Bitcoin Forum

35% normal, no attack: ~37.17% revenue
35% selfish, no sybil: ~37.57% revenue
35% sybil: ~37.05% revenue
35% selfish, sybil: ~48.8% revenue

20% normal, no attack: ~20.92% revenue
20% selfish, no sybil: ~10.9% revenue
20% sybil: ~21.55% revenue
20% selfish, sybil: ~23.11%

var btc = new Node()
btc.use(PeerMgr) // peermgr.js
btc.use(Inventory) // inventory.js
btc.use(Transactions) // transactions.js
btc.use(Blockchain) // blockchain.js
btc.use(Miner) // miner.js

var net = new Network()
net.add(100, btc)

net.run(10000) // run 10 seconds

(height = 2016) Difficulty adjustment: from 1000 to 1441.9452528101006 (1.4419452528101004x)

btc.init(function(self) {
	switch(self.id) {
		case 0:
			self.mine(0.31) // btcguild
		break;
		case 1:
			self.mine(0.22)
		break;
		case 2:
			self.mine(0.13)
		break;
		case 3:
			self.mine(0.06)
		break;
		case 4:
			self.mine(0.05)
		break;
		case 5:
			self.mine(0.03)
		break;
		case 6:
			self.mine(0.02)
		break;
		case 7:
			self.mine(0.02)
		break;
		default:
			if (self.id < 100)
				self.mine(true);
			else
				self.mine(false);
		break;
	}
});

this.delay = Math.floor((Math.log(1-Math.random())/-1) * (1 / (this.ptotal)));

function selfish(Nsim, PercentSelfish, MaxOrphanLen, PlotFlag, PauseValue, RndState)
% ------------------------------------------------------------------------------------------------------------
% function selfish()
% function selfish(Nsim, PercentSelfish, MaxOrphanLen, PlotFlag, PauseValue, RndState)
%
% This function simulates and ilustrates the selfish bitcoin mining.
%
% As we see, selfish mining works if the mining power of the selfish miner is more than one 3rd of the total
% mining power.
%
% Network propagation times are not modelled and are assumed to be zero (best case from selfish miner's
% perspective)
%
% Optional arguments:
% * Nsim (def.=100): Length of simulation time in terms of number of blocks on the public main blockchain
% * PercentSelfish (def.=40.586): Percent of the selfish miner's overall network hashing power
% * MaxOrphanLen (def.=5): Selfish miner will avoid creating orphans on main chain longer than this nb of blocks.
% * PlotFlag (def.=1=true): If set to =false or =0, no illustratetive plot will be made -> set =false for long simulations!
% * PauseValue (def.=inf): When plotting is active, this many seconds of waiting time is added after each block.
%                          Set =inf to require keypress after each block.
%                          For Non-Matlab, default = 0.1 [sec] and =inf is not supported.
% * RndState (def.=sum(100*clock)): set to a certain value (e.g. integer number) to set random seed.
%
% Example function calls:
%    > selfish % run with default settings - good for learning and demonstration purposes                                           <-- good for educational purposes
%    > selfish(40, 48, 3, true, inf, 8) % short interactive simulation with limitation of the orphan lengths in the main chain      <-- very good for educational purposes
%    > selfish(200, 41, inf, true, 0.01, 1) % self-running simulation, watch while running. Certain random seed for reproducibility <-- very good for educational purposes
%    > selfish(200, 41, inf, true, 0.01) % self-running simulation, watch while running. Random seed is different each time
%    > selfish(1e4, 45, inf, false, false, 4) % run a long simulation without plotting during simulation time
% ------------------------------------------------------------------------------------------------------------
% Tested with Matlab R2007b, Octave 3.0.0 (Linux) and FreeMat 4.1.1 (Windows).
% Restriction for FreeMat: only works for PlotFlag=false
%
% Octave is open-source freeware, available for Windows and Linux.
% FreeMat is open-source freeware, available for Windows.
%
% If you start Octave (or Matlab or FreeMat), you see a command window (console).
% There you simply enter (where ">" denotes the console's command prompt):
%    > cd the_path/where/this_file/is_located
%    > selfish <press Enter>
%
% Note: In the comments of this file, the terms "selfish miner" and "attacker" are used interchangeably,
%       they refer to the same thing.
% ------------------------------------------------------------------------------------------------------------
% 
% License:
% --------
% * Use is permitted as long as the user has donated an amount that he/she considers reasonable, or if the
%   user truly thinks that a donation is not required.
%
% * Reuse/modify/extend as you like, commercially or non-commercially.
% 
% * The only condition is that you include this license condition in the source code, and include a reference
%   to the original author and the bitcoin donation address both in the source code and being displayed
%   by the running program.
% 
% Bitcoin Donations to the author: 1MichaS16UMKFgNjanKrtfD51HpBkqPAwD (Michael_S at bitcointalk.org)
% ------------------------------------------------------------------------------------------------------------

