Alexander Russell

Benjamin Fuller, Abigail Harrison, Alexander Russell

Risk-limiting audits (RLAs) are post-election auditing procedures that rigorously guarantee a specified maximum probability that an incorrect electoral outcome will not be detected. Aside from ready access to physical ballots, known RLAs require a software-independent accounting of the sizes of each ballot batch, called a ballot manifest. While typical electoral procedures automatically provide rough estimates for batch sizes, even slight inaccuracies (commensurate with the margin of the contest under audit) completely invalidate conventional RLAs (Lindeman et al., EVT 2012). Thus, establishing a sufficiently accurate manifest often requires handling every ballot and can be the dominant cost of conducting the RLA. We propose two new risk-limiting techniques: 1) A statistical mechanism for ensuring that the batch sizes reported by an untrusted tabulation are, in fact, an accurate manifest; this effectively bootstraps from a rough manifest to an accurate one with sublinear effort. 2) We propose a new class of RLAs called direct ballot selection. This method reverses the traditional comparison procedure and compares uniformly selected ballots against their cast vote records, requiring a new statistical test for identifier duplication but efficiently supporting elections without in order identifiers. These techniques reduce the complexity of RLAs across many elections. Our two main findings are as follows: 1) The time to create a manifest can be drastically reduced with a modest increase in the number of ballots sampled in the audit. At a 3% margin and a large population, there is a reduction in the overall audit time of at least an order of magnitude across methods. 2) Direct ballot selection improves over state-of-the-art polling for small margins. For Connecticut (29th in population) at a 1% margin, it beats Minerva (Security 2022) by 55% in ballot sample complexity.

Benjamin Fuller, Abigail Harrison, Alexander Russell

Risk-limiting audits (RLAs) are rigorous statistical procedures meant to detect invalid election results. RLAs examine paper ballots cast during the election to statistically assess the possibility of a disagreement between the winner determined by the ballots and the winner reported by tabulation. The most ballot efficient approaches proceed by "ballot comparison." However, ballot comparison requires an untrusted declaration of the contents of each cast ballot, rather than a simple tabulation of vote totals. This "cast-vote record table" (CVR) is then spot-checked against ballots for consistency. In many practical settings, the cost of generating a suitable CVR dominates the cost of conducting the audit, preventing widespread adoption of these sample-efficient techniques. We introduce a new RLA procedure: an "adaptive ballot comparison" audit. In this audit, a global CVR is never produced; instead, a three-stage procedure is iterated: 1) a batch is selected, 2) a CVR is produced for that batch, and 3) a ballot within the batch is sampled, inspected by auditors, and compared with the CVR. We prove that such an audit can achieve risk commensurate with standard comparison audits while generating a fraction of the CVR. We present three main contributions: 1) a formal adversarial model for RLAs; 2) definition and analysis of an adaptive audit procedure with rigorous risk limits and an associated correctness analysis accounting for the incidental errors arising in typical audits; and 3) an analysis of practical efficiency. This method can be organized in rounds (as is typical for comparison audits) where sampled CVRs are produced in parallel. Using data from Florida's 2020 presidential election with 5% risk and 1% margin, only 22% of the CVR is generated; at 10% margin, only 2% is generated.

Aggelos Kiayias, Saad Quader, Alexander Russell

We improve the fundamental security threshold of eventual consensus Proof-of-Stake (PoS) blockchain protocols under the longest-chain rule by showing, for the first time, the positive effect of rounds with concurrent honest leaders. Current security analyses reduce consistency to the dynamics of an abstract, round-based block creation process that is determined by three events associated with a round: (i) event $A$: at least one adversarial leader, (ii) event $S$: a single honest leader, and (iii) event $M$: multiple, but honest, leaders. We present an asymptotically optimal consistency analysis assuming that an honest round is more likely than an adversarial round (i.e., $\Pr[S] + \Pr[M] > \Pr[A]$); this threshold is optimal. This is a first in the literature and can be applied to both the simple synchronous communication as well as communication with bounded delays. In all existing consistency analyses, event $M$ is either penalized or treated neutrally. Specifically, the consistency analyses in Ouroboros Praos (Eurocrypt 2018) and Genesis (CCS 2018) assume that $\Pr[S] - \Pr[M] > \Pr[A]$; the analyses in Sleepy Consensus (Asiacrypt 2017) and Snow White (Fin. Crypto 2019) assume that $\Pr[S] > \Pr[A]$. Moreover, all existing analyses completely break down when $\Pr[S] < \Pr[A]$. These thresholds determine the critical trade-off between the honest majority, network delays, and consistency error. Our new results can be directly applied to improve the security guarantees of the existing protocols. We also provide an efficient algorithm to explicitly calculate these error probabilities in the synchronous setting. Furthermore, we complement these results by analyzing the setting where $S$ is rare, even allowing $\Pr[S] = 0$, under the added assumption that honest players adopt a consistent chain selection rule.

Erica Blum, Aggelos Kiayias, Cristopher Moore et al.

