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Data Encryption Standard (DES)

Data Encryption Standard (DES)

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18 Aug 2012 (Updated )

The last generation of encryption standard, good for cryptography study and cipher design.

DES(input64,mode,key)
function [varargout] = DES(input64,mode,key)
%DES: Data Encryption Standard
% Encrypt/Decrypt a 64-bit message using a 64-bit key using the Feistel Network
% -------------------------------------------------------------------------
% Inputs: 
%        input64 = a 64-bit message 
%           mode = either 'ENC' encryption or 'DEC' decryption (default 'ENC')
%            key = a 56/64-bit key (optional under 'ENC', but mandatory under 'DEC')
% Outputs:
%   varargout{1} = output64, a 64-bit message after encryption/decryption
%   varargout{2} = a 64-bit key, if a 64-bit key is not provided as an input
% -------------------------------------------------------------------------
% Demos:
%   plaintext = round(rand(1,64));
%   [ciphertext,key] = DES(plaintext);       % Encryption syntex 1
%   [ciphertext1,key] = DES(plaintext,'ENC'); % Encryption syntex 2
%   deciphertext1 = DES(ciphertext1,'DEC',key);% Decryption syntex
% 
%   key56 = round(rand(1,56));
%   [ciphertext2,key64] = DES(plaintext,'ENC',key56);% Encryption syntex 3 (56-bit key)
%   deciphertext2 = DES(ciphertext2,'DEC',key64);     % Decryption syntex   (64-bit key)
%   ciphertext3 = DES(plaintext,'ENC',key64);       % Encryption syntex 3 (64-bit key)
%   deciphertext3 = DES(ciphertext3,'DEC',key56);     % Decryption syntex   (56-bit key)
%   
%   % plot results
%   subplot(4,2,1),plot(plaintext),ylim([-.5,1.5]),xlim([1,64]),title('plaintext')
%   subplot(4,2,2),plot(ciphertext),ylim([-.5,1.5]),xlim([1,64]),title('ciphertext')
%   subplot(4,2,3),plot(deciphertext1),ylim([-.5,1.5]),xlim([1,64]),title('deciphertext1')
%   subplot(4,2,4),plot(ciphertext1),ylim([-.5,1.5]),xlim([1,64]),title('ciphertext1')
%   subplot(4,2,5),plot(deciphertext2),ylim([-.5,1.5]),xlim([1,64]),title('deciphertext2')
%   subplot(4,2,6),plot(ciphertext2),ylim([-.5,1.5]),xlim([1,64]),title('ciphertext2')
%   subplot(4,2,7),plot(deciphertext3),ylim([-.5,1.5]),xlim([1,64]),title('deciphertext3')
%   subplot(4,2,8),plot(ciphertext3),ylim([-.5,1.5]),xlim([1,64]),title('ciphertext3')
% -------------------------------------------------------------------------
% NOTE: 
% 1. If a 64-bit key is provided, then its bit parities will be checked. If
%    a 56-bit key is provided, then it is automatically added 8 partity
%    checking bits. However, the 8 parity bits are never used in
%    DES encryption/decryption process. They are included just for the 
%    completeness of a DES implementation. 
% 2. Cipher modes are not provided in this simple script. If you are 
%    interested or do not know what does cipher modes mean, please go to page
%    http://en.wikipedia.org/wiki/Block_cipher_modes_of_operation
%    for details. Please keep in mind that selecting an inappropriate working
%    mode may extremely weaken the security of your messages.
% 3. A general description of DES can be found at its wiki page:
%    http://en.wikipedia.org/wiki/Data_Encryption_Standard
%    The detailed cryptographical primitives can be found under the page:
%    http://en.wikipedia.org/wiki/DES_supplementary_material
%    If you want to speed-up the DES code here, you can simply store these
%    primitives in memory and call them when you need. 
% -------------------------------------------------------------------------
% By Yue (Rex) Wu
% ECE Dept @ Tufts Univ.
% 08/18/2012
% If you find bugs, please email me via ywu03@ece.tufts.edu
% -------------------------------------------------------------------------


%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%%                           0. Initialization                           %%
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
% 0.1 check input
error(nargchk(1,3,nargin));
switch nargin
    case 1
        mode = 'ENC';
        K = round(rand(8,7));
        K(:,8) = mod(sum(K,2),2); % note these eight bits of key are never used in encryption
        K = reshape(K',1,64);
        varargout{2} = K;
    case 2
        switch mode
            case 'ENC'
                K = round(rand(8,7));
                K(:,8) = mod(sum(K,2),2); % note these eight bits of key are never used in encryption
                K = reshape(K',1,64);
                varargout{2} = K;
            case 'DEC'
                error('Key has to be provided in decryption mode (DEC)')
            otherwise 
                error('WRONG working mode!!! Select either encrtyption mode: ENC or decryption mode: DEC !!!')
        end
    case 3 
        if isempty(setdiff(unique(key),[0,1])) % check provided key type
            if numel(key) == 64  % check provided key parity
                keyParityCheck = @(k) (sum(mod(sum(reshape(k,8,8)),2))==0);
                if keyParityCheck(key) == 1
                    K = key(:)';
                else
                    error('Key parity check FAILED!!!')
                end
            elseif numel(key) == 56 % add parity bits
                K = reshape(key,7,8)';
                K(:,8) = mod(sum(K,2),2); % note these eight bits of key are never used in encryption
                K = reshape(K',1,64);
                varargout{2} = K;
                display('Key parity bits added')
            else
                error('Key has to be either 56 or 64-bit long!!!')
            end
        else
            error('Key has to be binary!!!')
        end
end
        