global power_attack % selfish miner's hasing power share
global THR_orphanes_publish % max number of orpans that the selfish miner will create on the public main chain
global Pause_value % pause in seconds after each block, when plotting is active

ismatlab = false;
v=version;% typical Matlab version string: "7.5.0.338 (R2007b)"; typical Octave version string: "3.0.0"
if ~isempty(strfind(v,'R2')), % Matlab version string contains "R2" in it.
    ismatlab = true;
end

%% 0 - Parameters (adjust to your liking)

% - - - - - Parameters that can be overruled by function arguments: - - - - -

% 0.1 - Change as desired: (may be overruled by function arguments)
%power_attack = 0.17; % between 0 and 1 (0.40586 yields 50% of the blocks, 0.5 yields 100%)
power_attack = 0.40586; % between 0 and 1 (0.40586 yields 50% of the blocks, 0.5% yields 100%)
%power_attack = 0.44; % between 0 and 1 (0.40586 yields 50% of the blocks, 0.5 yields 100%)
%power_attack = 0.51; % between 0 and 1 (0.40586 yields 50% of the blocks, 0.5 yields 100%)

% 0.2 - Change as desired: (may be overruled by function arguments)
% The selfish miner gets the highest yield when setting the following parameter to "inf", but this might be "impractical".
% Setting this to e.g. =5 or =10 gives a yield close to theoretical maximum while avoiding creation of too long orphans in the main chain.
% Hence, e.g. setting it to =5 might be a reasonable choice, to ensure that blocks of depth=6 in the public main chain are never orphaned by the selfish miner.
THR_orphanes_publish = 5; % (>=1) [best is =inf] If the attacker creates so many orphans in the main chain, he publishes before even more orphans are created.
%THR_orphanes_publish = inf; % (>=1) [best is =inf] If the attacker creates so many orphans in the main chain, he publishes before even more orphans are created.

% 0.3 - Change as desired: (may be overruled by function arguments)
N = 1e6; % number of blocks to be simulated
N = 1e5; % number of blocks to be simulated
N = 100; % number of blocks to be simulated

% 0.4 - Change as desired: (may be overruled by function arguments)
plot_flag = 1;% =1 for plotting illustrative block chain and interactive keypress; =0 for not plotting (faster).

% 0.5 - Change as desired: (may be overruled by function arguments)
try
    rand('state', 1);% set random generator seed
    rand('state', sum(100*clock));% set random generator seed
catch
    % Freemat does understand the above format, but instead this:
    seed(1,1);% set random generator seed
    seed(sum(100*clock),sum(100*clock));% set random generator seed
end

% - - - - - Parameters that can NOT be overruled by function arguments: - - - - -

% 0.6 - Normally keep the "best" values!
THR_attack_give_up = 1; % (>=1) [best is =1] If main chain is so much longer than the own "secret" chain, then attacker gives up and adopts the main chain's blocks.
THR_attack_publish = inf; % (>=2) [best is =inf] If the attacker has so many secret blocks, he will publish them (e.g. to avoid loosing them due to checkpointing).


