Distributed Protocols at the Rescue for Trustworthy Online Voting

TL;DR

This paper explores the potential of distributed, blockchain-inspired online voting protocols to enhance security and trustworthiness without relying on trusted authorities, emphasizing their robustness and alignment with paper-based voting.

Contribution

It introduces a taxonomy of distributed online voting notions and analyzes blockchain-based protocols as promising solutions for secure, trustless online voting.

Findings

Blockchain protocols resemble paper voting in security features

Distributed protocols increase robustness by removing single points of failure

Blockchain-based online voting shows promising security properties

Abstract

While online services emerge in all areas of life, the voting procedure in many democracies remains paper-based as the security of current online voting technology is highly disputed. We address the issue of trustworthy online voting protocols and recall therefore their security concepts with its trust assumptions. Inspired by the Bitcoin protocol, the prospects of distributed online voting protocols are analysed. No trusted authority is assumed to ensure ballot secrecy. Further, the integrity of the voting is enforced by all voters themselves and without a weakest link, the protocol becomes more robust. We introduce a taxonomy of notions of distribution in online voting protocols that we apply on selected online voting protocols. Accordingly, blockchain-based protocols seem to be promising for online voting due to their similarity with paper-based protocols.

Tables

Table 1. Table 1: Quality of distribution of selected online voting protocols.

Protocol	Degree of Specialisation	Topology	Distributed Phases
Paper-based Voting	none (flexible)	distributed	all
Helios, [1]	selected authorities	centralised	verification
SPP, [10]	random authorities	structured, tree	aggregation
DPol, [12]	none	structured, ring	all
Blockchain-based Voting	none (flexible)	distributed	all

Full text

1 VOTING IN THE DIGITAL AGE

Online services have emerged during the last decade in most areas of every day life. Online banking, online auctions, online shopping, online learning and online dating, to name a few, have become serious alternatives to their offline counterparts for the additional convenience they provide. Most online services are available 24 hours a day 7 days a week and can be accessed from any place with an internet connection. In particular, online social networks gained a lot of momentum. Many people are permanently connected to communicate with friends and colleagues. The social network Facebook, for instance, reports on $1.71$ billion monthly active users as of June 2016 which is more than $20\text{\,}\mathrm{\char 37\relax}$ of the world population. The adoption of online services increases further with the global dissemination of internet-enabled devices.

In these circumstances of pervasive online services, the paper-based voting procedure used to carry out elections in many democracies appears like a legacy from the past. This is even more the case for the generation of Digital Natives that is used to the convenience offered by online services.

Paper-based voting requires voters to cast their ballot within a given time frame at a particular location. In contrast, remote electronic voting, in short online voting, allows voters to cast their ballot from home or any other place. The time and effort to vote decreases. Consequently, the overall voter turnout is expected to increase [5]. Moreover, the ballot casting is carried out using a special software which improves the voter convenience as the ballot presentation considers for instance the voter’s spoken language and possible disabilities.

The voter convenience is especially important if voters are often asked to vote, e.g. for elements of direct democracy such as referenda. Not only doubts in the integrity of the voting outcome, but also a low voter turnout can negatively impact the legitimacy of the result.

Despite the advantages, only few countries employ online voting for general elections, e.g. Estonia [23], Canada [11] and Australia [4], and for those, security concerns have been addressed repeatedly by the scientific community \autocitesivoting-ccs2014halderman2015. Other countries have abandoned online voting trials or banned online voting for their insufficient security, as it happened in Germany. In fact, the provision of the same set of security properties as known from paper-based voting for online voting proves to be challenging with no universal solution, but with different potential concessions.

In this paper, we address the issue of trustworthy online voting protocols with regard to the potential of distributed protocols. Starting from paper-based voting with its broadly accepted trustworthiness (Sec. 2), we give a high-level review of the principle security concepts of online voting protocols and deliver an overview of their trust assumptions (Sec. 3). The capacity of authorities and of the voters defined by the protocols are hereby of primary concern. We show that the trustworthiness in those approaches is limited due to the concentration of power and argue hereinafter that distributed protocols are promising to increase the trustworthiness due to their similarity with paper-based protocols. Bitcoin, an electronic currency with no trusted authority, is introduced in Sec. 4. Moreover, the development towards online voting is compared with those to Bitcoin and BitTorrent. Sec. 5 is dedicated to the prospects of distributed protocols for trustworthy online voting. Then in Sec. 6, different notions of distribution are introduced in order to analyse a selection of existing online voting protocols for their degree of distribution. Our conclusion follows in Sec. 7.

Our findings motivate our ongoing research on distributed online voting protocols with a novel distributed protocol currently in preparation for publication.

