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nheninnhenin
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CIP????- Ouroboros Φalanx
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‎CIP-????/Readme.md‎

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‎CIP-????/graph/NhandNa.py‎

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import matplotlib.pyplot as plt
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# Adjusted data to ensure matching lengths
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s_a_values = [0.005, 0.01, 0.02, 0.05, 0.1, 0.2, 0.25, 0.3, 0.33, 0.4, 0.45, 0.49, 0.5]
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N_a_values = [269, 434, 730, 1537, 2794, 5204, 6384, 7554, 8252, 9872, 11024, 11942, 12171]
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N_h_values = [19645, 19541, 18713, 17680, 15618, 14590, 13563, 12949, 11517, 10498, 9685, 9482, 9482]
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# Plot
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plt.figure(figsize=(14, 6))
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# Left plot: Max #Adversarial blocks
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plt.subplot(1, 2, 1)
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plt.plot([x * 100 for x in s_a_values], N_a_values, marker='o', label="N_a")
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plt.title("Nₐ s.t. Pr(Xₐ < Nₐ) = 1 - 2⁻¹²⁸")
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plt.xlabel("Adversarial stake sₐ (%)")
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plt.ylabel("Max #Adversarial blocks")
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plt.grid(True)
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plt.legend()
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# Right plot: Min #Honest blocks
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plt.subplot(1, 2, 2)
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plt.plot([x * 100 for x in s_a_values], N_h_values, marker='o', color='orange', label="N_h")
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plt.title("Nₕ s.t. Pr(Xₕ > Nₕ) = 2⁻¹²⁸")
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plt.xlabel("Adversarial stake sₐ (%)")
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plt.ylabel("Min #Honest blocks")
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plt.grid(True)
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plt.legend()
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plt.tight_layout()
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plt.show()

‎CIP-????/graph/extended_error_series_corrected.csv‎

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‎CIP-????/graph/scenario-cost-cross-thresholds.py‎