% ------------------------------------------------------------------------------------------------------------
% ------------------------------------------------------------------------------------------------------------

%% 1.1 - Overruling pre-set parameters with function arguments:
if exist('Nsim', 'var'),
    N = Nsim;
end
if exist('PercentSelfish', 'var'),
    power_attack = PercentSelfish/100;
end
if exist('MaxOrphanLen', 'var'),
    THR_orphanes_publish = MaxOrphanLen;
end
if exist('PlotFlag', 'var'),
    plot_flag = PlotFlag;
end
if ~exist('PauseValue', 'var'),
    Pause_value = inf;
else
    Pause_value = PauseValue;
end
if exist('RndState', 'var'),
    try
        rand('state', RndState);
    catch
        seed(RndState,RndState);
    end
end

%% 1.2 - Pre-Processing
power_normal = 1-power_attack;% mining power (share of the total) of the normal (=honest) miners

gen_time_attack = 10/power_attack;% average time needed to generate a block, in minutes, by attacker
gen_time_normal = 10/power_normal;% average time needed to generate a block, in minutes, by normal (=honest) miners

N_force_terminate = ceil(1.1*N);% ceil(1.1*N) by default

%% 2 - Simulate
% Pre-allocate memory - this is important for simulation time:
blocks_won = NaN*ones(1,ceil(N_force_terminate)); % vector indicating which block was won by the selfish mining attacker
chn = blocks_won;% vector showing the normal (public) chain
cha = blocks_won;% vector showing the chain that the attacker works on
Nb_of_blocks_orphaned_by_attacker = NaN*ones(1,ceil(N_force_terminate));

cnt_event_orphaned = 0;% counter for the *nb of events* that a selfish miner published his secretly mined blocks and thereby orphans honestly mined coins.

kn = 0;% kn is the length of the "official" blockchain that the normal (=honest) miners work on
ka = 0;% ka is the number of mined blocks that the attacker's chain has in common with the official chain.
sa = 0;% sa is the number of blocks already mined secretly by the attacker

Time.Total = 0;% To output timestamps during the simulation, whenever a new block is found

time_next_attack = -gen_time_attack*log(rand());% time until attacker finds the next block
time_next_normal = -gen_time_normal*log(rand());% time until normal (=honest) miners find the next block

cnt_blocks.found_normal    = 0;% counts nb of blocks found by honest miners
cnt_blocks.orphaned_normal = 0;% ...of which so many got orphaned (replaced) by blocks found by the selfish miner.
cnt_blocks.found_attack    = 0;% counts nb of blocks found by selfish miner
cnt_blocks.orphaned_attack = 0;% ...of which so many got orphaned (replaced) by blocks found by the honest miners.
cnt_blocks.in_main_chain   = 0;% counts the number of blocks in the (public) main chain.

if plot_flag, [hdn, hda] = plot_chain([0], [0]); end;% pro forma plot
while 1;

    % --- Finding new block, depending on whether normal (=honest) miners or attacker find the next block:
    if time_next_normal < time_next_attack,% the next block is found by the normal (=honest) miners
        cnt_blocks.found_normal = cnt_blocks.found_normal + 1;
        cnt_blocks.in_main_chain = cnt_blocks.in_main_chain + 1;
        Time.Delta = time_next_normal;
        Time.Total = Time.Total + Time.Delta;
        kn = kn + 1;% official block chain grows by one block
        blocks_won(kn) = 0;% block nb. kn found by the normal (=honest) miners [not final, might still be reverted later on]
        chn(kn) = 0;
        if sa == 0, % attacker has no secret blocks
            cha(ka+1:kn) = 0;
            ka = kn;% attacker stays at the official chain
            sa = 0;% attacker stays at the official chain
            time_next_attack = -gen_time_attack*log(rand());% time until attacker finds the next block
            time_next_normal = -gen_time_normal*log(rand());% time until normal (=honest) miners find the next block
        elseif kn >= ka + sa + THR_attack_give_up, % normal (=honest) miners have too many blocks, attacker gives up
            cha(ka+1:kn-THR_attack_give_up) = 0.1;% attacker replaces his secret blocks by the official blocks
            chn(ka+1:kn-THR_attack_give_up) = 0.1;% attacker replaces his secret blocks by the official blocks
            cha(kn-THR_attack_give_up+1:kn) = 0;% attacker takes latest official block to his own chain
            cnt_blocks.orphaned_attack = cnt_blocks.orphaned_attack + (kn-THR_attack_give_up-ka);
            ka = kn;% attacker switches to the official chain
            sa = 0;% attacker switches to the official chain
            time_next_attack = -gen_time_attack*log(rand());% time until attacker finds the next block
            time_next_normal = -gen_time_normal*log(rand());% time until normal (=honest) miners find the next block
        else % attacker remains on his own chain
            time_next_attack = time_next_attack - time_next_normal;% time until attacker finds the next block
            time_next_normal = -gen_time_normal*log(rand());% time until normal (=honest) miners find the next block
        end