2 PAPER-BASED VOTING

The paper-based voting protocol used today in many democracies is the result of a development rooted in Ancient Greece where pebbles were casted in an urn for votings. Since then, many provisions have been added to ensure the voting outcome reflects indeed the aggregated choice of all eligible voters. Neglecting local particularities, we give a sketch of a paper-based voting protocol to recall afterwards how basic security properties are implemented.

Preparation Phase

The voting station is the dedicated location to receive voters on voting day and is run by volunteering voters that become thus occasionally voting officers. For large numbers of voters, the voters are partitioned by locality to a reasonable number of voting districts with each one voting station. Every station is provided with undistinguishable voting ballots and a list of eligible voters issued by the central voter registry.

Casting Phase

On arrival at the voting station, voters have to present a proof of identity in order to proceed to the casting. Once the voter is confirmed to be eligible, a blank ballot is handed out and the voter list is annotated accordingly to prevent that voters can get more than one ballot. Under public supervision, the voter enters alone the voting booth to fill and fold in secret the paper ballot. Again under public supervision, the filled ballot is thrown into a transparent ballot box.

Aggregation and Evaluation

Phase

Once, the casting phase is terminated, ballot boxes are opened and ballots are tabulated to determine the tally that is published independently along with the derived voting outcome, e.g. using the majority rule.

Verification Phase

Every voter is allowed to attend all phases to supervise the compliance with the voting protocol.

Conflicting Security

Properties

Paper-based voting resolves the dilemma of voting protocols to ensure secrecy of the ballot and voter eligibility at the same time [16] in a straight-forward way. Voting officers and voters control that only eligible voters get one single paper ballot and that every voter puts only one ballot into the ballot box. Secrecy of the ballot is provided, because every voter fills and folds its ballot alone and once deposited in the ballot box, all ballots are indistinguishable and cannot be linked back to the voter. By eye-sight, ballots can be followed from its distribution, through its casting into the transparent ballot box until the tallying of all ballots. Verifiability is realised by the observation of the physical ballot transport, which is called chain of custody. This verification does not require any special knowledge. Hence, neither trust in the authority carrying out the voting, nor in employed technology is imposed.

3 ONLINE VOTING CONCEPTS

The development of online voting protocols, that preserve the security properties known from paper-based voting, is proven to be difficult. Electronic ballots can be cloned with no effort and their physical transport via wire cannot be observed. That is why special cautions must be taken to prevent the casting of illegitimate ballots, e.g. of ineligible voters or voters that seek to cast more than one ballot. Various concepts have been considered to ensure secrecy, eligibility and verifiability of online voting. Nonetheless, the overwhelming majority of current online voting protocols, as we detail hereafter, are either lacking properties, so that trust in authorities to carry out essential tasks must be assumed, or use advanced cryptography, which imposes trust in technology as expert knowledge cannot be implied.

One can distinguish online voting protocols by the following concepts to ensure both secrecy of the ballot and eligibility [16]:

Trusted Authorities

A very basic approach is to assume trust in all or a subset of the authorities. Voters transmit their ballot to the authorities using an authenticated channel that allows to verify the eligibility. Authorities are trusted to keep ballots confidential and to produce the correct tally.

Anonymous Voting

Using an authenticated channel, voters acquire from one authority an eligibility token, e.g. using blind signatures [6], that cannot be linked to the voter’s identity, but allows to verify its eligibility. Then, voters send both ballot and token through an anonymous channel to the authority. Technological trust is assumed in the secrecy ensured by the token. Authorities are trusted to produce the correct tally.

Random Perturbation

Voters send encrypted ballots to a group of authorities that shuffle one after each other the set of all ballots. Shuffling can be realised using a secure multi-party computation called Mix-Nets [7]. This way, ballots cannot be linked to voters if at least one authority is honest. Afterwards, ballots are decrypted to compute the tally. Technological trust and trust in at least one authority is assumed.

Homomorphic Encryption

With homomorphic encryption, encrypted ballots are tallied and decrypted only afterwards [2]. To prevent early decryption, $(k,n)$-threshold cryptography [20] is used, which requires the cooperation of $k$ out of $n$ authorities. The use of cryptography implies technological trust and trust in authorities to the extent that less than $k$ out of $n$ authorities are dishonest.

