Andreas Vogt

Accountability: definition and relationship to verifiability

Many cryptographic tasks and protocols, such as non-repudiation, contract-signing, voting, auction, identity-based encryption, and certain forms of secure multi-party computation, involve the use of (semi-)trusted parties, such as notaries and authorities. It is crucial that such parties can be held accountable in case they misbehave as this is a strong incentive for such parties to follow the protocol. Unfortunately, there does not exist a general and convincing definition of accountability that would allow to assess the level of accountability a protocol provides. In this paper, we therefore propose a new, widely applicable definition of accountability, with interpretations both in symbolic and computational models. Our definition reveals that accountability is closely related to verifiability, for which we also propose a new definition. We prove that verifiability can be interpreted as a weak form of accountability. Our findings on verifiability are of independent interest. As a proof of concept, we apply our definitions to the analysis of protocols for three different tasks: contract-signing, voting, and auctions. Our analysis unveils some subtleties and unexpected weaknesses, showing in one case that the protocol is unusable in practice. However, for this protocol we propose a fix to establish a reasonable level of accountability.

Clash Attacks on the Verifiability of E-Voting Systems

Verifiability is a central property of modern e-voting systems. Intuitively, verifiability means that voters can check that their votes were actually counted and that the published result of the election is correct, even if the voting machines/authorities are (partially) untrusted. In this paper, we raise awareness of a simple attack, which we call a clash attack, on the verifiability of e-voting systems. The main idea behind this attack is that voting machines manage to provide different voters with the same receipt. As a result, the voting authorities can safely replace ballots by new ballots, and by this, manipulate the election without being detected. This attack does not seem to have attracted much attention in the literature. Even though the attack is quite simple, we show that, under reasonable trust assumptions, it applies to several e-voting systems that have been designed to provide verifiability. In particular, we show that it applies to the prominent Three Ballot and VAV voting systems as well as to two e-voting systems that have been deployed in real elections: the Wombat Voting system and a variant of the Helios voting system. We discuss countermeasures for each of these systems and for (various variants of) Helios provide a formal analysis based on a rigorous definition of verifiability. More precisely, our analysis of Helios is with respect to the more general and in the area of e-voting often overlooked notion of accountability.

A Game-Based Definition of Coercion-Resistance and Its Applications

Coercion-resistance is one of the most important and intricate security requirements for voting protocols. Several definitions of coercion-resistance have been proposed in the literature, both in cryptographic settings and more abstract, symbolic models. However, unlike symbolic approaches, only very few voting protocols have been rigorously analyzed within the cryptographic setting. A major obstacle is that existing cryptographic definitions of coercion-resistance tend to be complex and limited in scope: They are often tailored to specific classes of protocols or are too demanding. In this paper, we therefore present a simple and intuitive, yet widely applicable cryptographic definition of coercionresistance, in the style of game-based definitions. This definition allows to precisely measure the level of coercion-resistance a protocol provides. As a proof of concept, we apply our definition to two voting systems, namely, the Bingo voting system and ThreeBallot. The results we obtain are out of the scope of existing approaches. We show that the Bingo voting system provides the same level of coercion-resistance as an ideal voting system. We also precisely measure the degradation of coercion-resistance of ThreeBallot in case the so-called short ballot assumption does not hold and show that the level of coercion-resistance ThreeBallot provides is significantly lower than that of an ideal system, even in case of short ballots.

Verifiability, Privacy, and Coercion-Resistance: New Insights from a Case Study

In this paper, we present new insights into central properties of voting systems, namely verifiability, privacy, and coercion-resistance. We demonstrate that the combination of the two forms of verifiability considered in the literature -- individual and universal verifiability -- are, unlike commonly believed, insufficient to guarantee overall verifiability. We also demonstrate that the relationship between coercion-resistance and privacy is more subtle than suggested in the literature. Our findings are partly based on a case study of prominent voting systems, Three Ballot and VAV, for which, among others, we show that, unlike commonly believed, they do not provide any reasonable level of verifiability, even though they satisfy individual and universal verifiability. Also, we show that the original variants of Three Ballot and VAV provide a better level of coercion-resistance than of privacy.