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import numpy as np
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import matplotlib.pyplot as plt
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from matplotlib.patches import Patch
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# Define the range for rho (Grinding Depth)
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rho = np.linspace(1, 256, 1000)
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f = 0.05
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cost_per_cpu_hour = 0.01
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w_O = 20 * (2 * rho - 1)
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w_O_hours = w_O / 3600
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epsilon = 1e-100 # Avoid log(0)
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# Praos cost functions
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def ant_glance_praos(rho): return 5e-10 * 2**(rho - 2)
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def ant_patrol_praos(rho): return 5e-10 * 2**(rho - 1) + 2.16e-2 * 2**(rho - 1) / rho
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def owl_stare_praos(rho): return 5e-10 * 2**(rho - 2) + 5e-2 * 2**(rho - 1) / rho
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def owl_survey_praos(rho): return 5e-10 * 2**(rho - 2) + 7.16e-2 * 2**(rho - 1) / rho
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# Phalanx cost function
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def phalanx_cost(rho, scale): return (scale * 2**(rho - 1)) / rho
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# Compute log10(Cost) from CPU count
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def log_cost(n_cpu): return np.log10(np.maximum(n_cpu * cost_per_cpu_hour * w_O_hours, epsilon))
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# Curves for Praos
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praos_curves = {
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'Ant Glance Praos': ('blue', log_cost(ant_glance_praos(rho))),
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'Ant Patrol Praos': ('orange', log_cost(ant_patrol_praos(rho))),
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'Owl Stare Praos': ('green', log_cost(owl_stare_praos(rho))),
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'Owl Survey Praos': ('red', log_cost(owl_survey_praos(rho))),
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}
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# Curves for Phalanx configurations
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phalanx_curves = {
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'Phalanx$_{1/100}$': ('#6A5ACD', log_cost(phalanx_cost(rho, 2.16e2))),
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'Phalanx$_{1/10}$': ('#228B22', log_cost(phalanx_cost(rho, 2.16e3))),
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'Phalanx$_{max}$': ('#B22222', log_cost(phalanx_cost(rho, 2.16e4))),
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}
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# Feasibility zones
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zones = [
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(-10, 4, 'green', 'Trivial'),
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(4, 6, 'yellow', 'Feasible'),
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(6, 9, '#FFA07A', 'Possible'),
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(9, 12, '#FF6347', 'Borderline Infeasible'),
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(12, 90, 'red', 'Infeasible')
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]
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# Function to find crossing points and annotate
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def annotate_crossings(log_costs, color, threshold, position='above'):
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# Find indices where the curve crosses the threshold
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indices = np.where((log_costs[:-1] < threshold) & (log_costs[1:] >= threshold))[0]
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if len(indices) > 0:
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idx = indices[0]
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rho_val = rho[idx]
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plt.scatter(rho_val, threshold, color=color, marker='o', s=50, zorder=5)
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# Position above or below based on the curve
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if position == 'below':
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plt.annotate(f'{rho_val:.1f}',
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xy=(rho_val, threshold),
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xytext=(rho_val + 1.1, threshold - 0.4),
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fontsize=8, color=color)
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elif position == 'green':
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plt.annotate(f'{rho_val:.1f}',
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xy=(rho_val, threshold),
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xytext=(rho_val - 0.6, threshold - 0.9),
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fontsize=8, color=color)
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else:
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plt.annotate(f'{rho_val:.1f}',
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xy=(rho_val, threshold),
