Permissionless distributed ledgers, such as those arising from blockchain protocols, have been touted as the centerpiece of an upcoming security-critical information technology infrastructure. Their basic properties-consistency and liveness-can be guaranteed under specific constraints on the resources available to an adversary relative to the resources of the participants that follow the protocol. Given their permissionless participation convention and their intended long-livedness, a critical open security question is their behavior-and potential resilience-to temporary spikes in adversarial resources. In this work we give the first thorough treatment of the self-healing properties of Nakamoto ledgers, addressing both proof-of-work (PoW) and proof-of-stake (PoS) protocols. First, we present a unified model that allows us to define self-healing for both of these protocol classes. Then we provide a formal analysis establishing self-healing with respect to both consistency and liveness in both classes, quantifying the resulting vulnerability period as a function of the magnitude of the spike. Finally, we provide numerical simulations giving explicit quantitative bounds relevant for practice.

We study the problem of committee selection in the context of proof-of-stake consensus mechanisms or distributed ledgers. These settings determine a family of participating parties---each of which has been assigned a non-negative ''stake''---and are subject to an adversary that may corrupt a subset of the parties. The challenge is to select a committee of participants that accurately reflects the proportion of corrupt and honest parties, as measured by stake, in the full population. The trade-off between committee size and the probability of selecting a committee that over-represents the corrupt parties is a fundamental factor in both security and efficiency of proof-of-stake consensus, as well as committee-run layer-two protocols.

Nakamoto proof-of-work ledger consensus currently underlies the majority of deployed cryptocurrencies and smart-contract blockchains. While a long and fruitful line of work has succeeded to identify its exact security region---that is, the set of parametrizations under which it possesses asymptotic security---the existing theory does not provide concrete settlement time guarantees that are tight enough to inform practice.

We establish the optimal security threshold for the Bitcoin protocol in terms of adversarial hashing power, honest hashing power, and network delays. Specifically, we prove that the protocol is secure if [ra < 1/Δ0 + 1/rh,,] where rh is the expected number of honest proof-of-work successes in unit time, ra is the expected number of adversarial successes, and no message is delayed by more than Δ0 time units. In this regime, the protocol guarantees consistency and liveness with exponentially decaying failure probabilities. Outside this region, the simple private chain attack prevents consensus. Our analysis immediately applies to any Nakamoto-style proof-of-work protocol; in the full version of this paper we also present the adaptations needed to apply it in the proof-of-stake setting, establishing a similar threshold there.

Sidechains have long been heralded as the key enabler of blockchain scalability and interoperability. However, no modeling of the concept or a provably secure construction has so far been attempted. We provide the first formal definition of what a sidechain system is and how assets can be moved between sidechains securely. We put forth a security definition that augments the known transaction ledger properties of liveness and safety to hold across multiple ledgers and enhance them with a new “firewall” security property which safeguards each blockchain from its sidechains, limiting the impact of an otherwise catastrophic sidechain failure. We then provide a sidechain construction that is suitable for proof-of-stake (PoS) sidechain systems. As an exemplary concrete instantiation we present our construction for an epoch- based PoS system consistent with Ouroboros (Crypto 2017), the PoS blockchain protocol used in Cardano which is one of the largest pure PoS systems by market capitalisation, and we also comment how the construction can be adapted for other protocols such as Ouroboros Praos (Eurocrypt 2018), Ouroboros Genesis (CCS 2018), Snow White and Algorand. An important feature of our construction is merged-staking that prevents “goldfinger” attacks against a sidechain that is only carrying a small amount of stake. An important technique for pegging chains that we use in our construction is cross-chain certification which is facilitated by a novel cryptographic primitive we introduce called ad-hoc threshold multisignatures (ATMS) which may be of independent interest. We show how ATMS can be securely instantiated by regular and aggregate digital signatures as well as succinct arguments of knowledge such as STARKs and bulletproofs with varying degrees of storage efficiency.