Balancing Verifiability and Secrecy of the

Ballot

Online voting protocols offering end-to-end verifiability [3] allow voters to verify the online voting outcome using cryptographic proofs. However, the very nature of the mentioned cryptographic protocols prevents to have both universal verifiability of the voting outcome and unconditional secrecy of the ballot [8]. Eventually, authorities have to be trusted to either respect the secrecy of the ballot or deliver the correct voting outcome. For a trustworthy voting, it is reasonable to let all voters choose their trusted authorities. Hence, the number of authorities is in the order of voters, which is infeasible for large scale elections with protocols based on the presented cryptographic concepts, because of an amount of required resources polynomial (or worse) in the number of authorities. As the distribution of powers in retrospect seems to be problematic, we consider in the next sections dedicated distributed protocols.

4 DISTRIBUTED PROTOCOLS

Without consensus on trusted authorities, it is reasonable to omit authorities altogether if possible and assume instead equipotency of all voters.

Bitcoin [19] demonstrates the feasibility to find such protocols without trusted authority. It establishes an electronic currency without inherent value, prevents its duplication, thus, double spending, and allows for fast online transactions between peers from many internet-enabled devices. Therefore, the protocol assumes that the majority of computing resources is controlled by honest peers. Technically, Bitcoin can be interpreted as an approach to the situation in the past, when traders used mostly currencies of inherent value such as gold, and no trust in online banking systems or authorities like central banks were assumed [21]. Hence, after technological progress allowed a shift from distributed offline to centralised online systems, Bitcoin presents a distributed online alternative, c.f. Fig. 1 (c). A similar analogy is given with BitTorrent [9] that allows its peers to share their resources to provide information (files) online, when before central online servers had to be used. The notion of peer empowerment/democracy in both Bitcoin and BitTorrent offers inspiration for the development of novel online voting protocols and is further detailed in the following section.

5 EMPOWERMENT OF VOTERS

In his essay ‘Authoritarian and Democratic Technics’, [18] explained the arising conflict if technology for democratic purposes is based on authorities. Indeed, protocols that omit distinct authorities and instead make provisions for equally privileged, equipotent voters sharing the same responsibilities, seem to better reflect the basic democratic concept of equally powerful voters. We assume further a distributed online voting protocol in which voters are represented as equipotent peers.

In BitTorrent and Bitcoin, peers cooperate, because they share a common goal. Peers are providers and consumers at the same time. Applied to online voting, we find a constellation similar to paper-based voting where voters serve as voting officers to run the voting station and carry out the supervision.

Even though not all tasks can be carried out by everyone at the same time, equipotent peers can replace each other easily. All peers are responsible to enforce the protocol policy, while byzantine peers with inconsistent behaviour are often tolerated to a certain degree. These properties contribute to the robustness of the protocol as there is no weakest link or bottleneck. Therefore, distributed protocols offer great potential for resilience against Distributed Denial of Service (DDoS) attacks.

The peers joining a distributed system, contribute with their own resources, e.g. communication capacity, memory and computation power. The global resources grow and diminish with peers joining or leaving the system offering potential for great scalability. Further, distributed protocols allow for ephemeral databases that vanishes entirely when all peers have left the system, offering new avenues for applications with sensitive data such as voting. In the case of centralised online voting protocols, ballots are most often encrypted, but there might be potential for a malicious decryption at some point in the future, if the implementation of cryptographic routines turns out to be flawed, secret keys leak or computing power got sufficiently cheap to brute-force the encryption.

As every peer has only partial knowledge of the global information, any unintentional or intentional disclosure is locally bounded. The impact of an attack, and thus its incentive, is reduced. In contrast, a disclosure by the authorities of centralised online voting can impact the secrecy of all casted ballots.

6 TOWARDS ONLINE VOTING WITHOUT

AUTHORITIES

As presented in Sec. 3, cryptographic algorithms allow to limit the power of authorities in online voting protocols. Note, that there is a trade-off. Less trust in authorities is assumed if authorities are less powerful, but as the protocol complexity increases, more technological trust is required. Using Anonymous Voting for example, voters do not have to present their ballot in clear, but have to trust in the properties of the eligibility token.

Further, online voting protocols employing many authorities might assign authorities either equal roles like in Random Perturbation or Homomorphic Encryption where authorities carry out the same tasks, or different roles. In Anonymous Voting, one authority ensures the eligibility of voters while the other aggregates all ballots and produces the tally. If all authorities are equipotent and their number can match the number of voters allowing for an identification between authorities and voters, the protocol becomes essentially distributed. In between, there is room for different kinds of partially distributed protocols that we want to characterise as follows. Note, that the registration phase shall not be considered in this paper.

Degree of Specialisation

ranging from equipotent voters with no specialisation to authorities with dedicated powers

Topology

ranging from centralised over decentralised to distributed topologies, c.f. Fig. 1

Phase

Authorities can intervene either not at all, only in few or in all phases (not distributed).

