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Secure Multiparty Computation – compute without looking


Secure Multiparty Computation (SMC) is a technology that allows computation on encrypted data. This might sound impossible at first but in fact, by using the right kind of cryptography, it is not. This enables companies to collaborate (securely) in new ways. The technology is useful in for example benchmarking and online auctions.

With SMC, two or more servers can jointly compute the result of any function without learning the input to the function. The servers can for example compute the result of an auction without learning the bids. This is achieved by providing each server with only partial information on each bid. The partial information given to a single server (in some cases even several servers) reveals nothing about the actual bid. Nevertheless, using the right cryptographic tools, the servers can work together and compute the result.

This enables parties who do not necessarily trust each other to develop collaborative solutions based on encrypted data without ever disclosing any private information. As opposed to performing the computation on a traditional PC, SMC is considered more secure as a hacker will have to compromise all servers to reveal the input. 


Secret sharing of data brings new opportunities

A central result in cryptography is that the ideas behind secret sharing can be extended to allow the computation of any function that a traditional computer can compute. Of course, due to the fact that computation is distributed across a number of servers, performance suffers. The technological building block behind Partisia Market Design is a robust and efficient implementation of these cryptographic ideas. This implementation provides confidentiality of encrypted data to a level that corresponds to modern commercial cryptographic primitives such as RSA and AES.

One such cryptographic tool is called secret sharing. Suppose that a secret x=42 is to be shared among 2 servers. If we choose two random numbers x1 and x2 such that x=x1+x2 (e.g. x1=50 and x2= -8) and give x1 to the first server and x2 to the second, then neither server will know the secret x. Indeed, the first server only learns the number 50, and from its point of view, the other number could be any integer. Of course, 50 + anything can result in anything.

Similarly, we might secret share another number y=23 between the two servers (e.g. y1=20 and y2=3). The two servers can now compute x+y and make this, without ei-ther server learning x nor y. The first server simply computes x1+y1 and sends the result to the second server, which can then compute x1+y1+x2+y2=x+y - all of this without any server learning anything about x nor y, other than the sum.

SMC provides high-level security and simple administration​

Securing input confidentiality in a computation like an auction would traditionally (without SMC) be done in two separate steps: 1) encrypting the bids in transit from the bidder to the auctioneer (but decrypted when they arrive at the auctioneer), and 2) ensuring that the auctioneer keeps the bids confidential. The latter is normally ensured by enforcing security policies restricting which employees of the auctioneer have access to the bids and when. Unfortunately, this latter step is notoriously hard, and consequently the realized solution only provides shallow confidentiality.

Using secure multiparty computation this latter part can be entirely avoided. Bids are never decrypted. No complex security policies are required. We call this deep confidentiality. This is the essence of secure multiparty computation. It provides a high degree of security, simple administration and consequently efficient deployment of solutions needed for confidential handling of data. 


The Alexandra Institute has thorough knowledge and experience of SMC from a wide range of commercial and R&D projects. 

One of the most well-known global SMC projects is SIMAP which is a research project we carried out in collaboration with Aarhus University, the University of Copenhagen, Copenhagen Business School and Danisco. The project was funded by the Danish Council for Strategic Research and focused on commercial application of SMC. The project led to the creation of the start-up Partisia who has developed an SMC-based contract exchange for the Danish sugar industry. 

Another practical implementation of SMC is the development of and the start-up Sepior that develops cloud-encryption software. 

In the COBE project – Confidential Benchmarking – we use SMC to enable banks to benchmark the financial performance of their agricultural customers in collaboration with the agricultural consultancy firm SEGES who provides accounting data from many farmers. With SMC, the accounting data of each farmer remains confidential, and the bank’s portfolio of agricultural customers is never disclosed.

PRACTICE is a large-scale EU FP7 project that builds on the prototype from COBE. The role of the Alexandra Institute is to design the architecture and implement a platform for secure computing, including implementation of relevant third-party protocols.

In the Big Data by Security project we deploy SMC in two different cases: 1) development of secure credit assessment methods and 2) development of a system for benchmarking industrial power consumption. Both cases are relevant in a wider perspective, and it is therefore essential that Danish companies benefit from the solutions developed – for example to get better access to funding or to reduce energy costs.

Scalable Oblivious Data Analytics (SODA) is an innovation project that investigates the use of SMC in relation to data analytics and big data. With SMC it is possible to extract valuable data from data sets, while at the same time protecting people’s privacy. The project also investigates SMC in relation to GDPR as SMC solves many of the issues that may arise in the wake of GDPR. 

During recent years, the Alexandra Institute has contributed to the development of the open source framework FRESCO in collaboration with our spin-off company Partisia. FRESCO is being used in most of our SMC projects. The framework makes it easy and manageable for developers with no cryptology experience to develop SMC applications without having to worry about what exactly goes on ‘behind the scenes’. This also allows fast and easy implementation of new SMC protocols, which are the magic behind the technology. However, despite the ease of use, we strongly advise that you team up with one of the Alexandra Institute’s experts before you start working with SMC in order to avoid the pitfalls.


Head of Security Lab, PhD
+45 24 26 99 11
Åbogade 34, 8200 Aarhus N
Hopper building, 2nd floor room 226