Small Scale AES Toolbox: Algebraic and Propositional Formulas, Circuit-Implementations and Fault Equations

Cryptography is one of the key technologies ensuring security in the digital domain. As such, its primitives and implementations have been extensively analyzed both from a theoretical, cryptoanalytical perspective, as well as regarding their capabilities to remain secure in the face of various attacks. One of the most common ciphers, the Advanced Encryption Standard (AES) (thus far) appears to be secure in the absence of an active attacker. To allow for the testing and development of new attacks or countermeasures a small scale version of the AES with a variable number of rounds, number of rows, number of columns and data word size, and a complexity ranging from trivial up to the original AES was developed. In this paper we present a collection of various implementations of the relevant small scale AES versions based on hardware (VHDL and gate-level), algebraic representations (Sage and CoCoA) and their translations into propositional formulas (in CNF). Additionally, we present fault attack equations for each version. Having all these resources available in a single and well structured package allows researchers to combine these different sources of information which might reveal new patterns or solving strategies. Additionally, the fine granularity of difficulty between the different small scale AES versions allows for the assessment of new attacks or the comparison of different attacks

Spectral-element simulations of long-term fault slip: Effect of low-rigidity layers on earthquake-cycle dynamics

We develop a spectral element method for the simulation of long-term histories of spontaneous seismic and aseismic slip on faults subjected to tectonic loading. Our approach reproduces all stages of earthquake cycles: nucleation and propagation of earthquake rupture, postseismic slip and interseismic creep. We apply the developed methodology to study the effects of low-rigidity layers on the dynamics of the earthquake cycle in 2-D. We consider two cases: small (M ~ 1) earthquakes on a fault surrounded by a damaged fault zone and large (M ~ 7) earthquakes on a vertical strike-slip fault that cuts through shallow low-rigidity layers. Our results indicate how the source properties of repeating earthquakes are affected by the presence of a damaged fault zone with low rigidity. Compared to faults in homogeneous media, we find (1) reduction in the earthquake nucleation size, (2) amplification of slip rates during dynamic rupture propagation, (3) larger recurrence interval, and (4) smaller amount of aseismic slip. Based on linear stability analysis, we derive a theoretical estimate of the nucleation size as a function of the width and rigidity reduction of the fault zone layer, which is in good agreement with simulated nucleation sizes. We further examine the effects of vertically-stratified layers (e.g., sedimentary basins) on the nature of shallow coseismic slip deficit. Our results suggest that low-rigidity shallow layers alone do not lead to coseismic slip deficit. While the low-rigidity layers result in lower interseismic stress accumulation, they also cause dynamic amplification of slip rates, with the net effect on slip being nearly zero

Stability of pulse-like earthquake ruptures

Pulse-like ruptures arise spontaneously in many elastodynamic rupture simulations and seem to be the dominant rupture mode along crustal faults. Pulse-like ruptures propagating under steady-state conditions can be efficiently analysed theoretically, but it remains unclear how they can arise and how they evolve if perturbed. Using thermal pressurisation as a representative constitutive law, we conduct elastodynamic simulations of pulse-like ruptures and determine the spatio-temporal evolution of slip, slip rate and pulse width perturbations induced by infinitesimal perturbations in background stress. These simulations indicate that steady-state pulses driven by thermal pressurisation are unstable. If the initial stress perturbation is negative, ruptures stop; conversely, if the perturbation is positive, ruptures grow and transition to either self-similar pulses (at low background stress) or expanding cracks (at elevated background stress). Based on a dynamic dislocation model, we develop an elastodynamic equation of motion for slip pulses, and demonstrate that steady-state slip pulses are unstable if their accrued slip $b$ is a decreasing function of the uniform background stress $\tau_\mathrm{b}$. This condition is satisfied by slip pulses driven by thermal pressurisation. The equation of motion also predicts quantitatively the growth rate of perturbations, and provides a generic tool to analyse the propagation of slip pulses. The unstable character of steady-state slip pulses implies that this rupture mode is a key one determining the minimum stress conditions for sustainable ruptures along faults, i.e., their ``strength''. Furthermore, slip pulse instabilities can produce a remarkable complexity of rupture dynamics, even under uniform background stress conditions and material properties

The physics of earthquakes

Earthquakes occur as a result of global plate motion. However, this simple picture is far from complete. Some plate boundaries glide past each other smoothly, while others are punctuated by catastrophic failures. Some earthquakes stop after only a few hundred metres while others continue rupturing for a thousand kilometres. Earthquakes are sometimes triggered by other large earthquakes thousands of kilometres away. We address these questions by dissecting the observable phenomena and separating out the quantifiable features for comparison across events. We begin with a discussion of stress in the crust followed by an overview of earthquake phenomenology, focusing on the parameters that are readily measured by current seismic techniques. We briefly discuss how these parameters are related to the amplitude and frequencies of the elastic waves measured by seismometers as well as direct geodetic measurements of the Earth's deformation. We then review the major processes thought to be active during the rupture and discuss their relation to the observable parameters. We then take a longer range view by discussing how earthquakes interact as a complex system. Finally, we combine subjects to approach the key issue of earthquake initiation. This concluding discussion will require using the processes introduced in the study of rupture as well as some novel mechanisms. As our observational database improves, our computational ability accelerates and our laboratories become more refined, the next few decades promise to bring more insights on earthquakes and perhaps some answers