% 0.2 check message length and type
if numel(input64) == 64 && isempty(setdiff(unique(input64),[0,1]))
    P = input64;
else
    error('Message has to be a 64-bit message!!!')
end
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%%                   1. Cryptographical primitives                       %%
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
% 1.1 define splitting function
HALF_L = @(message) message(1:32);
HALF_R = @(message) message(33:64);
% 1.2 define expansion function
EF = @(halfMessage) [halfMessage([32,4:4:28])',(reshape(halfMessage,4,8))',halfMessage([5:4:29,1])'];
% 1.3 define key mixing (KM)
KM = @(expandedHalfMessage,rK) xor(expandedHalfMessage,reshape(rK,6,8)');
% 1.4 define eight substitution tables
% input: 0	1   2   3   4   5   6   7   8   9   10  11  12  13  14  15
st{1} = [14	4	13	1	2	15	11	8	3	10	6	12	5	9	0	7;...
         0  15	7	4	14	2	13	1	10	6	12	11	9	5	3	8;...
         4	1	14	8	13	6	2	11	15	12	9	7	3	10	5	0;...
         15	12	8	2	4	9	1	7	5	11	3	14	10	0	6	13];
st{2} = [15	1	8	14	6	11	3	4	9	7	2	13	12	0	5	10;...
    	3	13	4	7	15	2	8	14	12	0	1	10	6	9	11	5;...
		0	14	7	11	10	4	13	1	5	8	12	6	9	3	2	15;...
		13	8	10	1	3	15	4	2	11	6	7	12	0	5	14	9];
st{3} = [10	0	9	14	6	3	15	5	1	13	12	7	11	4	2	8;...
		13	7	0	9	3	4	6	10	2	8	5	14	12	11	15	1;...
		13	6	4	9	8	15	3	0	11	1	2	12	5	10	14	7;...
		1	10	13	0	6	9	8	7	4	15	14	3	11	5	2	12];
st{4} = [7	13	14	3	0	6	9	10	1	2	8	5	11	12	4	15;...
		13	8	11	5	6	15	0	3	4	7	2	12	1	10	14	9;...
		10	6	9	0	12	11	7	13	15	1	3	14	5	2	8	4;...
		3	15	0	6	10	1	13	8	9	4	5	11	12	7	2	14];
st{5} = [2	12	4	1	7	10	11	6	8	5	3	15	13	0	14	9;...
		14	11	2	12	4	7	13	1	5	0	15	10	3	9	8	6;...
		4	2	1	11	10	13	7	8	15	9	12	5	6	3	0	14;...
		11	8	12	7	1	14	2	13	6	15	0	9	10	4	5	3];
st{6} = [12	1	10	15	9	2	6	8	0	13	3	4	14	7	5	11;...
		10	15	4	2	7	12	9	5	6	1	13	14	0	11	3	8;...
		9	14	15	5	2	8	12	3	7	0	4	10	1	13	11	6;...
		4	3	2	12	9	5	15	10	11	14	1	7	6	0	8	13];
st{7} = [4	11	2	14	15	0	8	13	3	12	9	7	5	10	6	1;...
		13	0	11	7	4	9	1	10	14	3	5	12	2	15	8	6;...
		1	4	11	13	12	3	7	14	10	15	6	8	0	5	9	2;...
		6	11	13	8	1	4	10	7	9	5	0	15	14	2	3	12];
st{8} = [13	2	8	4	6	15	11	1	10	9	3	14	5	0	12	7;...
		1	15	13	8	10	3	7	4	12	5	6	11	0	14	9	2;...
		7	11	4	1	9	12	14	2	0	6	10	13	15	3	5	8;...
		2	1	14	7	4	10	8	13	15	12	9	0	3	5	6	11];
% the eight binary s-boxes
for i = 1:8
    ST{i} = mat2cell(blkproc(st{i},[1,1],@(x) de2bi(x,4,'left-msb')),ones(1,4),ones(1,16)*4);
end
% 1.5 define subsitution function (SBOX)
SUBS = @(expandedHalfMessage,blkNo) ST{blkNo}{bi2de(expandedHalfMessage(blkNo,[1,6]),'left-msb')+1,bi2de(expandedHalfMessage(blkNo,[2:5]),'left-msb')+1};
SBOX = @(expandedHalfMessage) [SUBS(expandedHalfMessage,1);SUBS(expandedHalfMessage,2);...
                               SUBS(expandedHalfMessage,3);SUBS(expandedHalfMessage,4);...
                               SUBS(expandedHalfMessage,5);SUBS(expandedHalfMessage,6);...
                               SUBS(expandedHalfMessage,7);SUBS(expandedHalfMessage,8)];
% 1.6 define permutation function (PBOX)
PBOX = @(halfMessage) halfMessage([16  7 20 21  29 12 28 17 ... 
                                    1 15 23 26   5 18 31 10 ...
                                    2  8 24 14  32 27  3  9 ...
                                   19 13 30  6  22 11  4  25]);
% 1.7 define initial permutation (IP)
IP = @(message) message([58	50	42	34	26	18	10	2 ...
                        60	52	44	36	28	20	12	4 ...
                        62	54	46	38	30	22	14	6 ...
                        64	56	48	40	32	24	16	8 ...
                        57	49	41	33	25	17	9	1 ...
