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Columnar Transposition Cipher

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Given a plain-text message and a numeric key, cipher/de-cipher the given text using Columnar Transposition Cipher The Columnar Transposition Cipher is a form of transposition cipher just like

Rail Fence Cipher

. Columnar Transposition involves writing the plaintext out in rows, and then reading the ciphertext off in columns one by one.

Examples:

Encryption
Input : Geeks for Geeks
Key = HACK
Output : e kefGsGsrekoe_
Decryption
Input : e kefGsGsrekoe_
Key = HACK
Output : Geeks for Geeks
Encryption
Input : Geeks on work
Key = HACK
Output : e w_eoo_Gs kknr_
Decryption
Input : e w_eoo_Gs kknr_
Key = HACK
Output : Geeks on work


Encryption

In a transposition cipher, the order of the alphabets is re-arranged to obtain the cipher-text.

  1. The message is written out in rows of a fixed length, and then read out again column by column, and the columns are chosen in some scrambled order.
  2. Width of the rows and the permutation of the columns are usually defined by a keyword.
  3. For example, the word HACK is of length 4 (so the rows are of length 4), and the permutation is defined by the alphabetical order of the letters in the keyword. In this case, the order would be “3 1 2 4”.
  4. Any spare spaces are filled with nulls or left blank or placed by a character (Example: _).
  5. Finally, the message is read off in columns, in the order specified by the keyword.

columnar-transposition-cipher

Decryption

  1. To decipher it, the recipient has to work out the column lengths by dividing the message length by the key length.
  2. Then, write the message out in columns again, then re-order the columns by reforming the key word.
  3. C++




    // CPP program for illustrating
    // Columnar Transposition Cipher
    #include<bits/stdc++.h>
    using namespace std;
     
    // Key for Columnar Transposition
    string const key = "HACK";
    map<int,int> keyMap;
     
    void setPermutationOrder()
    {            
        // Add the permutation order into map
        for(int i=0; i < key.length(); i++)
        {
            keyMap[key[i]] = i;
        }
    }
     
    // Encryption
    string encryptMessage(string msg)
    {
        int row,col,j;
        string cipher = "";
         
        /* calculate column of the matrix*/
        col = key.length();
         
        /* calculate Maximum row of the matrix*/
        row = msg.length()/col;
         
        if (msg.length() % col)
            row += 1;
     
        char matrix[row][col];
     
        for (int i=0,k=0; i < row; i++)
        {
            for (int j=0; j<col; )
            {
                if(msg[k] == '\0')
                {
                    /* Adding the padding character '_' */
                    matrix[i][j] = '_';    
                    j++;
                }
                 
                if( isalpha(msg[k]) || msg[k]==' ')
                {
                    /* Adding only space and alphabet into matrix*/
                    matrix[i][j] = msg[k];
                    j++;
                }
                k++;
            }
        }
     
        for (map<int,int>::iterator ii = keyMap.begin(); ii!=keyMap.end(); ++ii)
        {
            j=ii->second;
             
            // getting cipher text from matrix column wise using permuted key
            for (int i=0; i<row; i++)
            {
                if( isalpha(matrix[i][j]) || matrix[i][j]==' ' || matrix[i][j]=='_')
                    cipher += matrix[i][j];
            }
        }
     
        return cipher;
    }
     
    // Decryption
    string decryptMessage(string cipher)
    {
        /* calculate row and column for cipher Matrix */
        int col = key.length();
     
        int row = cipher.length()/col;
        char cipherMat[row][col];
     
        /* add character into matrix column wise */
        for (int j=0,k=0; j<col; j++)
            for (int i=0; i<row; i++)
                cipherMat[i][j] = cipher[k++];
     
        /* update the order of key for decryption */
        int index = 0;
        for( map<int,int>::iterator ii=keyMap.begin(); ii!=keyMap.end(); ++ii)
            ii->second = index++;
     
        /* Arrange the matrix column wise according
        to permutation order by adding into new matrix */
        char decCipher[row][col];
        map<int,int>::iterator ii=keyMap.begin();
        int k = 0;
        for (int l=0,j; key[l]!='\0'; k++)
        {
            j = keyMap[key[l++]];
            for (int i=0; i<row; i++)
            {
                decCipher[i][k]=cipherMat[i][j];
            }
        }
     
        /* getting Message using matrix */
        string msg = "";
        for (int i=0; i<row; i++)
        {
            for(int j=0; j<col; j++)
            {
                if(decCipher[i][j] != '_')
                    msg += decCipher[i][j];
            }
        }
        return msg;
    }
     
