Consensus Update #2 — Private Data Aggregation as a Blockchain Proof-of-Work

Leigh Diprose
Feb 1, 2019 · 6 min read

Our R&D team at Consensus has been working on a protocol update which uses the difficulty of the discrete log problem (DLP) to fulfil two essential tasks. The system aims to collect and aggregate provably-anonymous private data while simultaneously providing proof-of-work for securing a blockchain. The research we are doing into private data aggregation as a blockchain using proof-of-work is foundational for future government applications.

In this update we want to provide an overview of our latest paper on Private Data. It’s technical in nature, so if you wish to read the full extent of the paper you can read the PDF here. Otherwise, this update will provide a general summary with inclusion of some technical aspects.

Technical Analysis, Research, and Overview.

The technical analysis, research, and an overview of the project have undergone continuous theoretical tests by trusted mathematicians and cryptography experts to get to a point where we are now releasing news about the update publicly. As exciting as this is, we understand the Consensus system is intricate in detail and relatively unique to blockchain. It is for this very reason we wish to communicate our progress so far in the hope to gain further insight from our colleagues in various fields of cryptography, mathematics, and network security.

It is through this open communication we can further develop secure eGovernance tools, which will fulfil our aim to offer significant improvements in economic efficiency for governments around the world.

In saying this, the overview and premise of the network we are building is to collect private data from participants securely and transparently, without revealing individual identities (which as an example is well suited for governments requiring a voting system, but also extends to non-voting applications). For the system to be operational, a public record (or blockchain) provides a means for proving which participants’ data was sent, received and ideally counted.

From a technical stance, the process of this data collection is difficult and has similarities to the complication and computation of mining a block. The advantage of this type of network is the entire community can see the blockchain, while proving and validating the accuracy of the aggregated data. This ensures invalid contributions or values can be detected, penalized and dismissed.

Discrete Log Problem — Securing Private Data.

Private data aggregation is done in such a way that it is difficult for individuals to determine any single data point; this is what makes the data collection private. The resources of the mining community are used to solve the difficult problem of aggregating the data together, and this is done in such a way that it does not make it any easier to determine any individual data point. Thus, when new blocks are mined, the community can see the aggregate results, but no individual data point is available. The difficulty claims are based on established problems in cryptography, namely the difficulty of DLP in finite cyclic groups and the difficulty of the RSA problem.

In other words, data is provided from individuals and entities without having personal information published. Think of it as a doorway into a companies or entities data, but the public is blind to the individual identities associated with the data. The public only sees the published results after the mining process. Formulation of the partial results would be shown after a block is mined, allowing the community to see the aggregated results as they progress.

To function, let’s say in the form of a voting system, the algorithm begins with certain cryptographic data. Adding to this participants select a private value and publish a derived public value to the network. To achieve consensus or a result, miners aggregate many of the values in an attempt to solve the DLP. The process of solving DLP is difficult, which is why the work acts as a proof-of-work for the blockchain.

Mining Rewards

As the proof-of-work develops, miners receive rewards for solving valid blocks. A minimum number of data values (or votes) would need aggregation to receive a reward. As usual in blockchains, miners are incentivized to work on solving this difficult problem; and it is only solvable because the entire mining community would be working on the problem. Unlike traditional hash-based blockchains, the miner cannot disclose the solution directly. If a miner were to do this, it could give rise to hackers reverse engineering the system, leading to potentially stealing blocks or repurposing them.

Instead of revealing the solution, miners publish information that proves that they have solved the problem. This proof integrates the solution to the data aggregation problem, and it also takes known proof-of-work data from a previous block which makes it challenging to create alternate block histories. The result is proof-of-work that both performs the useful work of private data aggregation, while at the same time providing standard blockchain security, which is essential for government application.

Bitwise Encoding — Including Random Bits to Calculate the Vote Tally.

To provide a means for a secure system, known bits, plus random bits, must be included in a data set (in this case a voting system). While the formation and calculation of this process is technical in nature, let’s further explore how Bitwise Encoding will work in the Consensus system.

In its simplest form, to understand how the data is encoded for each “candidate,” we must break down 256 total bits into four bits (as shown above). Each of the four bits carries a separate value that combines to determine the user’s vote. The values represented are broken into four bits containing;

High bits — which are used to obfuscate votes.

Tally option A — forming bits 0–3 for candidate A.

Tally option B — forming bits 4–7 for candidate B.

Tally option C — forming bits 8–11 for candidate C.

Including high bits within the total 256-bits is necessary because without this inclusion an attacker could determine the user’s vote. They could work out a user’s vote by computing the known generator and a participant’s private value before comparing to the published value. To stop this from occurring the user must choose random bits (representing a total of 244-bits, which includes 4 empty bits) to insert in the high bits. The total data encoded results in an unpredictable 256-bit data set. Additionally, to this, a higher data set of information should be calculated at once. The reason for this inclusion is to mask the computational theory of identifying smaller groups of data. Instead, in this case, voting groups should be formed in the thousands or hundreds of thousands.

Further exploring the inclusion of random high bits, the miner can understand the possible values for each valid vote. To understand the total vote tally, a miner must aggregate the votes by computing the DLP while ignoring the high bits. Essentially, by including random high bits, it elevates a hacker from being able to compute and compare published values. As this is the case, once the mining process is complete, the miner can read off the results for candidate A, B, and C.

In conclusion, Consensus is on track to deliver future government applications which aim to add value to the decision making processes. Our R&D team has been working tirelessly to deliver on this as outlined in our latest paper. While the Consensus solution may seem complicated in design and application at times, at its core, the secure community system focuses on adding value to government departments through AI and blockchain technology. It’s for this reason; the future certainly looks bright for governments around the world.

Working with Consensus

We are now actively engaging with potential pilot partners. If your government organization at the city, state, or federal level is interested in working with Consensus, please reach out to our business development and strategy lead at

We will be happy to walk you through the Consensus solution and how it can be applied to your jurisdiction to add efficiency to planning and accelerate feedback loops between officials and citizens.

Consensus AI

Achieving collective governance based on interdependence…

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