                        59	51	43	35	27	19	11	3 ...
                        61	53	45	37	29	21	13	5 ...
                        63	55	47	39	31	23	15	7]);
% 1.8 define final permutation (FP)
FP = @(message) message([40	8	48	16	56	24	64	32 ...
                        39	7	47	15	55	23	63	31 ...
                        38	6	46	14	54	22	62	30 ...
                        37	5	45	13	53	21	61	29 ...
                        36	4	44	12	52	20	60	28 ...
                        35	3	43	11	51	19	59	27 ...
                        34	2	42	10	50	18	58	26 ...
                        33	1	41	9	49	17	57	25]);
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%%                           2. key schedule                             %%
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
% 2.1 define permuted choice 1 (PC1)
PC1L = @(key64) key64([57	49	41	33	25	17	9 ...
                    1	58	50	42	34	26	18 ...
                    10	2	59	51	43	35	27 ...
                    19	11	3	60	52	44	36]);
PC1R = @(key64) key64([63	55	47	39	31	23	15 ...
                    7	62	54	46	38	30	22 ... 
                    14	6	61	53	45	37	29 ...
                    21	13	5	28	20	12	4]);
% 2.2 define permuted choice 2 (PC2)
PC2 = @(key56) key56([14 17	11	24	1	5	3	28 ...
                     15	6	21	10	23	19	12	4 ...
                     26	8	16	7	27	20	13	2 ...
                     41	52	31	37	47	55	30	40 ...
                     51	45	33	48	44	49	39	56 ...
                     34	53	46	42	50	36	29	32]);
% 2.3 define rotations in key-schedule (RK)
% round# 1 2 3 4 5 6 7 8 9 0 1 2 3 4 5 6
   RK = [1 1 2 2 2 2 2 2 1 2 2 2 2 2 2 1];
% 2.4 define key shift function (KS)
KS = @(key28,s) [key28(s+1:end),key28(1:s)];    
% 2.5 define sub-keys for each round
leftHKey = PC1L(K); % 28-bit half key
rightHKey = PC1R(K);% 28-bit half key
for i = 1:16
    leftHKey = KS(leftHKey,RK(i));
    rightHKey = KS(rightHKey,RK(i));
    key56 = [leftHKey ,rightHKey];
    subKeys(i,:) = PC2(key56(:));
end
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%%                           3. DES main loop                            %%
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
% 3.1 initial permutation
C = IP(P);       
switch mode
    case 'ENC' % if encryption, split 64 message to two halves
        L{1} = HALF_L(C); % left-half 32-bit
        R{1} = HALF_R(C); % right-half 32-bit
    case 'DEC' % if decryption, swapping two halves
        L{1} = HALF_R(C);
        R{1} = HALF_L(C);       
end
% 3.2 cipher round 1 to 16
for i = 1:16
     L{i+1} = R{i}; % half key: 32-bit
     expended_R = EF(R{i}); % expended half key: 32-bit to 48-bit
     switch mode
        case 'ENC' % if encryption, apply sub-keys in the original order
            mixed_R = KM(expended_R,subKeys(i,:)); % mixed with sub-key: 48-bit
        case 'DEC' % if decryption, apply sub-keys in the reverse order
            mixed_R = KM(expended_R,subKeys(16-i+1,:)); % mixed with sub-key: 48-bit
     end
     substituted_R = SBOX(mixed_R); % substitution: 48-bit to 32-bit
     permuted_R = PBOX(reshape(substituted_R',1,32)); % permutation: 32-bit
     R{i+1} = xor(L{i},permuted_R); % Feistel function: 32-bit
end
% 3.3 final permutation
switch mode
    case 'ENC'
        C = [L{end},R{end}]; 
    case 'DEC'
        C = [R{end},L{end}];
end
output64 = FP(C);
varargout{1} = output64;
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%%                                   END                                 %%
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%

















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