015, San Jose, CA, USA, May 17-21, 2015, 2015, 377–394. doi: 10.1109/SP.2015.30. Google Scholar

[17]

PBC Library, The Pairing-based Cryptography Library, https://crypto.stanford.edu/pbc/.Google Scholar

[18]

L. Sardar and S. Ruj, Prototypes of secure link prediction schemes, GitHub repository, https://github.com/sardarlaltu/SecureLinkPrediction.Google Scholar

[19]

M. Shen, B. Ma, L. Zhu, R. Mijumbi, X. Du and J. Hu, Cloud-based approximate constrained shortest distance queries over encrypted graphs with privacy protection, IEEE Trans. Information Forensics and Security, 13 (2018), 940–953. doi: 10.1109/TIFS.2017.2774451. Google Scholar

[20]

D. X. Song, D. A. Wagner and A. Perrig, Practical techniques for searches on encrypted data, in 2000 IEEE Symposium on Security and Privacy, Berkeley, California, USA, May 14-17, 2000, 2000, 44–55.Google Scholar

[21]

E. Stefanov, M. van Dijk, E. Shi, C. W. Fletcher, L. Ren, X. Yu and S. Devadas, Path ORAM: An extremely simple oblivious RAM protocol, J. ACM, 65 (2018), Art. 18, 26 pp. doi: 10.1145/3177872. Google Scholar

[22]

Q. Wang, K. Ren, M. Du, Q. Li and A. Mohaisen, Secgdb: Graph encryption for exact shortest distance queries with efficient updates, in Financial Cryptography and Data Security - FC 2017, Sliema, Malta, April 3-7, 2017, Revised Selected Papers, 10322 (2017), 79–97. Google Scholar

[23]

A. C. Yao, Protocols for secure computations (extended abstract), in 23rd Annual Symposium on Foundations of Computer Science, Chicago, Illinois, USA, 3-5 November 1982, 1982, 160–164. Google Scholar

[24]

Y. Zheng, B. Wang, W. Lou and Y. T. Hou, Privacy-preserving link prediction in decentralized online social networks, in Computer Security - ESORICS 2015 - Vienna, Austria, September 21-25, 2015, Proceedings, Part II, 9327 (2015), 61–80. doi: 10.1007/978-3-319-24177-7_4. Google Scholar

