Autokey cipher
Start with a keyword, then keep going using the message itself.
What it does
An autokey cipher uses a short keyword to get started, then continues the key with the plaintext of the message itself. The key is therefore as long as the message and never repeats.
That single property removes the weakness that kills Vigenere. Kasiski examination works by finding the period of a repeating key. With no period, there is nothing to find.
Why decoding has to run in order
Encryption can be done in any order, because the whole key is known in advance. Decryption cannot. Each recovered letter of plaintext becomes part of the key used to recover the next one, so it has to proceed strictly left to right, and a single error propagates through everything after it.
How strong is it
Genuinely stronger than Vigenere, and Blaise de Vigenère’s own 1586 cipher was in fact an autokey, which makes the naming of both a historical accident.
It is still breakable. Plaintext is not random, and because the key is the plaintext, guessing a common word and sliding it through the ciphertext produces recognizable fragments where the guess is right. That is enough to unravel the whole message.
The idea survives into modern cryptography as cipher feedback, where each block of output feeds the encryption of the next.
Related
Beaufort fixes a different Vigenere annoyance, and Vigenere itself is where the family starts.