arXiv subjects

Julian Loss

Publications and source records attributed to Julian Loss.

3 recordsLinked to original sources

arXiv2026

Early-Stabilizing Counting

Synchronous Counting is the task of reaching agreement on a common round counter in a synchronous system of $n$ nodes with up to $t$ Byzantine faults in a self-stabilizing manner. That is, after transient faults may have arbitrarily corrupted the system state and ceased, the at least $n-t$ non-faulty nodes need to (re-)establish that (i) their local outputs are identical and (ii) increase by $1$ modulo $C$ in each round. An overhead-free reduction from consensus shows that all known lower bounds and impossibilities for consensus carry over to the counting problem. In the other direction, prior work has established that a consensus algorithm $\mathcal{A}$ can be turned into a counting algorithm at small overhead relative to the running time and bit complexity of $\mathcal{A}$, without losing resilience. Taking inspiration from early-stopping consensus protocols, in this work we introduce the concept of early stabilization. That is, if there are $0\le f\le t$ (persistent) faults in an execution, the algorithm should stabilize in a number of rounds that depends on $f$ only. Likewise, we seek to achieve an amortized bit complexity that is adaptive in the number of actual faults $f$. By developing a number of modular building blocks suitable to these goals, we develop a $C$-counting algorithm that stabilizes within asymptotically optimal $O(f+1)$ rounds, has message size $O(\log^2 n + \log C)$, and has amortized bit complexity $O(n(f\log C +\log^2 n))$.

cs.DC↗

arXiv2022

Optimal Clock Synchronization with Signatures

Cryptographic signatures can be used to increase the resilience of distributed systems against adversarial attacks, by increasing the number of faulty parties that can be tolerated. While this is well-studied for consensus, it has been underexplored in the context of fault-tolerant clock synchronization, even in fully connected systems. Here, the honest parties of an $n$-node system are required to compute output clocks of small skew (i.e., maximum phase offset) despite local clock rates varying between $1$ and $\vartheta>1$, end-to-end communication delays varying between $d-u$ and $d$, and the interference from malicious parties. So far, it is only known that clock pulses of skew $d$ can be generated with (trivially optimal) resilience of $\lceil n/2\rceil-1$ (PODC `19), improving over the tight bound of $\lceil n/3\rceil-1$ holding without signatures for \emph{any} skew bound (STOC `84, PODC `85). Since typically $d\gg u$ and $\vartheta-1\ll 1$, this is far from the lower bound of $u+(\vartheta-1)d$ that applies even in the fault-free case (IPL `01). We prove matching upper and lower bounds of $\Theta(u+(\vartheta-1)d)$ on the skew for the resilience range from $\lceil n/3\rceil$ to $\lceil n/2\rceil-1$. The algorithm showing the upper bound is, under the assumption that the adversary cannot forge signatures, deterministic. The lower bound holds even if clocks are initially perfectly synchronized, message delays between honest nodes are known, $\vartheta$ is arbitrarily close to one, and the synchronization algorithm is randomized. This has crucial implications for network designers that seek to leverage signatures for providing more robust time. In contrast to the setting without signatures, they must ensure that an attacker cannot easily bypass the lower bound on the delay on links with a faulty endpoint.

cs.DC↗

arXiv2020

Network-Agnostic State Machine Replication

We study the problem of state machine replication (SMR)---the underlying problem addressed by blockchain protocols---in the presence of a malicious adversary who can corrupt some fraction of the parties running the protocol. Existing protocols for this task assume either a synchronous network (where all messages are delivered within some known time $Δ$) or an asynchronous network (where messages can be delayed arbitrarily). Although protocols for the latter case give seemingly stronger guarantees, this is not the case since they (inherently) tolerate a lower fraction of corrupted parties. We design an SMR protocol that is network-agnostic in the following sense: if it is run in a synchronous network, it tolerates $t_s$ corrupted parties; if the network happens to be asynchronous it is resilient to $t_a \leq t_s$ faults. Our protocol achieves optimal tradeoffs between $t_s$ and $t_a$.

cs.CR↗