    else % the next block is found by the attacker
        cnt_blocks.found_attack = cnt_blocks.found_attack + 1;
        Time.Delta = time_next_attack;
        Time.Total = Time.Total + Time.Delta;
        sa = sa + 1;% attacker does not publish the block (yet), so the number of secret blocks is incremented
        cha(ka+sa) = 2;
        time_next_normal = time_next_normal - time_next_attack;% time until normal (=honest) miners find the next block
        time_next_attack = -gen_time_attack*log(rand());% time until attacker finds the next block
    end
    if plot_flag, [hdn, hda] = plot_chain(chn(1:kn), cha(1:ka+sa), hdn, hda, Time, cnt_blocks, 'pause'); end % illustrate state of block chains
    
    % --- Check out if the attacker publishes his secret blocks:
    if sa >= THR_attack_publish || (sa >= 2 && ka+sa == kn+1),% 2nd condition means: normal (=honest) miners get too close, so publish before it is too late.
        blocks_won(ka+1:ka+sa) = 1;% These blocks are (re-)credited to the attacker now
        chn(ka+1:kn) = 1;% orphaned
        chn(kn+1:ka+sa) = -1;% not orphaned
        cha(ka+1:ka+sa) = chn(ka+1:ka+sa);
        cnt_event_orphaned = cnt_event_orphaned + 1;
        Nb_of_blocks_orphaned_by_attacker(cnt_event_orphaned) = kn-ka;
        cnt_blocks.orphaned_normal = cnt_blocks.orphaned_normal + (kn-ka);
        cnt_blocks.in_main_chain = cnt_blocks.in_main_chain + (ka+sa-kn);
        kn = ka+sa; % attacker's secretly mined blocks become published and accepted by the normal (=honest) miners
        ka = kn;% all blocks of the attacker are now in common with the normal chain.
        sa = 0;% attacker has no secret blocks any more now.
        time_next_attack = -gen_time_attack*log(rand());% time until attacker finds the next block
        time_next_normal = -gen_time_normal*log(rand());% time until normal (=honest) miners find the next block
        Time.Delta = 0;
        if plot_flag, [hdn, hda] = plot_chain(chn(1:kn), cha(1:ka+sa), hdn, hda, Time, cnt_blocks, 'pause'); end % illustrate state of block chains
    elseif sa >= 2 && kn-ka >= THR_orphanes_publish,% attacker publishes some blocks to avoid that even more orphans are created on the main chain
        blocks_won(ka+1:ka+THR_orphanes_publish+1) = 1;% These blocks are published and (re-)credited to the attacker now
        chn(ka+1:ka+THR_orphanes_publish) = 1;% selfishly mined blocks replacing honest blocks
        chn(ka+THR_orphanes_publish+1) = -1;% another selfishly mined block, but not causing orphanes on the main chain
        cha(ka+1:ka+THR_orphanes_publish+1) = chn(ka+1:ka+THR_orphanes_publish+1);
        cnt_event_orphaned = cnt_event_orphaned + 1;
        cnt_blocks.in_main_chain = cnt_blocks.in_main_chain + (ka+THR_orphanes_publish+1-kn);
        Nb_of_blocks_orphaned_by_attacker(cnt_event_orphaned) = THR_orphanes_publish;
        cnt_blocks.orphaned_normal = cnt_blocks.orphaned_normal + THR_orphanes_publish;
        kn = ka + THR_orphanes_publish + 1;% attacker's secretly mined blocks become published and accepted by the normal (=honest) miners
        ka = ka + THR_orphanes_publish + 1;% all blocks of the attacker are now in common with the normal chain.
        sa = sa - THR_orphanes_publish - 1;% attacker has no secret blocks any more now.
        time_next_normal = -gen_time_normal*log(rand());% time until normal (=honest) miners find the next block
        Time.Delta = 0;
        if plot_flag, [hdn, hda] = plot_chain(chn(1:kn), cha(1:ka+sa), hdn, hda, Time, cnt_blocks, 'pause'); end % illustrate state of block chains
    end

