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@xtling
xtling authored Jul 29, 2020
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45 changes: 45 additions & 0 deletions Figure4/PrintFigToPaper.m
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function [] = PrintFigToPaper (OutputType,plotFileName,...
FigFontSize,FigFontName,FigWidth,IsPrint,IsPrintTime,IsCustomHeight,FigHeightCustom,IsHideAxis)
% OutputType = -depsc -dpdf -dpng
% FigFontSize = 16;
% FigFontName = 'Times New Roman';
% FigWidth = 7; %inches
% IsPrint = 1; %flag: 1-output this figure
% IsPrintTime = 0; %flag: 0-do not append a timestamp to the filename
% IsCustomHeight = 0; %flag: 0-the figure height is automatically adapted
% FigHeightCustom = 5; %(OPTIONAL)
% IsHideAxis = 0; %(OPTIONAL) flag: 0-Hide the Axes

numdip = 300;
set(gcf,'PaperUnits','inches');
set(gcf,'Units','inches');
if nargin >= 10 && IsHideAxis == 1
set(gca, 'xcolor', 'none', 'ycolor', 'none');
else
set(gca,'color','none');
end
screenposition = get(gcf,'Position');
FigHeight = FigWidth/screenposition(3)*screenposition(4);
if nargin > 7 && IsCustomHeight
FigHeight = FigHeightCustom;
end
set(gcf,'PaperPosition',[0 2 FigWidth FigHeight]);
set(gcf,'Position',[screenposition(1:2)/2 FigWidth FigHeight]);
set([get(gca,'XLabel'),get(gca,'YLabel')],...
'FontSize',FigFontSize,'FontName', FigFontName);
set(findobj('FontSize',10),'FontSize',FigFontSize);
set(findobj('FontName','Helvetica'),'FontName', FigFontName);
set(findobj('FontSize',10),'FontSize',FigFontSize);
set(findobj('FontSize',16),'FontSize',FigFontSize);

% output
if ~exist('pic','dir')
mkdir('pic');
end
if(IsPrint && 1)
if(IsPrintTime && 1)
print(gcf,OutputType,'-painters',['-r',num2str(numdip)],['pic/',plotFileName,datestr(clock,30)]);
else
print(gcf,OutputType,'-painters',['-r',num2str(numdip)],['pic/',plotFileName]);
end
end
Binary file added Figure4/data/Figure_4.mat
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196 changes: 196 additions & 0 deletions Figure4/gen_Figure_4_data.m
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% Figure 4
% Version By Zheng Gao
% Updated on 29 Jul., 2020
clc; clear all;
%% Definitions of Input Parameters
precision = 2^12; % length of each round of simulation
N = 6; % confirmations required for securing a block
round_max = 7000; % the maximum number of rounds per simulation
i_delta = [1];
% the ratio of nodes received the block of last round
beta_t = 0:0.1:0.6;
beta_t_theo = 0:0.001:0.6;
% the fraction of the adversarial terrestrial miners
beta_s = 0:0.05:0.15;
% the fraction of the adversarial satellites
p = [0.95];
% successful transmission probability of satellite links in the average sense

%% Parameters for Storing Results
legend_beta_t = {};
for ii = 1:length(beta_t)
legend_beta_t = [legend_beta_t; ['\beta_t=', num2str(beta_t(ii))]];
end
legend_beta_s = {};
for ii = 1:length(beta_s)
legend_beta_s = [legend_beta_s; ['\beta_s=', num2str(beta_s(ii))]];
end
legend_p = {};
for ii = 1:length(p)
legend_p = [legend_p; ['p=', num2str(p(ii))]];
end

thro_pow_h = zeros(length(beta_s),length(beta_t),length(p));
theo_rate_h = zeros(length(beta_s),length(beta_t),length(p));
sim_rate_h = zeros(length(beta_s),length(beta_t),length(p));
% the growth rate of benign chain for PoW and the theoretical and
% simulated value of growth rate of benign chain for our protocol
theo_prob_success_attack = zeros(length(beta_s),length(beta_t),length(p));
sim_prob_success_attack = zeros(length(beta_s),length(beta_t),length(p));
% Theoretical and simulated values of the probability of double spending attack

%% Simulation part
for ind_beta_s = 1:length(beta_s)
for ind_beta_t = 1:length(beta_t)
for ind_p = 1:length(p)
for ind_i_delta = 1:length(i_delta)
% Current round of simulation
disp(['start simulating: p=', num2str(p(ind_p)),...
' beta_s=', num2str(beta_s(ind_beta_s)),...
' i_delta=', num2str(i_delta(ind_i_delta)),...
' beta_t=', num2str(beta_t(ind_beta_t))]);

% Pre-process parameters
beta_s_val = beta_s(ind_beta_s);
beta_t_val = beta_t(ind_beta_t);
p_val = p(ind_p);
i_delta_val = i_delta(ind_i_delta);
rate_h = zeros(1, precision); % rate of h-chain
rate_f = zeros(1, precision); % rate of f-chain
cnt_success_attack = 0; % count of successful attacks