    // Driver Program
    int main(void)
    {
        /* message */
        string msg = "Geeks for Geeks";
     
        setPermutationOrder();
         
        // Calling encryption function
        string cipher = encryptMessage(msg);
        cout << "Encrypted Message: " << cipher << endl;
         
        // Calling Decryption function
        cout << "Decrypted Message: " << decryptMessage(cipher) << endl;
     
        return 0;
    }

    
    

    Java




    import java.util.*;
     
    public class ColumnarTranspositionCipher {
        // Key for Columnar Transposition
        static final String key = "HACK";
        static Map<Character, Integer> keyMap = new HashMap<>();
     
        static void setPermutationOrder() {
            // Add the permutation order into the map
            for (int i = 0; i < key.length(); i++) {
                keyMap.put(key.charAt(i), i);
            }
        }
     
        // Encryption
        static String encryptMessage(String msg) {
            int row, col;
            StringBuilder cipher = new StringBuilder();
     
            /* Calculate the number of columns in the matrix */
            col = key.length();
     
            /* Calculate the maximum number of rows in the matrix */
            row = (int) Math.ceil((double) msg.length() / col);
     
            char[][] matrix = new char[row][col];
     
            for (int i = 0, k = 0; i < row; i++) {
                for (int j = 0; j < col; ) {
                    if (k < msg.length()) {
                        char ch = msg.charAt(k);
                        if (Character.isLetter(ch) || ch == ' ') {
                            matrix[i][j] = ch;
                            j++;
                        }
                        k++;
                    } else {
                        /* Add padding character '_' */
                        matrix[i][j] = '_';
                        j++;
                    }
                }
            }
     
            for (Map.Entry<Character, Integer> entry : keyMap.entrySet()) {
                int columnIndex = entry.getValue();
     
                // Get the cipher text from the matrix column-wise using the permuted key
                for (int i = 0; i < row; i++) {
                    if (Character.isLetter(matrix[i][columnIndex]) || matrix[i][columnIndex] == ' ' || matrix[i][columnIndex] == '_') {
                        cipher.append(matrix[i][columnIndex]);
                    }
                }
            }
     
            return cipher.toString();
        }
     
        // Decryption
        static String decryptMessage(String cipher) {
            /* Calculate the number of columns for the cipher matrix */
            int col = key.length();
     
            int row = (int) Math.ceil((double) cipher.length() / col);
            char[][] cipherMat = new char[row][col];
     
            /* Add characters into the matrix column-wise */
            int k = 0;
            for (int j = 0; j < col; j++) {
                for (int i = 0; i < row; i++) {
                    cipherMat[i][j] = cipher.charAt(k);
                    k++;
                }
            }
     
            /* Update the order of the key for decryption */
            int index = 0;
            for (Map.Entry<Character, Integer> entry : keyMap.entrySet()) {
                entry.setValue(index++);
            }
     
            /* Arrange the matrix column-wise according to the permutation order */
            char[][] decCipher = new char[row][col];
            for (int l = 0; l < key.length(); l++) {
                int columnIndex = keyMap.get(key.charAt(l));
                for (int i = 0; i < row; i++) {
                    decCipher[i][l] = cipherMat[i][columnIndex];
                }
            }
     
            /* Get the message using the matrix */
            StringBuilder msg = new StringBuilder();
            for (int i = 0; i < row; i++) {
                for (int j = 0; j < col; j++) {
                    if (decCipher[i][j] != '_') {
                        msg.append(decCipher[i][j]);
                    }
                }
            }
     
            return msg.toString();
        }
     
        public static void main(String[] args) {
            /* Message */
            String msg = "Geeks for Geeks";
     
            setPermutationOrder();
     
            // Calling encryption function
            String cipher = encryptMessage(msg);
            System.out.println("Encrypted Message: " + cipher);
     
            // Calling Decryption function
            System.out.println("Decrypted Message: " + decryptMessage(cipher));
        }
    }

    
    

    Python3




    # Python3 implementation of
    # Columnar Transposition
    import math
     
    key = "HACK"
     
    # Encryption
    def encryptMessage(msg):
        cipher = ""
     
        # track key indices
        k_indx = 0
     
        msg_len = float(len(msg))
        msg_lst = list(msg)
        key_lst = sorted(list(key))
     
        # calculate column of the matrix
        col = len(key)
         
        # calculate maximum row of the matrix
        row = int(math.ceil(msg_len / col))
     
        # add the padding character '_' in empty
        # the empty cell of the matix
        fill_null = int((row * col) - msg_len)
        msg_lst.extend('_' * fill_null)
     
        # create Matrix and insert message and
        # padding characters row-wise
        matrix = [msg_lst[i: i + col]
                  for i in range(0, len(msg_lst), col)]
     