    % --- Termination condition(s) of the simulation:
    if kn > N && sa == 0,% terminate if enough blocks were simulated and the attacker has no more secret blocks
        break;
    end
    
    if ka+sa > N_force_terminate, % Force termination of the simulation. If attacker has more blocks than the normal (=honest) miners,
        % publish them now to get the blocks credited, and then terminate the simulation.
        if ka+sa > kn,
            blocks_won(ka+1:ka+sa) = 1;% These blocks are credited to the attacker
            chn(ka+1:kn) = 1;% orphaned
            chn(kn+1:ka+sa) = -1;% not orphaned
            cha(ka+1:ka+sa) = chn(ka+1:ka+sa);
            cnt_event_orphaned = cnt_event_orphaned + 1;
            Nb_of_blocks_orphaned_by_attacker(cnt_event_orphaned) = kn-ka;
            kn = ka+sa; % attacker's secretly mined blocks become published and accepted by the normal (=honest) miners
            Time.Delta = 0;
            if plot_flag, [hdn, hda] = plot_chain(chn(1:kn), cha(1:ka+sa), hdn, hda, Time, cnt_blocks); end % illustrate state of block chains
        end
        break;
    end
    
end% while 1

% Cut of the NaN entries from the results vector
blocks_won = blocks_won(1:kn);
Nb_of_blocks_orphaned_by_attacker = Nb_of_blocks_orphaned_by_attacker(1:cnt_event_orphaned);

%% 3 - Show results:
Number_of_blocks_simulated = kn %#ok<NOPTS>
Percentage_mining_power_selfish_miner = power_attack*100 %#ok<NOPTS>
Percentage_blocks_won_by_selfish_miner = sum(blocks_won)/length(blocks_won)*100 %#ok<NOPTS>
Percentage_of_mainchain_blocks_orphaned_by_selfish_miner = sum(Nb_of_blocks_orphaned_by_attacker)/kn*100 %#ok<NOPTS>

% Finally the histogram:
hfig=figure;
hist(Nb_of_blocks_orphaned_by_attacker,[1:max(2,max(Nb_of_blocks_orphaned_by_attacker))]); title('Lengths of Consecutive Blocks Orphaned on the Main Chain by the Selfish Miner'); xlabel('Event that this number of consecutive blocks were orphaned on the Main Chain'); ylabel('How often the rexpective event happened');
if ismatlab,% Octave does not understand the following formating
    set(0,'units','pixels');
    Pix_SS = get(0,'screensize');% info about the screen resolution in 'pixel'
    set(hfig, 'position', [0.25*Pix_SS(3), 1, 0.5*Pix_SS(3), 0.45*Pix_SS(4)]);% [x, y, width, height]
end


%% -----------------------------------------------------------------------------------------------------------
%% ---------------------------------------------- SUB-FUNCTION -----------------------------------------------
%% -----------------------------------------------------------------------------------------------------------

function [hdn, hda] = plot_chain(chn, cha, hdn, hda, Time, cnt_blocks, pause_flag)
% chn = the normal chain, row vector
% cha = the chain of the attacker
% The elements of the vector have the following meaning:
%       0 = block was mined by normal (=honest) miners
%     0.1 = block was mined by normal (=honest) miners and overruled a block from the selfish miner
%       1 = block was mined by attacker and caused an orphan of the normal (=honest) miners
%      -1 = block was mined by attacker and did not cause an orphan of the normal (=honest) miners
%       2 = (only in the attacker chain): secret block

global power_attack % selfish miner's hasing power share
global THR_orphanes_publish % max number of orpans that the selfish miner will create on the public main chain
global Pause_value % pause in seconds after each block, when plotting is active

