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⛄ 内容介绍
网络安全对工业控制系统（ICS）至关重要，如船舶自动化、制造、建筑和能源自动化系统。许多控制应用需要硬实时通道，其延迟和抖动在几毫秒或更少的水平。据我们所知，没有一种加密算法对于现有的工业现场总线的硬实时通道来说足够快，因此，使关键任务的应用容易受到网络攻击，如延迟和数据注入攻击。在这篇文章中，我们提出了一种新型的递归水印（RWM）算法，用于硬实时控制系统数据完整性验证。使用水印密钥，发射器将水印噪声应用于硬实时信号，并通过未加密的硬实时通道发送。同样的密钥通过加密的非实时信道传输给接收器。通过相同的密钥，接收器可以检测到数据是否被攻击者修改，并采取行动防止灾难性的破坏。我们提供分析和方法来设计适当的水印密钥以确保可靠的攻击检测。
⛄ 部分代码
%%
% Real time water mark signal prototype
% Zhen Song
% Parameter
Len=1000
Seed=123
mu=0.2
Nq=1024 % quantiation level
N0=1
% Nc=50 % reset every 50 cycles
% Attack Parameters prototype
AttTime = 400;
AttType = 'delay';
% AttType = 'inject';
rng(Seed) % pseudo rand
Hf=rand(Len,1);
% Hashing Dictionary
HashR=rand(Len,1);
%% Original signal
t=linspace(1,5*pi,Len)';
% Simple
%S=sin(t);
% More demanding
S=sin(t)+cos(2*t) + [2*ones(Len/2,1); transpose(linspace(2,-2,Len/4)) ;-2*ones(Len/4,1)];
Vsf=S+mu*Hf; %V = S+Hf*mu
Vsfr=zeros(length(S),1);
Vsfr(1)=S(1);
% Vsfr(2:end)=Vsf(2:end)+mu*HashPM1(Vsf(1:end-1), HashR); % scaling factor
% must be the same!
% %V = S+Hf*mu+Hr*mu
for idx=2:Len
Vsfr(idx)=S(idx)+mu*Hf(idx)+mu*HashPM1(Vsfr(idx-1), HashR) - mu;
end
%% Recovery without attack
Shat=zeros(length(Vsfr),1);
% Reset point
Shat(1)=Vsfr(1);
for idx=2:Len
Shat(idx)=Vsfr(idx)-mu*Hf(idx)-mu*HashPM1(Vsfr(idx-1), HashR)+mu;
end
Sdiff=Shat-S;
%% Man in the midle attack
% Injection attack
AttInjection = Vsfr + [0*ones(AttTime,1); transpose(linspace(0,5,Len/4)) ; 5*ones(Len-Len/4-AttTime,1)];
% Time delay (Replay) attack
AttDelay = [Vsfr(1:AttTime); Vsfr(AttTime); Vsfr(AttTime+1:end-1)];
% Choose the attack
if strcmp(AttType, 'delay')
Vhack1=AttDelay;
elseif strcmp(AttType, 'inject')
Vhack1=AttInjection;
else
Vhack1= Vsfr;
end
%% Recovery with attack
Shat_hack1=zeros(length(Vhack1),1);
% Reset point
Shat_hack1(1)=Vhack1(1);
for idx=2:Len
Shat_hack1(idx)=Vhack1(idx)-mu*Hf(idx)-mu*HashPM1(Vhack1(idx-1), HashR) + mu;
end
Sdiff_hack1=Shat_hack1-S;
%% Chi^2 square test calculation
chi2test=[0];
% Chi square test
clear Y Y_attack n
for idx=2:Len
chi2test(idx)=chi_2(Shat_hack1(idx),Shat_hack1(idx-1));
end
%% Displaying results
close all;
subplot(3,2,1)
plot(S);
hold on;
plot(Vsfr, 'k');
% legend('S', 'S+Hf', 'S+Hf+Hr');
legend('S', 'V')
title('With Water Mark');
subplot(3,2,2)
plot(Vsfr);
hold on;
plot(Vhack1, '-.r');
plot([AttTime AttTime],[1.3*min([Vsfr; Vhack1]) 1.3*max([Vsfr; Vhack1])],'k--')
legend('V', 'V hack');
title(strcat('Attack at t=',num2str(AttTime)));
subplot(3,2,3)
% recover
