MOTP (Multi One-Time Pad), as an extension of the OTP method, now assumes that if a key consists of true random numbers, any sequence of numbers from that key that starts at a different position is just as independent of other sequences from that key as if a new key were generated with true random numbers. So with MOTP, a random number sequence consists of not just one key, but a whole bunch of keys.
So there are as many different sequences with random numbers as the byte array has elements (bytes). The only requirement for decryption is that the ID of the key bundle and the chosen entry point must be added to the encrypted message.
The Encryption Factory prepares encryption in such a way that it uses a generator with true random numbers to determine the random entry point for each encryption and prepends this to the encrypted data in a header. This allows the recipient to select the correct key from the key bundle for decryption. From Encrypter-X the entry point is registered on both sides (encrypter and decrypter) and never used again for encryption.
But now the most important thing: Distribution. How do partners get new keys in a secure way? That is, after the same initial key bundle is on both sides (with Bob and Alice) and is at present the current one, quite simply and absolutely surely.
A new key bundle is created (e.g. by Bob) and encrypted with one of the keys of the current key bundle. This encrypted key ring can now be sent by mail, go on the journey to Alice via FTP, be made available for download on the Internet or whatever. It is of no use to an unauthorized person (Eve) if she gets hold of this data package. Without the associated key, this packet is worthless to her.
Now I can hear the prophets of doom shouting: "Just intercept enough!", "Statistics, statistics!". Yes, such a danger would be conceivable and one must think about it. So let's do that for once:
The initial key bundle was handed over, in person, by courier or mail, on a USB stick, SD card, or similar. This is required once at the beginning of a communication partnership between the users involved and after that, as already described above, there are other, faster and absolutely secure ways to supply or distribute keys.
Let the initial key bundle be 10MB in size. This means that there are 10,485,760 different entry points into the key bundle or keys. Since the data or messages to be encrypted are usually much smaller, there is no serious danger of keys overlapping in the case of, for example, 1000 encryptions, and only about 0.1% of the key bundle was used in doing so. This means that what has been encrypted so far can be regarded as pure OTP and therefore absolutely secure and is therefore immune to statistics.
To avoid actually relevant amounts of data coming together, the key bundles now simply need to be exchanged early on as described above.