I came across the idea of using multiple Vigenere keys of coprime lengths here. The idea is, what if you use multiple keys, whose lengths are all co-prime? Then your effective key length would be the product of the length of all keys since they never line up with each other until that point.
It would be fantastic for key management since with keys of lengths 29, 31, and 37, your effective key length would be over 33,000! You could reuse them for many messages as long as you keep track of effective key length usage.
How would one go about cracking such a ciphertext, when its length is shorter than the product of
N keys, whose lengths are all co-prime?