ismatlab = false;
v=version;% typical Matlab version string: "7.5.0.338 (R2007b)"; typical Octave version string: "3.0.0"
if ~isempty(strfind(v,'R2')), % Matlab version string contains "R2" in it.
    ismatlab = true;
end

if nargin > 2,
    try
        delete(hdn.n);
    catch
        disp('ERROR with this software! (maybe you are using FreeMat?)');
        disp('Try running the function "selfish" with PlotFlag=false, or use Matlab or Octave for full plot support.');
        disp(' ');
        pause
        return;
    end
    delete(hdn.d);
    delete(hdn.o);
    delete(hdn.m);
    
    delete(hda.n);
    delete(hda.d);
    delete(hda.o);
    delete(hda.m);
    delete(hda.z);

    delete(hdn.ti);
    delete(hdn.dt);
    
    delete(hdn.t1);
    delete(hdn.t2);
    delete(hdn.t3);
    delete(hdn.t4);
    delete(hdn.t5);
    delete(hdn.t6);
    delete(hdn.t7);
    delete(hdn.t8);
    
    delete(hdn.t9);
    delete(hdn.t10);
    delete(hdn.t11);
    
else % initial call
    if ismatlab,% Octave does not understand the following formating
        hfig = figure;
        set(0,'units','pixels');
        Pix_SS = get(0,'screensize');% info about the screen resolution in 'pixel'
        set(hfig, 'position', [0, Pix_SS(4), Pix_SS(3), 0.3*Pix_SS(4)]);% [x, y, width, height]
    else
        disp(' ')
        disp('*** Please manually change the width of the figure that will now appear, ***')
        disp('*** to take the full screen width for best visual results!               ***')
        disp(' ')
        disp('--> Press any key to continue <--')
        pause
        hfig = figure;
    end
end

% Only display a window of 100 blocks:
len = max(length(chn), length(cha));
if len > 100,
    chn = chn(len-99:end);
    cha = cha(len-99:end);
end

chn_0 = chn; chn_0(chn_0==1)=999; chn_0(chn_0==-1)=999; chn_0(chn_0==0.1)=999;%  0: green
chn_d = chn; chn_d(chn_d==1)=999; chn_d(chn_d==-1)=999; chn_d(chn_d==0)=999;  %  0: green
chn_1 = chn; chn_1(chn_1==0)=999; chn_1(chn_1==-1)=999; chn_1(chn_1==0.1)=999;%  1: red
chn_m = chn; chn_m(chn_m==1)=999; chn_m(chn_m== 0)=999; chn_m(chn_m==0.1)=999;% -1: pink

cha_0 = cha; cha_0(cha_0==1)=999; cha_0(cha_0==-1)=999; cha_0(cha_0==2)=999; cha_0(cha_0==0.1)=999;%  0: green
cha_d = cha; cha_d(cha_d==1)=999; cha_d(cha_d==-1)=999; cha_d(cha_d==2)=999; cha_d(cha_d==0)=999;  %  0: green
cha_1 = cha; cha_1(cha_1==0)=999; cha_1(cha_1==-1)=999; cha_1(cha_1==2)=999; cha_1(cha_1==0.1)=999;%  1: red
cha_m = cha; cha_m(cha_m==1)=999; cha_m(cha_m== 0)=999; cha_m(cha_m==2)=999; cha_m(cha_m==0.1)=999;% -1: pink
cha_z = cha; cha_z(cha_z==0)=999; cha_z(cha_z==-1)=999; cha_z(cha_z==1)=999; cha_z(cha_z==0.1)=999;%  2: black

chn_0(chn_0==0) = 1;
chn_d(chn_d==0.1) = 1;
chn_m(chn_m==-1) = 1;

cha_0(cha_0==0) = 1;
cha_d(cha_d==0.1) = 1;
cha_m(cha_m==-1) = 1;
cha_z(cha_z==2) = 1;