Proving coercion-resistance of scantegrity II

By now, many voting protocols have been proposed that, among others, are designed to achieve coercion-resistance, i.e., resistance to vote buying and voter coercion. Scantegrity II is among the most prominent and successful such protocols in that it has been used in several elections. However, almost none of the modern voting protocols used in practice, including Scantegrity II, has undergone a rigorous cryptographic analysis. In this paper, we prove that Scantegrity II enjoys an optimal level of coercion-resistance, i.e., the same level of coercion-resistance as an ideal voting protocol (which merely reveals the outcome of the election), except for so-called forced abstention attacks. This result is obtained under the (necessary) assumption that the workstation used in the protocol is honest. Our analysis is based on a rigorous cryptographic definition of coercionresistance we recently proposed. We argue that this definition is in fact the only existing cryptographic definition of coercion-resistance suitable for analyzing Scantegrity II. Our case study should encourage and facilitate rigorous cryptographic analysis of coercion-resistance also for other voting protocols used in practice.

Formal Analysis of Chaumian Mix Nets with Randomized Partial Checking

Mix nets with randomized partial checking (RPC mix nets) have been introduced by Jakobsson, Juels, and Rivest as particularly simple and efficient verifiable mix nets. These mix nets have been used in several implementations of prominent e-voting systems to provide vote privacy and verifiability. In RPC mix nets, higher efficiency is traded for a lower level of privacy and verifiability. However, these mix nets have never undergone a rigorous formal analysis. Recently, Kahazei and Wikstroem even pointed out several severe problems in the original proposal and in implementations of RPC mix nets in e-voting systems, both for so-called re-encryption and Chaumian RPC mix nets. While Kahazei and Wikstroem proposed several fixes, the security status of Chaumian RPC mix nets (with the fixes applied) has been left open, re-encryption RPC mix nets, as they suggest, should not be used at all. In this paper, we provide the first formal security analysis of Chaumian RPC mix nets. We propose security definitions that allow one to measure the level of privacy and verifiability RPC mix nets offer, and then based on these definitions, carry out a rigorous analysis. Altogether, our results show that these mix nets provide a reasonable level of privacy and verifiability, and that they are still an interesting option for the use in e-voting systems.

A game-based definition of coercion resistance and its applications

Coercion-resistance is one of the most important and intricate security requirements for voting protocols. Several definitions of coercion-resistance have been proposed in the literature, both in cryptographic settings and more abstract, symbolic models. However, unlike symbolic approaches, only very few voting protocols have been rigorously analyzed within the cryptographic setting. A major obstacle is that existing cryptographic definitions of coercion-resistance tend to be complex and limited in scope: They are often tailored to specific classes of protocols or are too demanding. In this paper, we therefore present a simple and intuitive, yet widely applicable cryptographic definition of coercionresistance, in the style of game-based definitions. This definition allows to precisely measure the level of coercion-resistance a protocol provides. As a proof of concept, we apply our definition to two voting systems, namely, the Bingo voting system and ThreeBallot. The results we obtain are out of the scope of existing approaches. We show that the Bingo voting system provides the same level of coercion-resistance as an ideal voting system. We also precisely measure the degradation of coercion-resistance of ThreeBallot in case the so-called short ballot assumption does not hold and show that the level of coercion-resistance ThreeBallot provides is significantly lower than that of an ideal system, even in case of short ballots.

Improving and Simplifying a Variant of Prêt à Voter

Recently, Xia et al. proposed a variant of Pret a Voter which enjoys several attractive properties. Their protocol is among the few verifiable and receipt-free paper-based voting protocols resistant against randomization attacks. Trust is distributed among several authorities and the voter interface is relatively simple. Also, approval and ranked elections are supported. In this paper, we improve and simplify the protocol by Xia et al. Among others, we propose a simpler way of producing ballots, which only involves the encryption and re-encryption of candidate names; homomorphic encryption and proxy re-encryption are not needed. Also, no machine involved in the production of ballots needs to store a secret key. Moreover, unlike the protocol by Xia et al., in our protocol all authorities can be held accountable in case they misbehave in an observable way.

On Bounded Universal Functions

We investigate boundedness properties of functions that are universal with respect to translations and “multiplicative translations”. It is well known that there exist entire functions which are universal in the sense of Birkhoff and are bounded on every line. We prove a negative result for multiplicative universal functions.