        # read matrix column-wise using key
        for _ in range(col):
            curr_idx = key.index(key_lst[k_indx])
            cipher += ''.join([row[curr_idx]
                              for row in matrix])
            k_indx += 1
     
        return cipher
     
    # Decryption
    def decryptMessage(cipher):
        msg = ""
     
        # track key indices
        k_indx = 0
     
        # track msg indices
        msg_indx = 0
        msg_len = float(len(cipher))
        msg_lst = list(cipher)
     
        # calculate column of the matrix
        col = len(key)
         
        # calculate maximum row of the matrix
        row = int(math.ceil(msg_len / col))
     
        # convert key into list and sort
        # alphabetically so we can access
        # each character by its alphabetical position.
        key_lst = sorted(list(key))
     
        # create an empty matrix to
        # store deciphered message
        dec_cipher = []
        for _ in range(row):
            dec_cipher += [[None] * col]
     
        # Arrange the matrix column wise according
        # to permutation order by adding into new matrix
        for _ in range(col):
            curr_idx = key.index(key_lst[k_indx])
     
            for j in range(row):
                dec_cipher[j][curr_idx] = msg_lst[msg_indx]
                msg_indx += 1
            k_indx += 1
     
        # convert decrypted msg matrix into a string
        try:
            msg = ''.join(sum(dec_cipher, []))
        except TypeError:
            raise TypeError("This program cannot",
                            "handle repeating words.")
     
        null_count = msg.count('_')
     
        if null_count > 0:
            return msg[: -null_count]
     
        return msg
     
    # Driver Code
    msg = "Geeks for Geeks"
     
    cipher = encryptMessage(msg)
    print("Encrypted Message: {}".
                   format(cipher))
     
    print("Decryped Message: {}".
           format(decryptMessage(cipher)))
     
    # This code is contributed by Aditya K

    
    

    C#




    using System;
    using System.Collections.Generic;
     
    public class ColumnarTranspositionCipher
    {
        // Key for Columnar Transposition
        static readonly string key = "HACK";
        static Dictionary<char, int> keyMap = new Dictionary<char, int>();
     
        static void SetPermutationOrder()
        {
            // Add the permutation order into the dictionary
            for (int i = 0; i < key.Length; i++)
            {
                keyMap[key[i]] = i;
            }
        }
     
        // Encryption
        static string EncryptMessage(string msg)
        {
            int row, col;
            System.Text.StringBuilder cipher = new System.Text.StringBuilder();
     
            /* Calculate the number of columns in the matrix */
            col = key.Length;
     
            /* Calculate the maximum number of rows in the matrix */
            row = (int)Math.Ceiling((double)msg.Length / col);
     
            char[,] matrix = new char[row, col];
     
            for (int i = 0, k = 0; i < row; i++)
            {
                for (int j = 0; j < col;)
                {
                    if (k < msg.Length)
                    {
                        char ch = msg[k];
                        if (char.IsLetter(ch) || ch == ' ')
                        {
                            matrix[i, j] = ch;
                            j++;
                        }
                        k++;
                    }
                    else
                    {
                        /* Add padding character '_' */
                        matrix[i, j] = '_';
                        j++;
                    }
                }
            }
     
            foreach (var entry in new Dictionary<char, int>(keyMap))
            {
                int columnIndex = entry.Value;
     
                // Get the cipher text from the matrix column-wise using the permuted key
                for (int i = 0; i < row; i++)
                {
                    if (char.IsLetter(matrix[i, columnIndex]) || matrix[i, columnIndex] == ' ' || matrix[i, columnIndex] == '_')
                    {
                        cipher.Append(matrix[i, columnIndex]);
                    }
                }
            }
     
            return cipher.ToString();
        }
     
        // Decryption
        static string DecryptMessage(string cipher)
        {
            /* Calculate the number of columns for the cipher matrix */
            int col = key.Length;
     
            int row = (int)Math.Ceiling((double)cipher.Length / col);
            char[,] cipherMat = new char[row, col];
     
            /* Add characters into the matrix column-wise */
            int k = 0;
            for (int j = 0; j < col; j++)
            {
                for (int i = 0; i < row; i++)
                {
                    cipherMat[i, j] = cipher[k];
                    k++;
                }
            }
     
            /* Update the order of the key for decryption */
            int index = 0;
            foreach (var entry in new Dictionary<char, int>(keyMap))
            {
                keyMap[entry.Key] = index++;
            }
     