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xytext=(rho_val - 1, threshold + 0.3),
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fontsize=8, color=color)
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# # Annotate where curves cross threshold lines
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# def annotate_crossings(log_costs, color, threshold, position='above'):
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# indices = np.where((log_costs[:-1] < threshold) & (log_costs[1:] >= threshold))[0]
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# if len(indices) > 0:
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# idx = indices[0]
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# rho_val = rho[idx]
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# plt.scatter(rho_val, threshold, color=color, marker='o', s=50, zorder=5)
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# offset = {'above': (1, 0.5), 'below': (1.1, -0.4), 'green': (-0.6, -0.9)}.get(position, (1, 0.5))
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# plt.annotate(f'{rho_val:.1f}', xy=(rho_val, threshold),
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# xytext=(rho_val + offset[0], threshold + offset[1]),
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# fontsize=8, color=color)
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# Unified curve list for annotation logic
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curves = [
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(praos_curves['Ant Glance Praos'][1], 'blue', 'above'),
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(praos_curves['Ant Patrol Praos'][1], 'orange', 'below'),
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(praos_curves['Owl Stare Praos'][1], 'green', 'green'),
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(praos_curves['Owl Survey Praos'][1], 'red', 'above'),
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(phalanx_curves['Phalanx$_{1/100}$'][1], '#6A5ACD', 'above'),
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(phalanx_curves['Phalanx$_{1/10}$'][1], '#228B22', 'above'),
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(phalanx_curves['Phalanx$_{max}$'][1], '#B22222', 'above')
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]
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# Plotting
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plt.figure(figsize=(12, 7))
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# Plot each Praos and Phalanx curve
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for label, (color, values) in praos_curves.items():
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plt.plot(rho, values, label=label, color=color, linewidth=2)
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for label, (color, values) in phalanx_curves.items():
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plt.plot(rho, values, label=label, color=color, linestyle='--', linewidth=2)
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# Add feasibility zones
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for y0, y1, color, label in zones:
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plt.axhspan(y0, y1, color=color, alpha=0.1, label=label)
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# Annotate crossings
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for threshold, _, _, _ in zones:
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for log_costs, color, position in curves:
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annotate_crossings(log_costs, color, threshold, position)
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# Axis labels and title
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plt.xlabel(r'$\rho$ (Grinding Depth)', fontsize=14)
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plt.ylabel(r'$\log_{10}(\mathrm{Cost\ (USD)})$', fontsize=14)
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plt.title('Cost of Grinding Attacks Across Praos and Phalanx Scenarios', fontsize=16)
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plt.grid(True, linestyle='--', alpha=0.7)
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plt.xlim(0, 256)
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y_max = max(np.max(v[np.isfinite(v)]) for _, v in list(praos_curves.values()) + list(phalanx_curves.values())) + 5
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plt.ylim(-5, y_max)
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# Custom legend
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legend_elements = [
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*[plt.Line2D([0], [0], color=color, lw=2, label=label) for label, (color, _) in praos_curves.items()],
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*[plt.Line2D([0], [0], color=color, lw=2, linestyle='--', label=label) for label, (color, _) in phalanx_curves.items()],
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*[Patch(facecolor=color, alpha=0.1, label=label) for _, _, color, label in zones]
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]
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plt.legend(handles=legend_elements, fontsize=10, loc='lower right',
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bbox_to_anchor=(1, 0), ncol=2, handletextpad=0.5, columnspacing=1.5)
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# Final layout and save
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plt.subplots_adjust(left=0.1, right=0.95, top=0.9, bottom=0.2)
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plt.show()