if nargin > 2, % normal section
    if ismatlab,
        hdn.n = plot(2*chn_0,'gs', 'MarkerFaceColor','g'); hold on;
        hdn.d = plot(2*chn_d,'cs', 'MarkerFaceColor','c'); hold on;
        hdn.o = plot(2*chn_1,'rs', 'MarkerFaceColor','r'); hold on;
        hdn.m = plot(2*chn_m,'ms', 'MarkerFaceColor','m'); hold on;
        
        hda.n = plot(1*cha_0,'gs', 'MarkerFaceColor','g'); hold on;
        hda.d = plot(1*cha_d,'cs', 'MarkerFaceColor','c'); hold on;
        hda.o = plot(1*cha_1,'rs', 'MarkerFaceColor','r'); hold on;
        hda.m = plot(1*cha_m,'ms', 'MarkerFaceColor','m'); hold on;
        hda.z = plot(1*cha_z,'ks', 'MarkerFaceColor','k'); hold on;
    else
        hdn.n = plot(2*chn_0,'gs'); hold on;
        hdn.d = plot(2*chn_d,'cs'); hold on;
        hdn.o = plot(2*chn_1,'rs'); hold on;
        hdn.m = plot(2*chn_m,'ms'); hold on;
        
        hda.n = plot(1*cha_0,'gs'); hold on;
        hda.d = plot(1*cha_d,'cs'); hold on;
        hda.o = plot(1*cha_1,'rs'); hold on;
        hda.m = plot(1*cha_m,'ms'); hold on;
        hda.z = plot(1*cha_z,'ks'); hold on;
    end
    cnt_blk_tot = cnt_blocks.found_normal + cnt_blocks.found_attack;
    hdn.ti = text(50,2.55,['Time = ',num2str(Time.Total),' min (Total blocks calculated = ', ...
        num2str(cnt_blk_tot),' --> 1 block per ',num2str(Time.Total/cnt_blk_tot),' min)']);
    hdn.dt = text(50,2.35,['Delta = ',num2str(Time.Delta),' min (Blocks on Main Chain = ', ...
        num2str(cnt_blocks.in_main_chain),' --> 1 block per ',num2str(Time.Total/cnt_blocks.in_main_chain),' min)']);
    
    hdn.t1 = text(50,1.80, 'Blocks calculated by...');
    hdn.t2 = text(50,1.60, ['...honest miners: ', num2str(cnt_blocks.found_normal), ' (',num2str(cnt_blocks.found_normal/cnt_blk_tot*100),'%)']);
    hdn.t3 = text(50,1.40, ['...selfish miner: ', num2str(cnt_blocks.found_attack), ' (',num2str(cnt_blocks.found_attack/cnt_blk_tot*100),'%)']);
    hdn.t4 = text(50,1.20, ['...Total number:  ', num2str(cnt_blk_tot),' (100%)']);
    
    hdn.t5 = text(68,1.80, ['--> of which orphaned (i.e. mined in vain):']);
    hdn.t6 = text(68,1.60, ['--> ',num2str(cnt_blocks.orphaned_normal),' (',num2str(cnt_blocks.orphaned_normal/cnt_blocks.found_normal*100),'%)']);
    hdn.t7 = text(68,1.40, ['--> ',num2str(cnt_blocks.orphaned_attack),' (',num2str(cnt_blocks.orphaned_attack/cnt_blocks.found_attack*100),'%)']);
    hdn.t8 = text(68,1.20, ['--> ',num2str(cnt_blocks.orphaned_normal+cnt_blocks.orphaned_attack), ...
        ' (',num2str((cnt_blocks.orphaned_normal+cnt_blocks.orphaned_attack)/cnt_blk_tot*100),'%)']);

    hdn.t9  = text(50,0.67, ['Number of blocks that were found in current Main Chain by...']);
    tmp_cnt_hon = cnt_blocks.found_normal - cnt_blocks.orphaned_normal;
    tmp_cnt_sel = cnt_blocks.in_main_chain - tmp_cnt_hon;
    hdn.t10 = text(50,0.47, ['...honest miners:  ',num2str(tmp_cnt_hon),' (',num2str(tmp_cnt_hon/(tmp_cnt_hon+tmp_cnt_sel)*100),'%)']);
    hdn.t11 = text(50,0.27, ['...selfish miners: ',num2str(tmp_cnt_sel),' (',num2str(tmp_cnt_sel/(tmp_cnt_hon+tmp_cnt_sel)*100),'%)']);