plot(S);
hold on;
plot(Shat,'-.r');
legend('S', 'S hat');
title('Recovered signal.');
% subplot(3,2,4)
% % plot(abs(fft(Shat)));
% plot(abs(fft(diff(Shat))));
% title('FFT(diff (S hat) )')
subplot(3,2,4)
% plot(abs(fft(Shat)));
hold on
plot(chi2test);
plot([AttTime AttTime],[0 1.2*max(chi2test)],'k--')
title('Chi^{2} test')
legend('Chi^{2} test');
subplot(3,2,5)
h1=plot(S);
hold on;
h2=plot(Shat_hack1, 'r');
legend([h1, h2], 'S', 'S hat hack1');
plot([AttTime AttTime],[1.3*min([Shat_hack1; S]) 1.3*max([Shat_hack1; S])],'k--')
title(strcat('Attack at t=',num2str(AttTime)));
subplot(3,2,6)
% plot(abs(fft(Shat_hack1)));
hold on
h1=plot(abs(fft(diff(Shat_hack1))));
h2=plot(abs(fft(diff(Shat))));
legend([h1,h2],'S', 'hacked');
title('FFT(diff(S hat hack1))')
% Correction with Hf
A=[Hf S];
disp('Raw data')
cor=corrcoef(A)
A0=[Hf Vsfr];
disp('Noise')
cor0=corrcoef(A0)
A1=[Hf Shat];
A2=[Hf Shat_hack1];
disp('No attack')
cor1=corrcoef(A1)
disp('With delay attack')
cor2=corrcoef(A2)
function y = HashPM1_old(in, hash_dict)
% in is a column vector [-1, 1]
dict_len=length(hash_dict);
y = zeros(size(in));
% for idx =1:length(in)
if max(in) > min(in)
idx_dict = round((in-min(in))/(max(in)-min(in))*dict_len);
else
idx_dict = round((in-1.5)/(2.5)*dict_len);
end
idx0 = find(idx_dict<=0);
idx_dict(idx0)=1;
idx1 = find(idx_dict>=dict_len);
idx_dict(idx1)=dict_len;
y = hash_dict(idx_dict);
% end
end
%% Simplified Hashing function
% The upper one did not work properly so I created this simplified one, I
% did not want to touch your code :)
function y = HashPM1(in, hash_dict)
% dictionary length
dict_len=length(hash_dict);
y = zeros(size(in));
% Simple index search
% Signal bounded on [-10,10]
idx_dict = mod(round((in+10)/20 * dict_len),dict_len)+1;
y = hash_dict(idx_dict);
end
%% Chi^2 test function
function [gk_chi] = chi_2(y,y_attack)
persistent Y Y_attack n
% time-window length
window =50;
% variance of the noise - amplification
Variance = 10e-3;
if isempty(Y)
n = 0;
Y = zeros(window,1);
Y_attack = zeros(window,1);
else
if(n > 2)
% simple system dynamics compensation
dY = Y(1)-Y(2);
%dY = 0;
else
dY = 0;
end
% Buffering signal
Y = [y; Y(1:end-1)];
Y_attack = [y_attack+dY; Y_attack(1:end-1)];
n=n+1;
end
% test calculation
gk_chi = sum((Y-Y_attack).*Variance^-1.*(Y-Y_attack));
end
⛄ 运行结果
⛄ 参考文献
[1] 孙爱娟. 基于AES加密算法的改进及其MATLAB实现[D]. 哈尔滨理工大学, 2010.
[2] 刘昭勇, 代安定, 李康,等. 基于复合混沌系统的彩色图像加密算法及Matlab实现[J]. 湖南城市学院学报(自然科学版), 2018.
[3] 张晓峰, 贾晓强. 一种基于数字音频信号的加密算法[J]. 电子设计工程, 2018, 26(14):5.
