Recently, I've been musing about cryptographic applications of theoretical future technologies for (breaking) secure interstellar communications. The setting is a video game (Stellaris) featuring several high-tech (mostly) humanoid space-colonizing states in the near future (starting from ~2200) capable of FTL-travel, among other things.
What follows is a list of several 'levels' in scientific advances with cryptographic applications. I'd like to know how realistic these levels are (within the setting as described), and whether there are some important 'levels' I've missed.
(starting tier, supposed to be roughly equivalent to modern widely available crypto) The symmetric AES system (used once keys have been exchanged) and Diffie-Helman on elliptic curves for public key cryptography allow for effective and secure communication over interstellar subspace signal relays, even if they're tapped by nefarious aliens. [Effects: provides encryption for interstellar communication]
(starting tier level minor milestone: side channel attacks) The discovery of side-channel attacks, by which crucial information is extracted from side channels, such as power levels, noise or background radiation, came as a shock to the cryptography community. Quickly, the leading cryptographers constructed systems both to be resistant against side-channel attacks and ways how to exploit unprepared systems. [Effects: provides high resistance again side-channel attacks; can preform side channel attacks on enemies, cheap but with rather low success chance, nearly worthless when facing side-channel resistant systems (but not entirely, there's always a chance of bugs ;^) )]
(near future tier, securing: Applied quantum entanglement) By equipping our ships with special entangled quantum units, we can transfer data without using any conventional medium, making most forms of eavesdropping futile. However, the data-stream is too slow to use for anything except a few emergency signals. (Note that this being actually secure is already fiction, see https://blog.cr.yp.to/20160516-quantum.html) [Effects: simple set of communications is secure against any attacker lacking with tech of level 6 or lower.]
(near future tier, breaking: Applied quantum computing) The result of practical Quantum Supremacy has enabled us to break a whole host of previously secure cryptosystems, by utilizing Grover's and Shor's algorithm. [Effects: can reliably break cryptosystems of level 2 or lower]
(near future tier, securing: Post quantum crypto) (Okay, people are working on this today, but this order makes more sense for the tech-progression here) Fortunately, there are enough systems for which quantum computing gives no significant boost to attackers. By developing them, we can protect our communications once again. [Effects: secure against attackers of level 3]
(future tier: P vs NP) This one's special. Flip a coin. If heads, it turns out that P=NP and we have a practical algorithm for solving NP-hard problems. If tails, it turns out that P!=NP and we have found a one-way functions, enabling the construction of unconditional trapdoor functions. (the coin flip only triggers for the first nation to complete research on P vs NP, all others get the same result) [Effects: If P=NP, all cryptosystems of level 5 or lower, except level 3, are easily broken. Additionally, the fact that most scheduling problems have become easy gives a boost into overall production efficiency. If P!=NP, current communication systems are unbreakable by any crypto of level 5 or lower. Additionally, the fact that NP-hardness is an unconditional lower bound improves research efficiency (due to avoiding various unsuccessful attempts at creating poly-time algos for hard problems)]
(scifi tier, breaking: Entropy reversion) Recent advances in thermodynamics suggest that 'true randomness' doesn't exist and that any so-called 'random' source can be reversed. This makes all conventional cryptosystems useless, as we can simply find out the value of any 'randomly' generated key. (The field of psychology has also been advanced enough to effectively guess keys constructed by sentient beings) [Effects: breaks all crypto of level 6 or lower]
(scifi tier, securing: Precognition) Advances in psionic theory (telepathy, mind-reading and such) have led to the development of 'paired precognition units' that simply know the communications entered in the other pair, no matter how far away (supposedly). So, we're finally able to efficiently and securely 'communicate', by actually not sending any communication signals at all! [Effects: 100% security against any attack of level 7 or lower]
(scifi tier, breaking: interstellar telepathy) Energies from certain rare minerals enable well-trained psi-aware individuals to enhance their powers to read minds light-years away. No cryptosystem can protect the information in the very minds of Alice and Bob. [Effect: breaks all cryptosystems]