# Encrypted control system using RSA

**URL:** <https://forumautomation.com/t/encrypted-control-system-using-rsa/5393>\
**Category:** Industrial Networking\
**Created:** [December 5, 2018, 8:33am UTC](https://forumautomation.com/t/encrypted-control-system-using-rsa/5393 "2018-12-05T08:33:56Z")\
**Posts on this page:** 1\
**Page:** 1

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**Author:** ![Flavio](https://forumautomation.com/letter_avatar_proxy/v4/letter/f/d07c76/32.png) [@Flavio](https://forumautomation.com/u/Flavio)\
**Post date:** [December 5, 2018, 8:33am UTC](https://forumautomation.com/t/encrypted-control-system-using-rsa/5393/1 "2018-12-05T08:33:56Z")

</div>

I am tying to implement an encrypted control system with Matlab using RSA encryption. The problem is that it is not working and i don’t get the correct output. In particular the scheme i am following is ![postare%20su%20internet](https://cdn.forumautomation.com/original/2X/2/2060853b4cee4c0bd56f27c4e6bbea740b182068.png) . My code is

```
A_p = [9.9998*(10)^-1 1.9700*(10)^-2; -1.970*(10)^-2 9.7025*(10)^-1];

```

B\_p = [9.9900\*(10)^-5; 9.8508\*(10)^-3]; C\_p = [1 0]; D\_p = 0;

X0 = [1;0]; %initial conditions for the plant

t = [0:0.01:5]; %sampling time

u = ones(1,length(t)); %encrypted input y\_p = zeros(1, length(t)); %output of the plant x\_p = zeros(2, length(t)); %state of the plant x\_c = zeros(2, length(t)); %state of the controller

x\_p(:, 1) = X0; %assign the initial values to the satet of the %plant

%parameters of the controller

A\_c = [1 0.0063; 0 0.3678]; B\_c = [0; 0.0063]; C\_c = [10 -99.90]; D\_c = 3;

end\_t = length(t);

N = 94399927; % N=p\*q e = 11; %public key d = 85800451; %private key

%encrypted parameters for the controller

A\_enc = mod(A\_c.^e, N); B\_enc = mod(B\_c.^e, N); C\_enc = mod(C\_c.^e, N); D\_enc = mod(D\_c.^e, N);

xc\_enc = zeros(2,length(t)); %x\_c encrypted y\_enc = zeros(1,length(t)); %y\_c encrypted

u\_dec = ones(1, length(t)); %u decripted

y\_quant = zeros(1, length(t));

for ind=1:end\_t-1

```
%plant

x_p(:, ind+1) = A_p*x_p(: ,ind) + B_p*u_dec(ind);
y_p(ind) = C_p*x_p(: ,ind);

 y_quant(ind) = uencode(y_p(ind),3); %quantization

%encryption of y_p

y_enc(ind) = modpow(y_quant(ind), e, N);;  

%controller with encrypted parameter
xc_enc(:, ind+1) = A_enc*xc_enc(:, ind) - B_enc*y_enc(ind);
u(ind+1) = C_enc*xc_enc(:, ind) - D_enc*y_enc(ind); 

%decrypting u
u_dec(ind+1) = modpow(u(ind+1),d,N);

```

%function to do the modular exponentiation with big numbers in Matlab

```
function result = modpow(base,exp,m) 
   result = 1;
   while (exp > 0) 
      if bitand(exp,1) > 0
         result = mod((result * base),m);
      end
      exp = bitshift(exp,-1);
      base = mod(base^2,m);
   end
end

```

end

figure plot(t,y\_enc);

figure plot(t,u);

I hope it is understandable, if not please tell me i will edit. Can somebody help me? Thank’s in advance.

p.s. I am trying to implement what is written in the paper “Cyber-Security Enhancement of Networked Control Systems Using Homomorphic Encryption” of Kiminao Kogiso and Takahiro Fujita.