Vigenere Cipher

Question

I have converted a piece of plaintext to cipher text using an 8 letter keyword. After attempting to solve my vigenere cipher, I realise it is very easily solveable. So my question is, how can I create a more difficult encryption using the vigenere cipher? (without using a one time pad) I have looked at using a key k1 and then another key K2, however the length of this key will just be lcm(k1,k2), thus it does not really make my ciphertext and harder to break.

Can i use the vigenere cipher, and then with the resulting ciphertext, perform a caeser shift on it? With what I understand, this will be slightly more difficult to decrypt than just a vigenere cipher. However I am unsure if in cryptography, it is permissable to combine these two such ciphers?

Answer 1

The extra shifts don't do anything for security. The key length stays the same and the alphabets are shifted versions of the plain alphabet.

The "best" Vigenère is to take a completely random 26 by 26 square of 26 mixed alphabets, al mixed differently, and assign each of the alphabets to a key letter, and take a longish random key to determine which alphabet is used. That way the key length is still easy to determine statistically (cannot be helped) but each position has to be solved as an independent monoalphabetic, and if texts are not too long the statistics on that might be thin too. It depends on the underlying language and its patters too.

A disadavantage is that the key needs to be known on two ends (and one simple "key word won't do anymore, you needs 26x26 letter keys, plus a periodic key.

One extra transformation that can make it more secure is an extra transposition layer, to break periodicity and $n$-gram statistics.

Answer 2

Using a Caeser Shift on Vigenre cipher won't change anything in the view of the attacker. The key values will be shifted, too to modulo 26.

Lets see by a anexample;

m = The quick brown fox jumps over 13 lazy dogs.
p = caasercaasercaasercaasercaasercaasercaaserc
o = vhi iyzek fjsnp fsp nlopw gzvt 13 lerc uqgw. //Vigenere output
c = ykl lbchn imvqs ivs qorsz jcyw 13 ohuf xtjz. //shift 3 ny mod 3

now, the attacker when see the cipher output $c$ will attack as normal Vigenere cipher and will get the key as fdhvhu this is just the $+3 \bmod 26$ of caeser.

There is nothing changed from the view of the attacker.