A protocol shall be called fully distributed if the topology is distributed and voters are equipotent during all phases but the registration.

Note, that we consider large scale elections for our analysis. First, we want to qualify paper-based voting as presented in Sec. 2. There are responsible voting officers, who can principally exchanged as no special knowledge is required. If we accept that every voter can become spontaneously voting officer, the protocol is actually fully distributed during all phases.

Helios

One of the few published, well-studied online voting protocols with unconditional end-to-end verifiability is Helios [1]. While the original version is based on Random Pertubation (Mix-Nets), the version available online111https://vote.heliosvoting.org/faq uses Homomorphic Encryption. In both cases trusted authorities are assumed for threshold decryption requiring communication costs polynomial in the number of authorities. Hence, the number of authorities must be small. During the aggregation, ballots are sent to the authorities for tallying, which corresponds to a centralised topology. The final step of end-to-end verification is the only distributed phase, because it can be carried out independently by all voters once the authorities have published the required material.

While Helios is as such an online voting protocol employing a central web server to receive ballots and produce the tally, other protocols do not require such a server as they omit an authority. A selection is presented hereafter.

Secure Multiparty

Computations

The aim of Secure Multiparty Computations (SMC) is to compute collectively a joint function over the private inputs of all participants. The correctness and secrecy properties rely on cryptography [24]. It seems to be an appropriate technique to compute the tally from the individual, secret ballots. However, several issues render an implementation of a decentralised voting protocol based on this scheme difficult. As [10] points out, the communication complexity for $n$ participants is $\mathcal{O}\left(n^{2}\right)$, or in the case of the existence of a trusted party, $\mathcal{O}\left(n\right)$. Both render the scheme impractical for large-scale distributed online voting. Though, SMC is suited for boardroom voting protocols with only few voters.

Furthermore, the employed cryptography is computationally extensive and provides often only computational instead of information-theoretic security.

Scalable and Secure Aggregation

Protocol

An intermediate solution between a centralised online voting protocol based on cryptography and an aggregation by the voters is given with Scalable and Secure Aggregation (SPP) [10]. Voters are grouped using a chord overlay into clusters of equal size in order to partition potential dishonest voters. The clusters are then arranged in a binary tree structure (Fig. 2 (b)). Voters assigned to the root cluster have to create a key pair for homomorphic public-key cryptography. Thus, a $(k,n)$-threshold decryption key pair is jointly created using a distributed key generation protocol. While the private key parts are distributed among the members of the root cluster, the public key is communicated to all child clusters in the tree.

Every voter encrypts its ballot and adds a non-interactive zero-knowledge-proof to back the validity of its vote. Encrypted ballots are gathered from voters in the same cluster to compute an intermediate aggregate for the cluster. From the tree leaves, aggregates are passed to all members of the parent cluster, who compute first the sub-tree aggregate taking into account the own aggregate and those of its child, and pass the result to all members of the parent cluster. By majority rule, voters decide in case of diverging results which aggregate has to be used for the computation.

At some point, the root cluster will possess the encrypted final tally of all ballots. A union of $k$ voters will carry out the joint decryption algorithm to compute the final tally that is subsequently propagated down the tree to all voters.

Even though all voters are involved in the aggregation procedure, the parity of knowledge is not given. The voters in the root cluster correspond effectively to randomly determined, trusted voting officers in a centralised protocol, that cannot be flexibly exchanged after the key pair generation.

Decentralised Polling

Another technique to realise distributed online voting is based on secret sharing schemes. A corresponding protocol known as Decentralised Polling (DPol) is described in [12]. $n$ voters are grouped to clusters of size $\sqrt{n}$. The clusters form a ring, so that each cluster has one preceding and one succeeding cluster (Fig. 2 (a)). Every voter gets accorded $2k+1$ recipient voters from the succeeding cluster and is itself recipient to $2k+1$ voters from the preceding cluster. $k$ is a privacy parameter. A ballot for a particular option from a set of size $d$ is represented by a vector in $\{0,1\}^{d}$. The voter issues then $2k+1$ vectors, $k+1$ towards its choice and $k$ for others. The vectors are distributed among the receivers. In the next step, received vectors are summed up and the result is exchanged with other voters of the same cluster in order to compute the tally for the preceding cluster. The tallies are then communicated to the succeeding clusters in the ring until every cluster is in possession of all the cluster tallies such that the final tally can be computed by every voter.

It is remarkable, that this scheme provides secrecy of the ballot without the employment of cryptography. The protocol authors describe means to determine dishonest voters with high probability without false-positives and tag them accordingly, e.g. in a public social network profile.

