3-D Vigenere Cipher using a “Vigenere Cube” Intro to Cryptography July 2003 Daniel Paluch Micah Acinapura

Extension of Vigenere Cipher Original Vigenere cipher: poly-alphabetic Uses Vigenere Squre One keyword Keyword letters pair up plaintext letters to choose Cipher alphabet. i.e. with a plaintext “hello” and a Key of “bye”: H E L O Plain B Y Key I C P M Cipher

3-D Vigenere Cipher H E L O G D B Y CharAt (H,G,B) (E,O,Y) (L,O,E) Instead of 2-D Vigenere table, 3-D Vigenere cube is used. Two Keywords. As in Vigenere the effective key is made out of the keyword with the plaintext concatonated on the end. A plaintext letter combines with a letter from each keyword to make a 3-D coordinate in space, or a position in our cube. I.e. Plaintext of “hello” and keys of “good” and “bye” H E L O Plain G D Key1 B Y Key2 CharAt (H,G,B) (E,O,Y) (L,O,E) (L,D,B) (O,G,Y) Cipher

Added Security Against Cryptanalysis One face of the cube will originally look like the Vigenere table, however the cube is primed using the keyword to increase security. Priming the cube consists of rotating specific columns, chosen based on the keyword. Columns are rotated after encryption of each letter, each column is rotated up or down, depending on the specific coordinates that selected that column. The plaintext that is concatenated onto the end of the keyword is transposed to eliminated ordered repetition in choosing cipher alphabets.. i.e. Plaintext of “helloworldhello” and a key of “bye” woul encode with “byehelloworldhe”, however with key transposition, “byeolwrhelodelo”, is now used to encode the plaintext, giving a much more random usage of cipher alphabets.

Sample Encryption Here we will use a smaller cube/alphabet of abc as an example. Our keys will be “bb” and “ac”. Our plaintext will be “abc”. Our Effective keys will be “bba” and “acb”. Here we select “a”from the coordinate {a,b,a} and Rotate. Cube primed with keys “bb” & “ac” Initial cube Cube after first rotation. Now we select “b” from the coordinate {b,b,c} and rotate again. Now we select “a” from the coordinate {c,a,b} and rotate again. Finally our plaintext of “abc” has been encoded to “aba”. Cube after Second rotation.

Sample Decryption Now we will decrypt “abb” with “bba” and “acb”. We will decrypt Starting at the end of our plaintext and encrypt backwards. Here we know that we find a “b” in column b, slice c, and we find it in row b, and unrotate again. Then we unrotate. Knowing that we have a “a” in column a, slice b, we can find it in row c. Again with our “a” in column b, slice a, we can find it in row a. Putting each row letter together we get cba, ou r plaintext backwards.

Recap Poly-alphabetic 3-D Vigenere cipher, using Vigenere cube. Two Keywords are used. Cube is “primed” (rotated) using keywords. Pi, K1i and K2i denote location in cube of Ci. Repeated keys are transposed to avoid ordered repetition. Cube is rotated after encryption of each letter.