Japanese scientists develop a chaos-based stream cipher to withstand quantum attacks
(HPCWire) Chaos theory is actively being studied as a basis for post-quantum era cryptosystems. In mathematics, chaos is a property of certain dynamic systems that makes them extremely sensitive to initial conditions. While technically deterministic (non-random), these systems evolve in such complex ways that predicting their long-term state with incomplete information is practically impossible, since even small rounding errors in the initial conditions yield diverging results. This unique characteristic of chaotic systems can be leveraged to produce highly secure cryptographic systems, as a team of researchers from Ritsumeikan University, Japan, showed in a recent study.
Led by Professor Takaya Miyano, the team developed an unprecedented stream cipher consisting of three cryptographic primitives based on independent mathematical models of chaos. The first primitive is a pseudorandom number generator based on the augmented Lorenz (AL) map. The pseudorandom numbers produced using this approach are used to create key streams for encrypting/decrypting messages, which take the stage in the second and perhaps most remarkable primitive—an innovative method for secret-key exchange.
This novel strategy for exchanging secret keys specifying the AL map is based on the synchronization of two chaotic Lorenz oscillators, which can be independently and randomly initialized by the two communicating users, without either of them knowing the state of the other’s oscillator. To conceal the internal states of these oscillators, the communicating users (the sender and the receiver) mask the value of one of the variables of their oscillator by multiplying it with a locally generated random number. The masked value of the sender is then sent to receiver and vice-versa. After a short time, when these back-and-forth exchanges cause both oscillators to sync up almost perfectly to the same state in spite of the randomization of the variables, the users can mask and exchange secret keys and then locally unmask them with simple calculations.
Finally, the third primitive is a hash function based on the logistic map (a chaotic equation of motion), which allows the sender to send a hash value and, in turn, allows the receiver to ensure that the received secret key is correct, i.e., the chaotic oscillators were synchronized properly.
The researchers showed that a stream cipher assembled using these three primitives is extremely secure and resistant to statistical attacks and eavesdropping since it is mathematically impossible to synchronize their own oscillator to either the sender’s or the receiver’s ones. This is an unprecedented achievement, as Prof. Miyano states: “Most chaos-based cryptosystems can be broken by attacks using classical computers within a practically short time. In contrast, our methods, especially the one for secret-key exchange, appear to be robust against such attacks and, more importantly, even hard to break using quantum computers.”