Committing to quantum resistance: a slow defence for Bitcoin against a fast quantum computing attack.

Quantum computers are expected to have a dramatic impact on numerous fields due to their anticipated ability to solve classes of mathematical problems much more efficiently than their classical counterparts. This particularly applies to domains involving integer factorization and discrete logarithms, such as public key cryptography. In this paper, we consider the threats a quantum-capable adversary could impose on Bitcoin, which currently uses the Elliptic Curve Digital Signature Algorithm (ECDSA) to sign transactions. We then propose a simple but slow commit-delay-reveal protocol, which allows users to securely move their funds from old (non-quantum-resistant) outputs to those adhering to a quantum-resistant digital signature scheme. The transition protocol functions even if ECDSA has already been compromised. While our scheme requires modifications to the Bitcoin protocol, these can be implemented as a soft fork.

Predicting patient arrivals to an accident and emergency department.

OBJECTIVES: To characterise and forecast daily patient arrivals into an accident and emergency (A&E) department based on previous arrivals data. METHODS: Arrivals between 1 April 2002 and 31 March 2007 to a busy case study A&E department were allocated to one of two arrival streams (walk-in or ambulance) by mode of arrival and then aggregated by day. Using the first 4 years of patient arrival data as a "training" set, a structural time series (ST) model was fitted to characterise each arrival stream. These models were used to forecast walk-in and ambulance arrivals for 1-7 days ahead and then compared with the observed arrivals given by the remaining 1 year of "unseen" data. RESULTS: Walk-in arrivals exhibited a strong 7-day (weekly) seasonality, with ambulance arrivals showing a distinct but much weaker 7-day seasonality. The model forecasts for walk-in arrivals showed reasonable predictive power (r = 0.6205). However, the ambulance arrivals were harder to characterise (r = 0.2951). CONCLUSIONS: The two separate arrival streams exhibit different statistical characteristics and so require separate time series models. It was only possible to accurately characterise and forecast walk-in arrivals; however, these model forecasts will still assist hospital managers at the case study hospital to best use the resources available and anticipate periods of high demand since walk-in arrivals account for the majority of arrivals into the A&E department.