Figure 1.  System model
Figure 2.  Example of a Maximum circuit with $ N = 7 $
Figure 3.  Different max blocks used in $ \mathtt{MAXIMUM} $ circuit
Figure 4.  Few circuit blocks
Figure 5.  Number of vertices and edges of the subgraphs
Figure 6.  comparison between $ \mathtt{SLP} $-$ \mathtt{I} $ and $ \mathtt{SLP} $-$ \mathtt{II} $ w.r.t. computation time when the primes are of 128 bits each
Figure 7.  Time taken by the proxy in $ \mathtt{SLP} $-$ \mathtt{II} $ for different datasets considering 128-bit primes
Figure 8.  Computational time in $ \mathtt{SLP} $-$ \mathtt{I} $ with 128,256 and 512-bit primes
Figure 9.  Computational time in $ \mathtt{SLP} $-$ \mathtt{II} $ with 128,256 and 512-bit primes
Table 1.  Complexity Comparison Table
Param Entity $ \mathtt{SLP} $-$ \mathtt{I} $ $ \mathtt{SLP} $-$ \mathtt{II} $ $ \mathtt{SLP} $-$ \mathtt{III} $
Leakage CS $ |V| $, $ \tau_{v_1},\tau_{v_2},\ldots $ $ |V| $, $ \tau_{v_1},\tau_{v_2},\ldots $ $ |V| $, $ \tau_{v_1},\tau_{v_2},\ldots $
PS $ S_{v},i_{res} $ $ S'_{v},i_{res} $ $ i_{res} $
client $ \lambda $ bits $ \lambda $ bits $ \lambda $ bits
Storage CS $ |V|^2\rho $ bits $ 2|V|^2\rho $ bits $ |V|^2\rho $ bits
PS $ \rho $ bits $ \rho $ bits $ \rho $ bits
client $ |V|^2(\mathsf{M}+\mathsf{A}) $ $ |V|^2(\mathsf{M}+\mathsf{A}+\mathsf{M_1}+\mathsf{A_1}) $ $ |V|^2(\mathsf{M}+\mathsf{A}) $
Compu- CS $ |V|^2 $ $ \mathsf{P} $ + $ |V| $ $ \mathsf{E} $ $ |V|^2 $ $ \mathsf{P} $ + $ |V|^2 $ $ \mathsf{P} $ + $ 4|V| $ $ \mathsf{E} $
tation + ($ |V|^2+ |V| $) $ \mathsf{M} $ ($ |V|^2+ 2|V| $) $ \mathsf{M} $ + ($ |V|^2+ 3|V| $) $ \mathsf{M} $ +
$ MGC_{const}{(\log |V|,|V|)} $
PS $ |V|log|V| (\mathsf{M+C}+\mathsf{M_1+C_1}) $ $ |V| (\mathsf{M_1+C_1}) $ + $ |V| (\mathsf{M+C}+\mathsf{M_1+C_1}) $+
+$ |V|log|V| \mathsf{C} $ +$ |V| log|V| \mathsf{C} $ $ MGC_{eval}{(\log |V|,|V|)} $
client$ \rightarrow $CS $ |V|^2 \rho $ bits $ 2 |V|^2 \rho $ bits $ |V|^2\rho $ bits
Commu- CS$ \rightarrow $PS $ 2|V|\rho $ bits $ |V|\rho $ bits $ 2|V|\rho $ bits + $ |V|OT ^{(\log |V| +1)}_{snd} $+
nication $ MGC_{size}{(\log |V|,|V|)} $ bits
PS$ \rightarrow $CS - - $ |V|OT ^{(\log |V| +1)}_{rcv} $
PS$ \rightarrow $client $ \log |V| $ bits $ 2|V| \log |V| $ bits $ \log |V| $ bits
$S_{v}$ - Set of scores of $v$ with all other vertices, $S'_{v} $- a subset of $ S_{v}$, $\rho $- length of elements in $\mathbb{G}$ or $\mathbb{G}_1$, $\mathsf{C}$- comparison in $\mathbb{G}$, $\mathsf{C_1}$- comparison in $\mathbb{G}_1$, $\mathsf{M}$- multiplication in $\mathbb{G}$, $\mathsf{M_1}$- multiplication in $\mathbb{G}_1$, $\mathsf{E}$- exponentiation in $\mathbb{G}$, $\mathsf{E_1}$- exponentiation in $\mathbb{G}_1$, $\mathsf{P}$- pairing/ bilinear map computation, $MGC_{size}{(\log |V|,|V|)}$- size of $MGC$ with $|V|$ $\log |V|$-bit inputs, $MGC_{const}{(\log |V|,|V|)}$- $MGC$ contraction with $|V|$ $\log |V|$-bit inputs, $MGC_{eval}{(\log |V|,|V|)}$- $MGC$ evaluation with $|V|$ $\log |V|$-bit inputs, $OT ^{(\log |V| +1)}_{snd}$- information to send for $(\log |V|+1) $-bit $OT$, $OT ^{(\log |V| +1)}_{rcv}$- information to receive for $\log |V| $-bit $OT$.
