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BTC32_Analysis/BTC32_dummy_analysis.m

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+% Dummy MATLAB script - analysis of 32BTC Puzzle private keys
+%
+% Donations could be sent here: 1QKjnfVsTT1KXzHgAFUbTy3QbJ2Hgy96WU
+% ( i am poor Ukrainian student that will really appreciate your 
+% donates - have no home, living in the dorm and trying to cope 
+% for the smallest flat in the city - with no success at the moment,
+% nearly 10% of desired amount)
+
+%% Clear all: command window, workspace, figures
+clc;
+clear all;
+close all;
+
+%% Load and prepare the data
+    % Read the private keys from the file - stored as decimal prefix
+    % (there are two columns: 1) is the wallet index (unknown bits amount),
+    % 2) priv key non-zero part in decimal.
+data = dlmread('btc32_keys_dec.csv');
+    % Evaluate the "reminder" of the non-zero priv key part - each priv key
+    % has a form of 2^(n-1) + <reminder> where n is an amount of unknown bits
+    % and <reminder> is actually unknown its part that lies in interval 
+    % 2^(n-1) -- 2^n
+rem_2 = vpa( data(:,2) - 2.^(data(:,1)-1) );
+    % Compute the relative position of the priv key inside the 
+    % 2^n -- 2^(n+1) interval - "describe the Private Keys in
+	% dimensionless form"
+alpha = rem_2 ./ vpa( 2.^(data(:,1)) - 2.^(data(:,1)-1));
+
+%% Plot raw numbers/ histograms / autocorrelation function
+
+    % raw numbers
+fig = figure();
+plot(data(:,1), double(alpha), 'o');
+hold on;
+xlabel('index');
+ylabel('Place within interval');
+plot([63.5 63.5],[0 1],'--r', 'LineWidth',2);
+ylim([0 1]);
+saveas(fig, 'raw_alpha.png');
+close(fig);
+
+    % histograms
+        % All known priv keys
+fig = figure();
+subplot(2,1,1);
+hist(double(alpha),10);
+title('Histogram for all keys');
+xlim([0 1]);
+subplot(2,1,2);
+hist(double(alpha),40);
+title('(smaller bars)');
+xlim([0 1]);
+saveas(fig, 'hist_all.png');
+close(fig);
+
+        % 1-63 keys 
+fig = figure();
+subplot(2,1,1);
+hist(double(alpha(1:(end-11))),10);
+title('Histogram for 1-63 keys');
+xlim([0 1]);
+subplot(2,1,2);
+hist(double(alpha(1:(end-11))),40);
+title('(smaller bars)');
+xlim([0 1]);
+saveas(fig, 'hist_1_63.png');
+close(fig);
+
+        % all upper 5th keys 
+fig = figure();
+subplot(2,1,1);
+hist(double(alpha((end-10):end)),10);
+title('Histogram for 5th keys');
+xlim([0 1]);
+subplot(2,1,2);
+hist(double(alpha((end-10):end)),40);
+title('(smaller bars)');
+xlim([0 1]);
+saveas(fig, 'hist_upper_5th.png');
+close(fig);
+
+        % look more closely
+fig = figure();
+hist(double(alpha),100);
+title('Histogram all keys: tiny bins');
+xlim([0 1]);
+saveas(fig, 'hist_all_tiny_bins.png');
+close(fig);
+
+        % even more closely 
+fig = figure();
+hist(double(alpha),2000)
+title('Histogram all keys: very tiny bins');
+xlim([0 1]);
+saveas(fig, 'hist_all_very_tiny_bins.png');
+close(fig);
+
+    % Autocorrelation
+        % 1-63 keys 
+fig = figure();
+plot(xcorr(double(alpha(1:(end-11))) - mean(double(alpha(1:(end-11))))), '--o');
+title('Autocorrelation for 1-63 keys');
+xlim([0 length(double(alpha(1:(end-11))))*2])
+saveas(fig, 'autocorr_1_63.png');
+close(fig);
+
+        % all upper 5th keys 
+fig = figure();
+plot(xcorr(double(alpha((end-10):end)) - mean(double(alpha((end-10):end)))), '--o');
+title('Autocorrelation for 5th keys');
+xlim([0 length(double(alpha((end-10):end)))*2])
+saveas(fig, 'autocorr_upper_5th.png');
+close(fig);
+
+    % Inspect those with alpha ~ 0.82
+        % Get indecies of ~0.82 withing its alpha value
+[data((double(alpha)<0.84) .* (double(alpha)>0.8)==1,1),alpha((double(alpha)<0.84) .* (double(alpha)>0.8)==1)]

BTC32_Analysis/BTC32_dummy_simulation.m

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+% Dummy MATLAB script - analysis of 32BTC Puzzle private keys - simulation
+% of the key randomization - inspecting histograms
+%
+% Donations could be sent here: 1QKjnfVsTT1KXzHgAFUbTy3QbJ2Hgy96WU
+% ( i am poor Ukrainian student that will really appreciate your 
+% donates - have no home, living in the dorm and trying to cope 
+% for the smallest flat in the city - with no success at the moment,
+% nearly 10% of desired amount)
+
+%% Clear all
+close all;
+clear all;
+clc;
+
+%% Compose alphas array in a "similar" to BTC32 way
+    % Define the maximum integer generated by random generator
+    % (BTC 32 have 2^255-2^256 i assume)
+MAX_RANDOM_NUMBER = 10^14;
+    % Define the maximum used/interesting integer - BTC 32 only the first
+    % 160 numbers are interesting now - they are generated by projection
+    % of the 2^255 random onto 2^{bits} space by taking the reminder i
+    % assume
+MAX_INTERESTING_NUMBER = 10^11;
+    % Intervals are also growing logarithmic integers like in the BTC32
+    % but with a smaller "logarithmic" step - MATLAB random integers are
+    % limited to 52 bit
+intervals = unique(ceil(logspace(0,log10(MAX_INTERESTING_NUMBER),160)'));
+num_raw = randi(MAX_RANDOM_NUMBER,length(intervals),1);
+
+for i=1:length(num_raw)
+    num(i) = rem(num_raw(i), intervals(i));
+    alpha(i) = num(i) / intervals(i);
+end
+
+%% Plot histograms for the first 60 alphas and the last alphas
+
+fig = figure('Position',[10 10 1000 600]);
+
+subplot(2,1,1);
+
+hist(alpha(1:60),100);
+title('first 60 alphas');
+grid on;
+
+subplot(2,1,2);
+hist(alpha(61:end),100);
+title('...all remind alphas');
+grid on;
+
+saveas(fig, 'alpha_simulation_hist.png');
+close(fig)

BTC32_Analysis/alpha.csv

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+1,0
+2,0.5
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+100,0.3698115766805314
+105,0.4339139536794416
+110,0.6797900857488874
+115,0.5149424275913059

BTC32_Analysis/btc32_keys_dec.csv

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+1,1
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