In cryptography, a cipher (or cypher) is an algorithm for performing encryption or decryption—a series of well-defined steps that can be followed as a procedure. An alternative, less common term is encipherment. To encipher or encode is to convert information into cipher or code. In common parlance, “cipher” is synonymous with “code“, as they are both a set of steps that encrypt a message; however, the concepts are distinct in cryptography, especially classical cryptography.
Codes generally substitute different length strings of character in the output, while ciphers generally substitute the same number of characters as are input. There are exceptions and some cipher systems may use slightly more, or fewer, characters when output versus the number that was input.
In this post, we will discuss the Hill Cipher. Hill Cipher is a cryptographic algorithm to encrypt and decrypt an alphabetic text. In this cipher, each letter is represented by a number (eg. A = 0, B = 1, C = 2). To encrypt a message, each block of n letters (considered as an n-component vector) is multiplied by an invertible n × n matrix, against modulus 26. To decrypt the message, each block is multiplied by the inverse of the matrix used for encryption.
We will use C++ to write this algorithm due to the standard template library support. Hence, we will write the program of the Hill Cipher algorithm in C++, although, it’s very similar to C.
Encryption
INPUT:
line 1: size of the key matrix (n)
next n lines: key matrix
next line: message to encrypt
OUTPUT:
line 1: Encrypted message (ans)
The following is the Hill Cipher encryption algorithm program in C++.
#include<iostream>
#include<vector>
using namespace std;
int main(){
int x,y,i,j,k,n;
cout<<"Enter the size of key matrix\n";
cin>>n;
cout<<"Enter the key matrix\n";
int a[n][n];
for(i=0;i<n;i++){
for(j=0;j<n;j++){
cin>>a[i][j];
}
}
cout<<"Enter the message to encrypt\n";
string s;
cin>>s;
int temp = (n-s.size()%n)%n;
for(i=0;i<temp;i++){
s+='x';
}
k=0;
string ans="";
while(k<s.size()){
for(i=0;i<n;i++){
int sum = 0;
int temp = k;
for(j=0;j<n;j++){
sum += (a[i][j]%26*(s[temp++]-'a')%26)%26;
sum = sum%26;
}
ans+=(sum+'a');
}
k+=n;
}
cout<<ans<<'\n';
return 0;
}
OUTPUT:
Enter the size of key matrix 2 Enter the key matrix 4 1 3 2 Enter the message to encrypt helloworld gdddaivyvn
Decryption
INPUT:
line 1: size of the key matrix (n)
next n lines: key matrix
next line: message to encrypt
OUTPUT:
line 1: decrypted message (ans)
The following is the Hill Cipher decryption algorithm program in C++.
#include<iostream>
#include<vector>
using namespace std;
int modInverse(int a, int m){
a=a%m;
for(int x=-m;x<m;x++)
if((a*x)%m==1)
return x;
}
void getCofactor(vector<vector<int> > &a, vector<vector<int> > &temp, int p, int q, int n){
int i=0,j=0;
for(int row=0;row<n;row++){
for(int col=0;col<n;col++){
if(row!=p&&col!=q){
temp[i][j++] = a[row][col];
if (j==n-1){
j=0;
i++;
}
}
}
}
}
int determinant(vector<vector<int> > &a, int n, int N){
int D = 0;
if(n==1)
return a[0][0];
vector<vector<int> > temp(N, vector<int>(N));
int sign = 1;
for(int f=0;f<n;f++){
getCofactor(a, temp, 0, f, n);
D += sign * a[0][f] * determinant(temp, n - 1, N);
sign = -sign;
}
return D;
}
void adjoint(vector<vector<int> > &a,vector<vector<int> > &adj,int N){
if(N == 1){
adj[0][0] = 1;
return;
}
int sign = 1;
vector<vector<int> > temp(N, vector<int>(N));
for(int i=0;i<N;i++){
for(int j=0;j<N;j++){
getCofactor(a, temp, i, j, N);
sign = ((i+j)%2==0)? 1: -1;
adj[j][i] = (sign)*(determinant(temp, N-1 , N));
}
}
}
bool inverse(vector<vector<int> > &a, vector<vector<int> > &inv, int N){
int det = determinant(a, N, N);
if(det == 0){
cout << "Inverse does not exist";
return false;
}
int invDet = modInverse(det,26);
cout<<det%26<<' '<<invDet<<'\n';
vector<vector<int> > adj(N, vector<int>(N));
adjoint(a, adj, N);
for(int i=0;i<N;i++)
for(int j=0;j<N;j++)
inv[i][j] = (adj[i][j]*invDet)%26;
return true;
}
int main(){
int x,y,i,j,k,n;
cout<<"Enter the size of key matrix\n";
cin>>n;
cout<<"Enter the key matrix\n";
vector<vector<int> > a(n, vector<int>(n));
vector<vector<int> > adj(n, vector<int>(n));
vector<vector<int> > inv(n, vector<int>(n));
for(i=0;i<n;i++){
for(j=0;j<n;j++){
cin>>a[i][j];
}
}
if(inverse(a,inv,n)){
cout<<"Inverse exist\n";
}
cout<<"Enter the message to decrypt\n";
string s;
cin>>s;
k=0;
string ans;
while(k<s.size()){
for(i=0;i<n;i++){
int sum = 0;
int temp = k;
for(j=0;j<n;j++){
sum += ((inv[i][j] + 26)%26*(s[temp++]-'a')%26)%26;
sum = sum%26;
}
ans+=(sum+'a');
}
k+=n;
}
//ans+='\0';
int f=ans.size()-1;
while(ans[f]=='x'){
f--;
}
for(i=0;i<=f;i++){
cout<<ans[i];
}
cout<<'\n';
return 0;
}
OUTPUT:
Enter the size of key matrix 2 Enter the key matrix 4 1 3 2 5 21 Inverse exist Enter the message to decrypt gdddaivyvn helloworld
Other cryptography algorithms:
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