Param Entity $ \mathtt{SLP} $-$ \mathtt{I} $ $ \mathtt{SLP} $-$ \mathtt{II} $ $ \mathtt{SLP} $-$ \mathtt{III} $
Leakage CS $ |V| $, $ \tau_{v_1},\tau_{v_2},\ldots $ $ |V| $, $ \tau_{v_1},\tau_{v_2},\ldots $ $ |V| $, $ \tau_{v_1},\tau_{v_2},\ldots $
PS $ S_{v},i_{res} $ $ S'_{v},i_{res} $ $ i_{res} $
client $ \lambda $ bits $ \lambda $ bits $ \lambda $ bits
Storage CS $ |V|^2\rho $ bits $ 2|V|^2\rho $ bits $ |V|^2\rho $ bits
PS $ \rho $ bits $ \rho $ bits $ \rho $ bits
client $ |V|^2(\mathsf{M}+\mathsf{A}) $ $ |V|^2(\mathsf{M}+\mathsf{A}+\mathsf{M_1}+\mathsf{A_1}) $ $ |V|^2(\mathsf{M}+\mathsf{A}) $
Compu- CS $ |V|^2 $ $ \mathsf{P} $ + $ |V| $ $ \mathsf{E} $ $ |V|^2 $ $ \mathsf{P} $ + $ |V|^2 $ $ \mathsf{P} $ + $ 4|V| $ $ \mathsf{E} $
tation + ($ |V|^2+ |V| $) $ \mathsf{M} $ ($ |V|^2+ 2|V| $) $ \mathsf{M} $ + ($ |V|^2+ 3|V| $) $ \mathsf{M} $ +
$ MGC_{const}{(\log |V|,|V|)} $
PS $ |V|log|V| (\mathsf{M+C}+\mathsf{M_1+C_1}) $ $ |V| (\mathsf{M_1+C_1}) $ + $ |V| (\mathsf{M+C}+\mathsf{M_1+C_1}) $+
+$ |V|log|V| \mathsf{C} $ +$ |V| log|V| \mathsf{C} $ $ MGC_{eval}{(\log |V|,|V|)} $
client$ \rightarrow $CS $ |V|^2 \rho $ bits $ 2 |V|^2 \rho $ bits $ |V|^2\rho $ bits
Commu- CS$ \rightarrow $PS $ 2|V|\rho $ bits $ |V|\rho $ bits $ 2|V|\rho $ bits + $ |V|OT ^{(\log |V| +1)}_{snd} $+
nication $ MGC_{size}{(\log |V|,|V|)} $ bits
PS$ \rightarrow $CS - - $ |V|OT ^{(\log |V| +1)}_{rcv} $
PS$ \rightarrow $client $ \log |V| $ bits $ 2|V| \log |V| $ bits $ \log |V| $ bits
$S_{v}$ - Set of scores of $v$ with all other vertices, $S'_{v} $- a subset of $ S_{v}$, $\rho $- length of elements in $\mathbb{G}$ or $\mathbb{G}_1$, $\mathsf{C}$- comparison in $\mathbb{G}$, $\mathsf{C_1}$- comparison in $\mathbb{G}_1$, $\mathsf{M}$- multiplication in $\mathbb{G}$, $\mathsf{M_1}$- multiplication in $\mathbb{G}_1$, $\mathsf{E}$- exponentiation in $\mathbb{G}$, $\mathsf{E_1}$- exponentiation in $\mathbb{G}_1$, $\mathsf{P}$- pairing/ bilinear map computation, $MGC_{size}{(\log |V|,|V|)}$- size of $MGC$ with $|V|$ $\log |V|$-bit inputs, $MGC_{const}{(\log |V|,|V|)}$- $MGC$ contraction with $|V|$ $\log |V|$-bit inputs, $MGC_{eval}{(\log |V|,|V|)}$- $MGC$ evaluation with $|V|$ $\log |V|$-bit inputs, $OT ^{(\log |V| +1)}_{snd}$- information to send for $(\log |V|+1) $-bit $OT$, $OT ^{(\log |V| +1)}_{rcv}$- information to receive for $\log |V| $-bit $OT$.
Table 2.  Detail of the graph datasets
Dataset Name #Nodes #Edges
bitcoin-alpha 3,783 24,186
ego-facebook 4,039 88,234
email-Enron 36,692 183,831
email-Eu-core 1,005 25,571
Wiki-Vote 7,115 103,689
Dataset Name #Nodes #Edges
bitcoin-alpha 3,783 24,186
ego-facebook 4,039 88,234
email-Enron 36,692 183,831
email-Eu-core 1,005 25,571
Wiki-Vote 7,115 103,689
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