Cryptographic security is usually defined as a guarantee that holds except when a bad event with negligible probability occurs, and nothing is guaranteed in that bad case. However, in settings where such failure can happen with substantial probability, one needs to provide guarantees even for the bad case. A typical example is where a (possibly weak) password is used instead of a secure cryptographic key to protect a session, the bad event being that the adversary correctly guesses the password. In a situation with multiple such sessions, a per-session guarantee is desired: any session for which the password has not been guessed remains secure, independently of whether other sessions have been compromised. A new formalism for stating such gracefully degrading security guarantees is introduced and applied to analyze the examples of password-based message authentication and password-based encryption. While a natural per-message guarantee is achieved for authentication, the situation of password-based encryption is more delicate: a per-session confidentiality guarantee only holds against attackers for which the distribution of password-guessing effort over the sessions is known in advance. In contrast, for more general attackers without such a restriction, a strong, composable notion of security cannot be achieved.

We show attacks on five data-independent memory-hard functions (iMHF) that were submitted to the password hashing competition (PHC). Informally, an MHF is a function which cannot be evaluated on dedicated hardware, like ASICs, at significantly lower hardware and/or energy cost than evaluating a single instance on a standard single-core architecture. Data-independent means the memory access pattern of the function is independent of the input; this makes iMHFs harder to construct than data-dependent ones, but the latter can be attacked by various side-channel attacks.

We present a novel Proof-of-Stake (PoS) protocol, Ouroboros Genesis, that enables parties to safely join (or rejoin) the protocol execution using only the genesis block information. Prior to our work, PoS protocols either required parties to obtain a trusted "checkpoint" block upon joining and, furthermore, to be frequently online or required an accurate estimate of the number of online parties to be hardcoded into the protocol logic. This ability of new parties to "bootstrap from genesis" was a hallmark property of the Bitcoin blockchain and was considered an important advantage of PoW-based blockchains over PoS-based blockchains since it facilitates robust operation in a setting with dynamic availability, i.e., the natural setting---without external trusted objects such as checkpoint blocks---where parties come and go arbitrarily, may join at any moment, or remain offline for prolonged periods of time. We prove the security of Ouroboros Genesis against a fully adaptive adversary controlling less than half of the total stake in a partially synchronous network with unknown message delay and unknown, varying levels of party availability. Our security proof is in the Universally Composable setting assuming the most natural abstraction of a hash function, known as the strict Global Random Oracle (ACM-CCS 2014); this highlights an important advantage of PoS blockchains over their PoW counterparts in terms of composability with respect to the hash function formalisation: rather than a strict GRO, PoW-based protocol security requires a "local" random oracle. Finally, proving the security of our construction against an adaptive adversary requires a novel martingale technique that may be of independent interest in the analysis of blockchain protocols.

Secret-key constructions are often proved secure in a model where one or more underlying components are replaced by an idealized oracle accessible to the attacker. This model gives rise to information-theoretic security analyses, and several advances have been made in this area over the last few years. This paper provides a systematic overview of what is achievable in this model, and how existing works fit into this view.

Most cryptographic security proofs require showing that two systems are indistinguishable. A central tool in such proofs is that of a game, where winning the game means provoking a certain condition, and it is shown that the two systems considered cannot be distinguished unless this condition is provoked. Upper bounding the probability of winning such a game, i.e., provoking this condition, for an arbitrary strategy is usually hard, except in the special case where the best strategy for winning such a game is known to be non-adaptive. A sufficient criterion for ensuring the optimality of non-adaptive strategies is that of conditional equivalence to a system, a notion introduced in [1]. In this paper, we show that this criterion is not necessary to ensure the optimality of non-adaptive strategies by giving two results of independent interest: 1) the optimality of non-adaptive strategies is not preserved under parallel composition; 2) in contrast, conditional equivalence is preserved under parallel composition.