Few extensions have been proposed, among them EPol [14], that generalises the DPol voting system in such a manner, that the actual social graph structure (with some assumptions) can be used and a ring social net overlay and a perfect square voter number is not a prerequisite anymore.

Both DPol and EPol provide for equipotent voters. The aggregation is a joint effort in which all voters are involved. Every voter computes the final tally and then the voting result. Similar to the SPP protocol, intermediate aggregates are employed to keep the information on individual ballots local in the overlay.

Blockchain-based Voting

Systems

Online voting based on Bitcoin technology, namely the global consensus algorithm given by its blockchain, is eagerly anticipated by some groups. Various prototypes and commercial solutions are or have been developed222https://github.com/domschiener/publicvotes, http://votem.com, http://www.bitcongress.org, http://followmyvote.com, http://cryptovoter.com, http://votosocial.github.io. However, the actual protocols are either lacking essential properties or remain obscure. Scientific results are very sparse. [25] present a protocol for a binary vote that requires a monetary deposit and a funding of the winner by all voters. Transactions to the winner and voter payback is controlled due to contracts enforced by the distributed network which limits the flexibility of the ballot.

To the author’s knowledge, most other approaches to online voting using Bitcoin are based on so-called coloured coins that allow to associate digital assets to Bitcoin addresses. Consequently, asset ownership can be traded like the Bitcoin currency and (pseudonymous) ownership is publicly verifiable by following the previous asset transactions.

To construct an online voting protocol, every voter must initially own a coloured coin representing its eligibility. Those coins are then transferred to a destination that corresponds to e.g. a candidate. Transactions are publicly verifiable, so that aggregation and evaluation can be carried out by every voter. Though, the publicity of all transactions endangers the secrecy of the ballot, because coins can be linked back to the voter that has been identified during the registration phase to receive its coin.

Different protocols have been proposed to provide anonymous Bitcoin transactions \autocitesmiers2013ibrahim2016 that are considered to ensure secrecy of the ballot in blockchain-based online voting. Also blind signatures may permit to distribute coins anonymously to voters. In that case, the protocol approaches the Anonymous Voting concept (c.f. Sec. 3). The authority carrying out the aggregation is hereby replaced by the distributed blockchain that serves as a public add-only bulletin board to log casted ballots. Consequently, tallying and verification can be carried out by every voter. The distributed topology is inherited from Bitcoin which uses gossiping to spread transactions (Fig. 2 (d)). Transactions are then gathered into blocks by voters or third parties that seek to confirm transactions. Every voter can as its own discretion engage in the confirmation procedure. There is no specialisation of voters.

It turns out that blockchain-based and paper-based voting are on par with respect to the notions of distribution and qualify both as fully distributed, c.f. Tab. 1.

7 CONCLUSION

Major votings in 2016, e.g. the Brexit referendum or the US presidential elections, demonstrated the importance of a high voter turnout for the legitimacy of the outcome, especially in the case of tight outcomes.

While online voting is generally considered with much hesitation, advances in technology are eroding the security of paper-based voting. Coercion-freeness, in the past a major argument for on-site ballot casting, is at stake due to omnipresent smart phone cameras. Exit polls on social media allow voters casting their ballot very late a more informed choice, which harms the fairness. More and more voters use early postal voting sacrificing thus their means of verification and the potential to change their vote last minute. Meanwhile, many online voting protocols seek to achieve those security properties that paper-based voting with optional postal voting can ensure less and less.

In this situation, distributed online voting offers a promising perspective. It does not assume a trusted authority and the integrity of the voting is enforced by the voters themselves. Without a weakest link, votings are difficult to interrupt. The damage in case of security breaches is locally bounded thanks to the distribution of data. Like in all online voting protocols, voting becomes more convenient, especially as ballots can be casted from remote. We acknowledge that still trust in technology or expert knowledge is assumed and leave it as an open issue.

So far, only few distributed online voting protocols have been proposed and even less are fully distributed. We hope to see more proposals in the future and plan to contribute to this subject with a novel fully distributed protocol. This work in progress follows the Anonymous Voting concept and uses techniques from BitTorrent to create a voter overlay network and from Bitcoin to ensure verifiability. Similar to DPol, secrecy is provided by a particular sharing scheme instead of cryptography. To achieve logarithmique complexity, it is based like SPP on a tree overlay network. Unlike in SPP, no decryption step is needed. Hence, all voters are equipotent.

ACKNOWLEDGEMENTS

The authors wish to thank Stéphane Frénot, Damien Reimert and Aurélien Faravelon for fruitful discussions on distributed voting protocols.