both myself and my collaborators are pure mathematicians with only tangential experience in the study of cryptographic systems, so if this question is unclear or does not belong here, please do let me know. I apologize for the length of this question, after necessary background my questions appear in the last part.
As previously stated, my collaborators and I are pure mathematicians and over the coming months we will be publishing work on a new class of mathematical system we have discovered (it relates to many different areas in mathematics, the details are not important for the purpose of this question). One of my collaborators pointed out that certain properties of this system make it ideal for use in cryptography, and indeed upon further analysis this is what we have found.
Using the Alice/Bob/Eve analogy, the basic distinguishing properties of such a cryptographic system are as follows. Because this is a symmetric key system, Alice and Bob must meet to generate their random key. Once Alice and Bob wish to send a message, they publicly chose a particular type of mathematical object at random, call it $T$ (the type of mathematical object is not important), and use this along with their key to generate a set of coordinate points that will each uniquely map to a 0 or a 1.
With this, Alice can send Bob a subset of these coordinates (with each coordinate mapping to 0 or 1), and because Bob has the same set of coordinates he can "decrypt" the message of coordinates to obtain the bit string Alice wished to share.
So far this description appears to offer nothing new, and in fact if Alice wishes to only send Bob one message this is equivalent to the one-time pad. The issue with the one-time pad of course and similar systems is that sending multiple messages with the same key leads to leaks, so for every new message Alice and Bob must use a new key, which of course means sharing the keys in the first place which is difficult.
The unique (we think) property of the cryptosystem offered by this mathematical discovery is that so long as Alice and Bob publicly choose a new particular mathematical object ($T$) to apply their key to before each message sent (of which there is a continuum of choices for $T$), they can use the same initially chosen key to send an arbitrary number of messages, for we can prove that it would be mathematically impossible for Eve to ever determine the key if such a method was used.
In fact, we can also prove that so long as Alice and Bob publicly choose a new $T$ for each message, to Eve each message of coordinates sent between Alice and Bob would random, so no cryptanalysis would work.
Further, one of my collaborators has a (light) background in quantum computing and is highly confident that this system is not susceptible to brute-force attack from quantum computers (much less classical ones). We also remark that this encryption scheme is highly efficient, and its encryption/decryption time complexity scales linearly with just the size of the secret key chosen (and the complexity of the encryption scales exponentially with the length of encryption key).
My questions are as follows. Does a cryptosystem exhibiting such properties already exist? Would a cryptosystem exhibiting these properties be of any possible use to the community? Even if not (ie. analogous systems already exist), should we pursue publishing the method in a journal? If so, can anyone here recommend any journals, and things to watch out for when publishing in cryptography?
I know I have been incredibly discrete in discussing the details of the mathematical system for I cannot give too much more at the moment, but I hope this information is sufficient for giving general answers to the questions.
Thank you all so much for your time and help.