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PrivKVM.m
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PrivKVM.m
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function [Freq, Mean] = PrivKVM(data,N_key,N_iter,epsilon)
% for key perturbation (1st round)
p1 = exp(epsilon/2)/(exp(epsilon/2)+1);
% for value perturbation (all rounds)
p2 = exp(epsilon/(2*N_iter))/(exp(epsilon/(2*N_iter))+1);
Mean = zeros(N_key,1);
counter = Perturb(data,N_key,p1,p2,Mean);
[Freq, Mean] = Calibrate(counter,N_key,p1,p2,Mean);
p1 = 0.5;
for i = 2:N_iter
counter = Perturb(data,N_key,p1,p2,Mean);
[~, Mean] = Calibrate(counter,N_key,p1,p2,Mean);
end
end
function counter = Perturb(data,N_key,p1,p2,Mean)
if isa(data,'cell') == 1
counter = Perturb_cell(data,N_key,p1,p2,Mean);
else
counter = Perturb_matrix(data,N_key,p1,p2,Mean);
end
end
function counter = Perturb_cell(data,N_key,p1,p2,Mean)
N_user = size(data,1);
counter = zeros(3,N_key); % output
randIndex = randi(N_key,N_user,1);
randBit = randsrc(N_user,1,[[0 1]; [p1 1-p1]]);
randSign = randsrc(N_user,1,[[-1 1]; [1-p2 p2]]);
for i = 1:N_user
S = data{i};
index = randIndex(i);
[~,loc] = ismember(index,S(:,1)); % whether key=index is in the first col
% perturb the key and discrete the value
if loc > 0
% key exists
key = randsrc(1,1,[[0 1]; [1-p1 p1]]);
value = randsrc(1,1,[[-1 1]; [(1-S(loc,2))/2 (1+S(loc,2))/2]]);
else
% key does not exist
m = Mean(index);
key = randBit(i);
value = randsrc(1,1,[[-1 1]; [(1-m)/2 (1+m)/2]]);
end
% perturb the value
value = key*value*randSign(i);
counter(1,index) = counter(1,index) + (value == 1);
counter(2,index) = counter(2,index) + (value == -1);
counter(3,index) = counter(3,index)+1;
end
end
function counter = Perturb_matrix(data,N_key,p1,p2,Mean)
N_user = size(data,1);
counter = zeros(3,N_key); % output
randIndex = randi(N_key,N_user,1);
randBit = randsrc(N_user,1,[[0 1]; [p1 1-p1]]);
randSign = randsrc(N_user,1,[[-1 1]; [1-p2 p2]]);
for i = 1:N_user
key = data(i,1); value = data(i,2);
index = randIndex(i);
% perturb the key and discrete the value
if index == key
% key exists
key = randsrc(1,1,[[0 1]; [1-p1 p1]]);
value = randsrc(1,1,[[-1 1]; [(1-value)/2 (1+value)/2]]);
else
% key does not exist
m = Mean(index);
key = randBit(i);
value = randsrc(1,1,[[-1 1]; [(1-m)/2 (1+m)/2]]);
end
% perturb the value
value = key*value*randSign(i);
counter(1,index) = counter(1,index) + (value == 1);
counter(2,index) = counter(2,index) + (value == -1);
counter(3,index) = counter(3,index)+1;
end
end
function [Freq, Mean] = Calibrate(counter,N_key,p1,p2,oldMean)
Freq = zeros(N_key,1);
Mean = zeros(N_key,1);
for i = 1:N_key
n1 = counter(1,i); n2 = counter(2,i);
N = n1+n2;
if N == 0
Freq(i) = 0;
Mean(i) = oldMean(i);
continue;
end
Freq(i) = (p1-1+N/counter(3,i))/(2*p1-1);
n1 = ((p2-1)*N+n1)/(2*p2-1); n1 = Clip(n1,0,N);
n2 = ((p2-1)*N+n2)/(2*p2-1); n2 = Clip(n2,0,N);
Mean(i) = Clip((n1-n2)/N,-1,1);
end
end
function x = Clip(x,lb,ub)
if x<lb
x=lb;
end
if x>ub
x=ub;
end
end