Is there a way to defeat statistical information leak in Vigenère cipher when the ciphertext is reasonably larger than the key size?

Question

I read in this answer here that if the ciphertext is reasonably larger than the key size, Vigenère cipher is easily breakable.

Is there a way to repeat the key if it is reasonably smaller that the ciphertext size and be immune to statistical information leak at the same same?

I have been thinking in XORing a keystream of a cryptographically secure hash function in Counter Mode in the plaintext before applying the key, can it defeat statistical information leak?

PS: In above paragraph, I assume the key and plaintext are in modulo 256.

Answer 1

I have been thinking in XORing a keystream of a cryptographically secure hash function in Counter Mode in the plaintext before applying the key, can it defeat statistical information leak?

It depends.

If the keystream is generated using a secret key (making that XOR a secure encryption algorithm), then yes, applying a secure encryption algorithm, and then doing an independently keyed Vigenère is secure. Of course, it's not clear why you're bothering with Vigenère...

If the keystream is public (that is, the attacker knows what the keystream is), it's not secure. Perhaps it might foil the specific attack you have in mind; however if the attacker correctly guesses a crib at a location $X$, that gives him the corresponding plaintext at locations $X + kN$ (for integer $k$ and $N$ the Vigenère length), and the attacker may be able (depending on the plaintext language) to use that to recover everything.