‎CIP-????/graph/scenario_cost_praos_vs_phalanx-full-scenarios.py‎

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import numpy as np
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import matplotlib.pyplot as plt
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from matplotlib.patches import Patch
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# Range for rho (Grinding Depth)
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rho = np.linspace(1, 256, 1000)
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f = 0.05
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cost_per_cpu_hour = 0.01 # $0.01 per CPU-hour
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# Time window for computation (w_O)
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w_O = 20 * (2 * rho - 1)
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w_O_hours = w_O / 3600
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# PRAOS cost functions
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def ant_glance_praos(rho): return 5e-10 * 2**(rho - 2)
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def ant_patrol_praos(rho): return ant_glance_praos(rho) + 2.16e-2 * 2**(rho - 1) / rho
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def owl_stare_praos(rho): return ant_glance_praos(rho) + 5e-2 * 2**(rho - 1) / rho
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def owl_survey_praos(rho): return ant_glance_praos(rho) + 7.16e-2 * 2**(rho - 1) / rho
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# PHALANX curves (generalized)
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def phalanx_curve(multiplier):
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return lambda rho: (multiplier * 2**(rho - 1)) / rho
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phalanx_1_100 = phalanx_curve(2.16e2)
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phalanx_1_10 = phalanx_curve(2.16e3)
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phalanx_max = phalanx_curve(2.16e4)
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# Convert to log10 cost
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def compute_log_cost(n_cpu):
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return np.log10(np.maximum(n_cpu * cost_per_cpu_hour * w_O_hours, 1e-100))
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# Scenario definitions
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scenarios = {
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"Ant Glance Praos": compute_log_cost(ant_glance_praos(rho)),
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"Ant Patrol Praos": compute_log_cost(ant_patrol_praos(rho)),
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"Owl Stare Praos": compute_log_cost(owl_stare_praos(rho)),
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"Owl Survey Praos": compute_log_cost(owl_survey_praos(rho)),
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"Phalanx$_{1/100}$": compute_log_cost(phalanx_1_100(rho)),
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"Phalanx$_{1/10}$": compute_log_cost(phalanx_1_10(rho)),
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"Phalanx$_{max}$": compute_log_cost(phalanx_max(rho)),
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}
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# Color map for plot lines
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color_map = {
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"Ant Glance Praos": "blue",
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"Ant Patrol Praos": "orange",
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"Owl Stare Praos": "green",
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"Owl Survey Praos": "red",
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"Phalanx$_{1/100}$": '#6A5ACD',
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"Phalanx$_{1/10}$": '#228B22',
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"Phalanx$_{max}$": "#B22222"
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}
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# Feasibility zones
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zones = [
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(-10, 4, 'green', 'Trivial'),
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(4, 6, 'yellow', 'Feasible'),
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(6, 9, '#FFA07A', 'Possible'),
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(9, 12, '#FF6347', 'Borderline Infeasible'),
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(12, 90, 'red', 'Infeasible')
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]
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# Plot
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plt.figure(figsize=(12, 7))
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# Draw curves
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for label, log_cost in scenarios.items():
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style = "-" if "Praos" in label else "--"
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plt.plot(rho, log_cost, label=label, color=color_map[label], linestyle=style, linewidth=2)
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# Draw feasibility zones
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for y0, y1, color_zone, label in zones:
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plt.axhspan(y0, y1, color=color_zone, alpha=0.1, label=label)
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# Axis labels and title
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plt.xlabel(r'$\rho$ (Grinding Depth)', fontsize=14)
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plt.ylabel(r'$\log_{10}(\mathrm{Cost\ (USD)})$', fontsize=14)
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plt.title('Cost of Grinding Attacks: Praos vs Phalanx Configurations', fontsize=16)
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plt.grid(True, linestyle='--', alpha=0.7)
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plt.xlim(0, 256)
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y_max = max(np.max(v[np.isfinite(v)]) for v in scenarios.values()) + 5
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plt.ylim(-5, y_max)
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# Delta annotations
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def draw_delta(rho_val, praos_label, phalanx_label, x_offset=3):
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idx = np.argmin(np.abs(rho - rho_val))
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delta = scenarios[phalanx_label][idx] - scenarios[praos_label][idx]
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mid = scenarios[phalanx_label][idx] - delta / 2
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plt.annotate('', xy=(rho_val, scenarios[phalanx_label][idx]),
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xytext=(rho_val, scenarios[praos_label][idx]),
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arrowprops=dict(arrowstyle='<->', color='black', lw=1))
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plt.text(rho_val + x_offset, mid, f'$\\Delta \\approx {delta:.1f}$', fontsize=12, color='black',
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bbox=dict(facecolor='white', alpha=0.8, edgecolor='none'), verticalalignment='center')
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draw_delta(50, "Ant Glance Praos", "Phalanx$_{1/100}$")
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draw_delta(125, "Owl Survey Praos", "Phalanx$_{1/100}$")
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draw_delta(150, "Owl Survey Praos", "Phalanx$_{1/10}$")
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draw_delta(175, "Owl Survey Praos", "Phalanx$_{max}$")
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# Legend
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legend_elements = [
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plt.Line2D([0], [0], color='blue', lw=2, label='Ant Glance Praos'),
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plt.Line2D([0], [0], color='orange', lw=2, label='Ant Patrol Praos'),
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plt.Line2D([0], [0], color='green', lw=2, label='Owl Stare Praos'),
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plt.Line2D([0], [0], color='red', lw=2, label='Owl Survey Praos'),
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plt.Line2D([0], [0], color='#6A5ACD', lw=2, linestyle='--', label='Phalanx$_{1/100}$'),
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plt.Line2D([0], [0], color='#228B22', lw=2, linestyle='--', label='Phalanx$_{1/10}$'),
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plt.Line2D([0], [0], color='#B22222', lw=2, linestyle='--', label='Phalanx$_{max}$'),
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*[Patch(facecolor=color, alpha=0.1, label=label) for _, _, color, label in zones]
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]
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plt.legend(handles=legend_elements, fontsize=10, loc='lower right', bbox_to_anchor=(1, 0), ncol=2)
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plt.subplots_adjust(left=0.1, right=0.95, top=0.9, bottom=0.2)
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plt.show()

