Optimal Clock Synchronization with Signatures

03/04/2022
by   Christoph Lenzen, et al.
0

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 ϑ>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 ⌈ n/2⌉-1 (PODC `19), improving over the tight bound of ⌈ n/3⌉-1 holding without signatures for any skew bound (STOC `84, PODC `85). Since typically d≫ u and ϑ-1≪ 1, this is far from the lower bound of u+(ϑ-1)d that applies even in the fault-free case (IPL `01). We prove matching upper and lower bounds of Θ(u+(ϑ-1)d) on the skew for the resilience range from ⌈ n/3⌉ to ⌈ n/2⌉-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, ϑ 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.

READ FULL TEXT

page 1

page 2

page 3

page 4

research
07/13/2018

A Tight Lower Bound for Clock Synchronization in Odd-Ary M-Toroids

Synchronizing clocks in a distributed system in which processes communic...
research
09/10/2018

Resilience Bounds of Sensing-Based Network Clock Synchronization

Recent studies exploited external periodic synchronous signals to synchr...
research
02/21/2019

Fault Tolerant Gradient Clock Synchronization

Synchronizing clocks in distributed systems is well-understood, both in ...
research
05/15/2020

Time- and Space-Optimal Clock Synchronization in the Beeping Model

We consider the clock synchronization problem in the (discrete) beeping ...
research
05/18/2023

Fault-Tolerant Consensus in Quantum Networks

Fault-tolerant consensus is about reaching agreement on some of the inpu...
research
10/03/2020

TRIX: Low-Skew Pulse Propagation for Fault-Tolerant Hardware

The vast majority of hardware architectures use a carefully timed refere...
research
12/21/2018

Quantifying the Security of Recognition Passwords: Gestures and Signatures

Gesture and signature passwords are two-dimensional figures created by d...

Please sign up or login with your details

Forgot password? Click here to reset