Abstract
There are many cryptographic protocols in the literature that are scientifically and mathematically sound. By extension, cryptography today seeks to respond to numerous properties of the communication process beyond confidentiality (secrecy), such as integrity, authenticity, and anonymity. In addition to the theoretical evidence, implementations must be equally secure. Due to the ever-increasing intrusion from governments and other groups, citizens are now seeking alternatives ways of communication that do not leak information. In this paper, we analyze multiparty computation (MPC), which is a sub-field of cryptography with the goal of creating methods for parties to jointly compute a function over their inputs while keeping those inputs private. This is a very useful method that can be used, for example, to carry out computations on anonymous data without having to leak that data. Thus, due to the importance of confidentiality in this type of technique, we analyze active and passive attacks using complexity measures (compression and entropy). We start by obtaining network traces and syscalls, then we analyze them using compression and entropy techniques. Finally, we cluster the traces and syscalls using standard clustering techniques. This approach does not need any deep specific knowledge of the implementations being analyzed. This paper presents a security analysis for four MPC frameworks, where three were identified as insecure. These insecure libraries leak information about the inputs provided by each party of the communication. Additionally, we have detected, through a careful analysis of its source code, that SPDZ-2’s secret sharing schema always produces the same results.
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Notes
Entropy is a measure of unpredictability of information content [31].
tcpdump is a tool that allows to inspect the traffic passing through the data network. Like all sniffers, tcpdump can be used for good (e.g., detecting communication errors), but also for evil (e.g., capturing personal data).
STrace allows the attacker to observe the system calls used by an application. STrace is useful because it can help the user to better understand what the system does during program execution, which can be a great help in tuning performance and resource management.
Approximate Entropy is a technique used to quantify the amount of regularity and the unpredictability of fluctuations over time-series data [32].
A network socket is an endpoint to the communication flow between two programs running over a network.
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Acknowledgements
The work of João S. Resende was supported by a scholarship from the Fundação para a Ciência e Tecnologia (FCT), Portugal (scholarship Number PD/BD/128149/2016). The work of Patrícia R. Sousa and Luís Antunes was supported by Project “NanoSTIMA: Macro-to-Nano Human Sensing: Towards Integrated Multimodal Health Monitoring and Analytics/NORTE-01-0145-FEDER-000016,” financed by the North Portugal Regional Operational Programme (NORTE 2020), under the PORTUGAL 2020 Partnership Agreement, and through the European Regional Development Fund (ERDF). The work of Rolando Martins was supported by a scholarship from the Fundação para a Ciência e Tecnologia (FCT), Portugal (scholarship Number SFRH/BPD/115408/2016). This work is financed by National Funds through the FCT—Fundação para a Ciência e a Tecnologia (Portuguese Foundation for Science and Technology) within the project CMU Portuga CMU/CS/0042/2017.
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Appendices
Appendix A: Millionaire’s problem code
The Code 7 represents the ABY code that allows the implementation of the millionaire’s problem. In this case, we read the input from a local file and, to perform the brute force, we just need to rewrite a file and rerun the program to have a different example.
Appendix B: Commands
The listings shows the commands used to produce the file of the output traffic of the protocol: network (Listing 3) and STrace (Listing 4). The machine that runs this process needs to have all the communications in the interface lo in idle, in order to have only the information correlated with the MPC process in the captures.
Tree with the entire clustering of the brute force attack
Appendix C: Output of code analysis
We have to analyze the values printed from the secret sharing (Listing 5), in order to see whether this output is always equal in all the iterations with the same set of inputs.
Appendix D: Entropy value influence
The padding of zeros can influence the entropy values. The following example shows two different input sizes (salary of Bill Gates) converted to 32 bits binary. We can see that if we convert only 6 digits of salary (896 000), we have a lot of padding of zeros at the left (00000000000011001110010011001000). The same does not occur in the input size 12 (896000000000 - 11000100101111011110110011000010). It may be detrimental to have padding of zeros left, as entropy is influenced in the wrong way.
We use the python command pyeeg to calculate the approximate entropy, used to present the entropy results in this paper.
Appendix E: SPDZ-2 maketree with complearn
Figure 6 represents the entire tree generated by complearn. The tree contains a high S(T) value, but the representation in some situation is complicated to visualize. In order to help the identification of different clusters, it has performed a set of “blue cuts” in the tree. This way, we can visualize a cluster flowing branch until the leaves.
In a highlight perspective, the tree can split each one of the traces connected to a similar example where we see all the 16 different types of communications perfectly split accordingly in the tree. The similar traces are formed of the same party’s communicating with a number from 0 to 4 where an example can be \(0\_gates\_zuck\) and \(2\_gates\_zuck\). Here, both are the same communication but in a different iteration, where 0 represents the first communication and 2 the third communication. This example has a communication between Gates and Zuck, where Gates is the initiator of the communication and Zuck the other party in the communication protocol.
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Resende, J.S., Sousa, P.R., Martins, R. et al. Breaking MPC implementations through compression. Int. J. Inf. Secur. 18, 505–518 (2019). https://doi.org/10.1007/s10207-018-0424-2
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DOI: https://doi.org/10.1007/s10207-018-0424-2