    
else % initialization section
    if ismatlab,
        hdn.n = plot(2*chn_0,'ws', 'MarkerFaceColor','w'); hold on;
        hdn.d = plot(2*chn_d,'ws', 'MarkerFaceColor','w'); hold on;
        hdn.o = plot(2*chn_1,'ws', 'MarkerFaceColor','w'); hold on;
        hdn.m = plot(2*chn_m,'ws', 'MarkerFaceColor','w'); hold on;

        hda.n = plot(1*cha_0,'ws', 'MarkerFaceColor','w'); hold on;
        hda.d = plot(1*cha_d,'ws', 'MarkerFaceColor','w'); hold on;
        hda.o = plot(1*cha_1,'ws', 'MarkerFaceColor','w'); hold on;
        hda.m = plot(1*cha_m,'ws', 'MarkerFaceColor','w'); hold on;
        hda.z = plot(1*cha_z,'ws', 'MarkerFaceColor','w'); hold on;
    else
        hdn.n = plot(2,'ws'); hold on;
        hdn.d = plot(2,'ws'); hold on;
        hdn.o = plot(2,'ws'); hold on;
        hdn.m = plot(2,'ws'); hold on;

        hda.n = plot(1,'ws'); hold on;
        hda.d = plot(1,'ws'); hold on;
        hda.o = plot(1,'ws'); hold on;
        hda.m = plot(1,'ws'); hold on;
        hda.z = plot(1,'ws'); hold on;
    end
    hdn.ti = text(50,2.35,[' ']);
    hdn.dt = text(50,2.35,[' ']);
    hdn.t1 = text(50,2.35,[' ']);
    hdn.t2 = text(50,2.35,[' ']);
    hdn.t3 = text(50,2.35,[' ']);
    hdn.t4 = text(50,2.35,[' ']);
    hdn.t5 = text(50,2.35,[' ']);
    hdn.t6 = text(50,2.35,[' ']);
    hdn.t7 = text(50,2.35,[' ']);
    hdn.t8 = text(50,2.35,[' ']);
    hdn.t9 = text(50,2.35,[' ']);
    hdn.t10 = text(50,2.35,[' ']);
    hdn.t11 = text(50,2.35,[' ']);

    xlabel('block number');
    ylabel('attacker''s chain (bottom)    |    public chain (top)');
    title(['Selfish Miner''s Hashing Power = ',num2str(power_attack*100),'% of Total Network; Max. Length of Orphans Caused by Selfish Miner = ',num2str(THR_orphanes_publish),]);
    text(5,1.80, 'Blockchain that the honest miners are working on (public Main Chain)');
    text(5,1.13, 'Blockchain that the attacker (selfish miner) is working on (secret chain)');

    text(75,0.37, 'by Michael\_S at bitcointalk.org');
    text(75,0.17, '1MichaS16UMKFgNjanKrtfD51HpBkqPAwD');
    
    axis([1 100 0 3]);
    
    plot(5, 2.55, 'gs', 'MarkerFaceColor','g'); text(6,2.52,'Block mined by honest miner');
    plot(5, 2.35, 'cs', 'MarkerFaceColor','c'); text(6,2.32,'Block first mined by selfish miner, then replaced by honest miner');
    plot(5, 0.70, 'ms', 'MarkerFaceColor','m'); text(6,0.67,'Block mined by selfish miner (without replacement)');
    plot(5, 0.50, 'rs', 'MarkerFaceColor','r'); text(6,0.47,'Block first mined by honest miner, then replaced by selfish miner');
    plot(5, 0.30, 'ks', 'MarkerFaceColor','k'); text(6,0.27,'Block mined secretly by selfish miner, not yet published');

end

if nargin > 6,
    if Pause_value==inf,
        if ~ismatlab,
            disp('--> Press any key to see next block (focus must be on console when you press the key) <--')
        end
        pause;
    else
        pause(Pause_value);
    end
end