Is this hand cipher any more secure than the Vigenère cipher? I know that inventing one's one crypto always sucks, but the problem is that hand ciphers are usually 


very insecure 
very slow. 


This is an attempt to make a relatively secure, keyable, and modular multi-round cipher by hand.

In each round of encryption the following two steps are done:


The text is permuted by concatenating the reverse of the even-numbered characters to the odd-numbered characters. This is equivalent to writing the first char in the first place, the second in the last place, the third in the second place, the fourth in the second-to-last place, etc and is very fast to do by hand, and can be mentally reversed simply by "zig-zagging" the eyes when reading. (12345 -> 13542)


   T H I S X I S X S E C R E T
=&gt; T I X S S C E T R E X I S H


The text is then added$\mod 26$ by repeating a series of numbers, i.e. the key. The numbers are from 0 to 10 so that they are easy to write underneath the letters and also because encryption can be done in head without memorizing, say, X is the 24th number of the alphabet. I'm especially concerned whether limiting this to numbers from 0 to 10 rather than from 0 to 25 seriously cripples security. (Obviously the digits of $\pi$ is a bad choice for a key but this is just an example)


   T I X S S C E T R E X I S H
   3 1 4 1 5 9 2 6 5 3 5 8 9 7
=&gt; W J A T X J G Z W H C Q B O




This encryption process is continued for 5 to 10 rounds. The reason for the permutation phase is to break patterns that weaken the Vignère cipher.

I have observed the weakness that the first letter is never permuted to another place; thus known-plaintext attacks can easily trivially find the first number of the keystream given the number of rounds. Other than that I haven't found any very serious flaws.

Does this cipher system have any mathematical advantage over older (but slower to compute!) ones such as Vigenère or Playfair?
Given that the permutation is fixed and the key step is independent of the permutation you can reduce this to an ordinary text-substitution cipher. 

If the key is as long as the input you have a weak one-time pad, because the per letter change is limited to 10 instead of 26.

However if the key is short then you have a Vigenère cipher (if you "decode" with $key=0$ then it is exactly a Vigenère cipher).

In essence you use 2 transformations: a character scramble ($P$  $P'$) and a "xor" ($X+$ and $X-$).

Your algorithm is $text1=X+(P(text_0),key)$for each phase. 

However this is equivalent to $text1= P(X+(text_0,P'(key)))$. 

Then the next fase is $text_2= P(X+(P(X+(text_0,P'(key))),P'(key)))$ which can be rewritten to $text2 = P(P(X+(X+(text0,P'(key) ), P'(P'(key))))$ and so on.

Given that P is easily reversible you can extract $X+(text, X+(P'(key), P'(P'(key)) )$.