‎CIP-????/graph/scenario_cost_praos_vs_phalanx.py‎

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import numpy as np
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import matplotlib.pyplot as plt
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from matplotlib.patches import Patch
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# Define the range for rho (Grinding Depth)
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rho = np.linspace(1, 256, 1000)
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f = 0.05
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cost_per_cpu_hour = 0.01 # $0.01 per CPU-hour
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# Compute w_O in seconds and hours
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w_O = 20 * (2 * rho - 1)
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w_O_hours = w_O / 3600
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# N_CPU functions with corrected Phalanx_{1/100} expressions
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def ant_glance_praos(rho):
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return 5e-10 * 2**(rho - 2)
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def ant_glance_phalanx(rho):
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return ant_glance_praos(rho) + 216 * 2**(rho - 1) / rho
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def ant_patrol_praos(rho):
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return ant_glance_praos(rho) + 2.16e-2 * 2**(rho - 1) / rho
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def ant_patrol_phalanx(rho):
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return ant_patrol_praos(rho) + 216 * 2**(rho - 1) / rho
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def owl_stare_praos(rho):
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return ant_glance_praos(rho) + 5e-2 * 2**(rho - 1) / rho
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def owl_stare_phalanx(rho):
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return owl_stare_praos(rho) + 216 * 2**(rho - 1) / rho
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def owl_survey_praos(rho):
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return ant_glance_praos(rho) + 7.16e-2 * 2**(rho - 1) / rho
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def owl_survey_phalanx(rho):
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return owl_survey_praos(rho) + 216 * 2**(rho - 1) / rho
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# Compute N_CPU and costs
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def compute_log_cost(n_cpu):
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return np.log10(np.maximum(n_cpu * cost_per_cpu_hour * w_O_hours, 1e-100))
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scenarios = {
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"Ant Glance Praos": compute_log_cost(ant_glance_praos(rho)),
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"Ant Glance Phalanx$_{1/100}$": compute_log_cost(ant_glance_phalanx(rho)),
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"Ant Patrol Praos": compute_log_cost(ant_patrol_praos(rho)),
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"Ant Patrol Phalanx$_{1/100}$": compute_log_cost(ant_patrol_phalanx(rho)),
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"Owl Stare Praos": compute_log_cost(owl_stare_praos(rho)),
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"Owl Stare Phalanx$_{1/100}$": compute_log_cost(owl_stare_phalanx(rho)),
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"Owl Survey Praos": compute_log_cost(owl_survey_praos(rho)),
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"Owl Survey Phalanx$_{1/100}$": compute_log_cost(owl_survey_phalanx(rho)),
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}
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# Plot
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plt.figure(figsize=(12, 7))
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colors = {"Ant Glance": "blue", "Ant Patrol": "orange", "Owl Stare": "green", "Owl Survey": "red"}
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for label, log_cost in scenarios.items():
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name = label.split()[0] + " " + label.split()[1]
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style = "--" if "Phalanx" in label else "-"
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plt.plot(rho, log_cost, label=label, color=colors[name], linestyle=style, linewidth=2)
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# Feasibility zones
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zones = [
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(-10, 4, 'green', 'Trivial'),
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(4, 6, 'yellow', 'Feasible'),
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(6, 9, '#FFA07A', 'Possible'),
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(9, 12, '#FF6347', 'Borderline Infeasible'),
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(12, 90, 'red', 'Infeasible')
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]
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for y0, y1, color, label in zones:
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plt.axhspan(y0, y1, color=color, alpha=0.1, label=label)
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# Labels and layout
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plt.xlabel('$\\rho$ (Grinding Depth)', fontsize=14)
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plt.ylabel('$\\log_{10}(\\text{Cost (USD)})$', fontsize=14)
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plt.title('Cost of Grinding Attacks: Praos vs Phalanx$_{1/100}$ Scenarios', fontsize=16)
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plt.grid(True, linestyle='--', alpha=0.7)
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plt.xlim(0, 256)
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y_max = max(np.max(v[np.isfinite(v)]) for v in scenarios.values()) + 5
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plt.ylim(-5, y_max)
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# Delta annotations
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def draw_delta(rho_val, praos_label, phalanx_label, x_offset=3):
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idx = np.argmin(np.abs(rho - rho_val))
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delta = scenarios[phalanx_label][idx] - scenarios[praos_label][idx]
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mid = scenarios[phalanx_label][idx] - delta / 2
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plt.annotate('', xy=(rho_val, scenarios[phalanx_label][idx]),
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xytext=(rho_val, scenarios[praos_label][idx]),
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arrowprops=dict(arrowstyle='<->', color='black', lw=1))
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plt.text(rho_val + x_offset, mid, f'$\\Delta \\approx {delta:.1f}$', fontsize=12, color='black',
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bbox=dict(facecolor='white', alpha=0.8, edgecolor='none'), verticalalignment='center')
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draw_delta(50,"Ant Glance Praos" , "Owl Survey Phalanx$_{1/100}$" )
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draw_delta(100, "Owl Survey Praos", "Owl Survey Phalanx$_{1/100}$" )
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# Legend
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legend_elements = [
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plt.Line2D([0], [0], color='blue', lw=2, label='Ant Glance Praos'),
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plt.Line2D([0], [0], color='blue', lw=2, linestyle='--', label='Ant Glance Phalanx$_{1/100}$'),
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plt.Line2D([0], [0], color='orange', lw=2, label='Ant Patrol Praos'),
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plt.Line2D([0], [0], color='orange', lw=2, linestyle='--', label='Ant Patrol Phalanx$_{1/100}$'),
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plt.Line2D([0], [0], color='green', lw=2, label='Owl Stare Praos'),
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plt.Line2D([0], [0], color='green', lw=2, linestyle='--', label='Owl Stare Phalanx$_{1/100}$'),
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plt.Line2D([0], [0], color='red', lw=2, label='Owl Survey Praos'),
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plt.Line2D([0], [0], color='red', lw=2, linestyle='--', label='Owl Survey Phalanx$_{1/100}$'),
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*[Patch(facecolor=color, alpha=0.1, label=label) for _, _, color, label in zones]
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]
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plt.legend(handles=legend_elements, fontsize=10, loc='lower right',
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bbox_to_anchor=(1, 0), ncol=2, handletextpad=0.5, columnspacing=1.5)
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plt.subplots_adjust(left=0.1, right=0.95, top=0.9, bottom=0.2)
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plt.show()

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