The blockchain data structure maintained via the longest-chain rule---popularized by Bitcoin---is a powerful algorithmic tool for consensus algorithms. Such algorithms achieve consistency for blocks in the chain as a function of their depth from the end of the chain. While the analysis of Bitcoin guarantees consistency with error $2^{-k}$ for blocks of depth $O(k)$, the state-of-the-art of proof-of-stake (PoS) blockchains suffers from a quadratic dependence on $k$: these protocols, exemplified by Ouroboros (Crypto 2017), Ouroboros Praos (Eurocrypt 2018) and Sleepy Consensus (Asiacrypt 2017), can only establish that depth $Θ(k^2)$ is sufficient. Whether this quadratic gap is an intrinsic limitation of PoS---due to issues such as the nothing-at-stake problem---has been an urgent open question, as deployed PoS blockchains further rely on consistency for protocol correctness. We give an axiomatic theory of blockchain dynamics that permits rigorous reasoning about the longest-chain rule and achieve, in broad generality, $Θ(k)$ dependence on depth in order to achieve consistency error $2^{-k}$. In particular, for the first time, we show that PoS protocols can match proof-of-work protocols for linear consistency. We analyze the associated stochastic process, give a recursive relation for the critical functionals of this process, and derive tail bounds in both i.i.d. and martingale settings via associated generating functions.

Gorjan Alagic, Christian Majenz, Alexander Russell

We consider the problem of efficiently simulating random quantum states and random unitary operators, in a manner which is convincing to unbounded adversaries with black-box oracle access. This problem has previously only been considered for restricted adversaries. Against adversaries with an a priori bound on the number of queries, it is well-known that $t$-designs suffice. Against polynomial-time adversaries, one can use pseudorandom states (PRS) and pseudorandom unitaries (PRU), as defined in a recent work of Ji, Liu, and Song; unfortunately, no provably secure construction is known for PRUs. In our setting, we are concerned with unbounded adversaries. Nonetheless, we are able to give stateful quantum algorithms which simulate the ideal object in both settings of interest. In the case of Haar-random states, our simulator is polynomial-time, has negligible error, and can also simulate verification and reflection through the simulated state. This yields an immediate application to quantum money: a money scheme which is information-theoretically unforgeable and untraceable. In the case of Haar-random unitaries, our simulator takes polynomial space, but simulates both forward and inverse access with zero error. These results can be seen as the first significant steps in developing a theory of lazy sampling for random quantum objects.

Gorjan Alagic, Christian Majenz, Alexander Russell et al.

Formulating and designing authentication of classical messages in the presence of adversaries with quantum query access has been a longstanding challenge, as the familiar classical notions of unforgeability do not directly translate into meaningful notions in the quantum setting. A particular difficulty is how to fairly capture the notion of "predicting an unqueried value" when the adversary can query in quantum superposition. We propose a natural definition of unforgeability against quantum adversaries called blind unforgeability. This notion defines a function to be predictable if there exists an adversary who can use "partially blinded" oracle access to predict values in the blinded region. We support the proposal with a number of technical results. We begin by establishing that the notion coincides with EUF-CMA in the classical setting and go on to demonstrate that the notion is satisfied by a number of simple guiding examples, such as random functions and quantum-query-secure pseudorandom functions. We then show the suitability of blind unforgeability for supporting canonical constructions and reductions. We prove that the "hash-and-MAC" paradigm and the Lamport one-time digital signature scheme are indeed unforgeable according to the definition. To support our analysis, we additionally define and study a new variety of quantum-secure hash functions called Bernoulli-preserving. Finally, we demonstrate that blind unforgeability is stronger than a previous definition of Boneh and Zhandry [EUROCRYPT '13, CRYPTO '13] in the sense that we can construct an explicit function family which is forgeable by an attack that is recognized by blind-unforgeability, yet satisfies the definition by Boneh and Zhandry.

Gorjan Alagic, Alexander Russell

Recent results of Kaplan et al., building on previous work by Kuwakado and Morii, have shown that a wide variety of classically-secure symmetric-key cryptosystems can be completely broken by quantum chosen-plaintext attacks (qCPA). In such an attack, the quantum adversary has the ability to query the cryptographic functionality in superposition. The vulnerable cryptosystems include the Even-Mansour block cipher, the three-round Feistel network, the Encrypted-CBC-MAC, and many others. In this work, we study simple algebraic adaptations of such schemes that replace $(\mathbb Z/2)^n$ addition with operations over alternate finite groups--such as $\mathbb Z/{2^n}$--and provide evidence that these adaptations are qCPA-secure. These adaptations furthermore retain the classical security properties (and basic structural features) enjoyed by the original schemes. We establish security by treating the (quantum) hardness of the well-studied Hidden Shift problem as a basic cryptographic assumption. We observe that this problem has a number of attractive features in this cryptographic context, including random self-reducibility, hardness amplification, and--in many cases of interest--a reduction from the "search version" to the "decisional version." We then establish, under this assumption, the qCPA-security of several such Hidden Shift adaptations of symmetric-key constructions. We show that a Hidden Shift version of the Even-Mansour block cipher yields a quantum-secure pseudorandom function, and that a Hidden Shift version of the Encrypted CBC-MAC yields a collision-resistant hash function. Finally, we observe that such adaptations frustrate the direct Simon's algorithm-based attacks in more general circumstances, e.g., Feistel networks and slide attacks.