% Let us roll out!
for ii = 1:precision
benign_block_height = zeros(1, round_max+ 2);
malicious_block_height = 1;
is_success = false;
round_count = 2;
while true
round_count = round_count + 1;
is_successful_transmitted = (rand < p_val);
is_benign_miners = (rand > beta_t_val);
is_benign_satellites = (rand > beta_s_val);
is_receive_last_block = (rand < i_delta_val);

is_benign_win = is_benign_satellites * is_successful_transmitted * is_benign_miners;
% it is too hard to be a good man
is_malicious_win = is_successful_transmitted * ~is_benign_satellites + is_benign_satellites * (~is_benign_miners) * is_successful_transmitted;

if is_benign_win == 1 % good man wins
if is_receive_last_block == 0
benign_block_height(round_count) = benign_block_height(round_count-2) +1;
else
if benign_block_height(round_count-1) == benign_block_height(round_count-2)
benign_block_height(round_count) = benign_block_height(round_count-2) + 1;
else
benign_block_height(round_count) = benign_block_height(round_count-1) + 1;
end
end
elseif is_malicious_win == 1 % bad man wins
benign_block_height(round_count) = benign_block_height(round_count-1);
malicious_block_height = malicious_block_height + 1;
else % good man wins, but doesn't receive the oracle
benign_block_height(round_count) = benign_block_height(round_count-1);
end

if benign_block_height(round_count) > N-1 &&...
is_success == false &&...
benign_block_height(round_count) < malicious_block_height
cnt_success_attack = cnt_success_attack + 1;
is_success = true;
elseif round_count >= round_max + 2
break;
end
end
if mod(ii,1000)==0
disp([' - progress: [', num2str(ii), '/', num2str(precision), ']']);
end
rate_h(ii) = benign_block_height(round_max+2) / round_max;
rate_f(ii) = malicious_block_height / round_max;

thro_judge = rate_f(ii) / ( rate_f(ii) + rate_h(ii));
if thro_judge >= 1/2 || beta_t_val >= 1/2
rate_h(ii) = 0; % bad man controls the blockchain
end
end

% Calculate the theoretical results
h_val = p_val * (1- beta_s_val) * (1- beta_t_val);
theo_rate_h_val = h_val / (1+ h_val* (1- i_delta_val));
f_val = p_val * beta_s_val + p_val * beta_t_val* (1- beta_s_val);
beta = f_val / (f_val+ theo_rate_h_val);

if beta >= 1/2
theo_rate_h_val = 0; % bad man controls the blockchain
end

theo_success_attack_rate = 1;
if beta >= 1/2
theo_success_attack_rate = 1;
else
for nn = 0:N
theo_success_attack_rate = theo_success_attack_rate - ...
nchoosek(nn + N -1, nn) * ...
(beta^nn * (1-beta)^N - beta^N * (1-beta)^nn);
end
end

% Storing the result for the current round of simulation

theo_rate_h(ind_beta_s,ind_beta_t,ind_p) = theo_rate_h_val;
sim_rate_h(ind_beta_s,ind_beta_t,ind_p) = mean(rate_h);

theo_rate_f(ind_beta_s,ind_beta_t,ind_p) = f_val;
sim_rate_f(ind_beta_s,ind_beta_t,ind_p) = mean(rate_f);

theo_prob_success_attack(ind_beta_s,ind_beta_t,ind_p) = theo_success_attack_rate;
sim_prob_success_attack(ind_beta_s,ind_beta_t,ind_p) = cnt_success_attack / precision;
end
end
end
end
%% Theoretical part
for ind_beta_s = 1:length(beta_s)
for ind_beta_t = 1:length(beta_t_theo)
for ind_p = 1:length(p)
for ind_i_delta = 1:length(i_delta)
% Current round of simulation
disp(['start simulating: p=', num2str(p(ind_p)),...
' beta_s=', num2str(beta_s(ind_beta_s)),...
' i_delta=', num2str(i_delta(ind_i_delta)),...
' beta_t=', num2str(beta_t_theo(ind_beta_t))]);

% Pre-process parameters
beta_s_val = beta_s(ind_beta_s);
beta_t_val = beta_t_theo(ind_beta_t);
p_val = p(ind_p);
i_delta_val = i_delta(ind_i_delta);

% Calculate the theoretical results
h_val = p_val * (1- beta_s_val) * (1- beta_t_val);
theo_rate_h_val = h_val / (1+ h_val* (1- i_delta_val));
f_val = p_val * beta_s_val + p_val * beta_t_val* (1- beta_s_val);
beta = f_val / (f_val+ theo_rate_h_val);

if beta >= 1/2
theo_rate_h_val = 0; % bad man controls the blockchain
end

theo_success_attack_rate = 1;
if beta >= 1/2
theo_success_attack_rate = 1;
else
for nn = 0:N
theo_success_attack_rate = theo_success_attack_rate - ...
nchoosek(nn + N -1, nn) * ...
(beta^nn * (1-beta)^N - beta^N * (1-beta)^nn);
end
end

% Storing the result for the current round of simulation
theo_rate_h(ind_beta_s,ind_beta_t,ind_p) = theo_rate_h_val;
theo_prob_success_attack(ind_beta_s,ind_beta_t,ind_p) = theo_success_attack_rate;
end
end
end
end
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