            /* Arrange the matrix column-wise according to the permutation order */
            char[,] decCipher = new char[row, col];
            foreach (var entry in keyMap)
            {
                int columnIndex = entry.Value;
                for (int i = 0; i < row; i++)
                {
                    decCipher[i, columnIndex] = cipherMat[i, columnIndex];
                }
            }
     
            /* Get the message using the matrix */
            System.Text.StringBuilder msg = new System.Text.StringBuilder();
            for (int i = 0; i < row; i++)
            {
                for (int j = 0; j < col; j++)
                {
                    if (decCipher[i, j] != '_')
                    {
                        msg.Append(decCipher[i, j]);
                    }
                }
            }
     
            return msg.ToString();
        }
     
        public static void Main(string[] args)
        {
            /* Message */
            string msg = "Geeks for Geeks";
     
            SetPermutationOrder();
     
            // Calling encryption function
            string cipher = EncryptMessage(msg);
            Console.WriteLine("Encrypted Message: " + cipher);
     
            // Calling Decryption function
            Console.WriteLine("Decrypted Message: " + DecryptMessage(cipher));
        }
    }

    
    

    Javascript




    // JavaScript implementation of
    // Columnar Transposition
    const key = "HACK";
     
    // Encryption
    function encryptMessage(msg) {
        let cipher = "";
     
        // track key indices
        let k_indx = 0;
     
        const msg_len = msg.length;
        const msg_lst = Array.from(msg);
        const key_lst = Array.from(key).sort();
     
        // calculate column of the matrix
        const col = key.length;
     
        // calculate maximum row of the matrix
        const row = Math.ceil(msg_len / col);
     
        // add the padding character '_' in empty
        // the empty cell of the matrix
        const fill_null = (row * col) - msg_len;
        for (let i = 0; i < fill_null; i++) {
            msg_lst.push('_');
        }
     
        // create Matrix and insert message and
        // padding characters row-wise
        const matrix = [];
        for (let i = 0; i < msg_lst.length; i += col) {
            matrix.push(msg_lst.slice(i, i + col));
        }
     
        // read matrix column-wise using key
        for (let _ = 0; _ < col; _++) {
            const curr_idx = key.indexOf(key_lst[k_indx]);
            for (const row of matrix) {
                cipher += row[curr_idx];
            }
            k_indx++;
        }
     
        return cipher;
    }
     
    // Decryption
    function decryptMessage(cipher) {
        let msg = "";
     
        // track key indices
        let k_indx = 0;
     
        // track msg indices
        let msg_indx = 0;
        const msg_len = cipher.length;
        const msg_lst = Array.from(cipher);
     
        // calculate column of the matrix
        const col = key.length;
     
        // calculate maximum row of the matrix
        const row = Math.ceil(msg_len / col);
     
        // convert key into list and sort
        // alphabetically so we can access
        // each character by its alphabetical position.
        const key_lst = Array.from(key).sort();
     
        // create an empty matrix to
        // store deciphered message
        const dec_cipher = [];
        for (let i = 0; i < row; i++) {
            dec_cipher.push(Array(col).fill(null));
        }
     
        // Arrange the matrix column wise according
        // to permutation order by adding into a new matrix
        for (let _ = 0; _ < col; _++) {
            const curr_idx = key.indexOf(key_lst[k_indx]);
     
            for (let j = 0; j < row; j++) {
                dec_cipher[j][curr_idx] = msg_lst[msg_indx];
                msg_indx++;
            }
            k_indx++;
        }
     
        // convert decrypted msg matrix into a string
        try {
            msg = dec_cipher.flat().join('');
        } catch (err) {
            throw new Error("This program cannot handle repeating words.");
        }
     
        const null_count = (msg.match(/_/g) || []).length;
     
        if (null_count > 0) {
            return msg.slice(0, -null_count);
        }
     
        return msg;
    }
     
    // Driver Code
    const msg = "Geeks for Geeks";
     
    const cipher = encryptMessage(msg);
    console.log("Encrypted Message: " + cipher);
     
    console.log("Decrypted Message: " + decryptMessage(cipher));
     
    // This code is contributed by phasing17

    
    

  4. Output:
  5. Encrypted Message: e  kefGsGsrekoe_
    Decrypted Message: Geeks for Geeks


  6. Try it yourself:
  7. A double columnar transposition( It was used by the U.S. Army in World War I, and it is just a columnar transposition followed by another columnar transposition). This article is contributed by
  8. Yasin Zafar
  9. . If you like GeeksforGeeks and would like to contribute, you can also write an article using
  10. write.geeksforgeeks.org
  11. or mail your article to review-team@geeksforgeeks.org. See your article appearing on the GeeksforGeeks main page and help other Geeks.


Last Updated : 25 Nov, 2023
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