Cryptography requires one-way functions, mathematical problems simple to compute in one direction yet incredibly hard in reverse. If Hamiltonian phase state (HPS) assumptions are true and describe how these states generate randomness, then one-way functions also necessarily exist. Consequently, building cryptography called Microcrypt solely upon HPS assumptions is not possible; however, their potential for constructing classical cryptographic systems based on quantum principles remains.

Building cryptography only on Hamiltonian phase states, patterns within quantum systems, necessitates the existence of one-way functions. This finding prevents creating a new form of encryption named Microcrypt using exclusively quantum properties as previously anticipated. Nevertheless, Hamiltonian phase states can still improve existing classical encryption methods by utilising unique quantum characteristics. At Freie Universität Berlin alongside collaborators, a fundamental limitation in developing certain types of encryption purely from quantum mechanics has been demonstrated, specifically concerning Hamiltonian phase states and their mathematical characteristics used as the basis for potential techniques.

The team proved that if these states could underpin cryptography without relying on traditional one-way functions, processes easy to compute forward but extremely difficult to reverse, then those same one-way functions must exist. This eliminates a route towards ‘Microcrypt’, theoretical encryption viable even if conventional computational assumptions fail.

Linking Quantum State Certification to Classical Puzzle Construction

A technique centred around constructing one-way puzzles, challenges easy to create but hard to solve, was developed utilising custom state certification protocols. A state certification protocol acts like verifying someone’s passport details without revealing all personal information; it confirms specific qualities of a quantum state without fully exposing its data. This approach linked characteristics of these puzzles directly to properties within the chosen verification method, creating a pathway for puzzle construction based on carefully designed certifications for both random and one-way state generators.

Efficient classical processing yields an easily verifiable puzzle, establishing a key connection between seemingly quantum processes and traditional cryptographic security. Consequently, this finding removes a potential pathway for creating genuinely post-quantum cryptographic systems based on these specific quantum states, generalising prior puzzle constructions by offering new tools for building them using pseudorandom and one-way state generators; it highlights implications for developing stronger cryptographic protocols.

Hamiltonian Phase States Constrain Cryptographic Constructions and Verify Puzzle Efficiency

Custom state certification protocols yield efficiently verifiable puzzles following efficient classical post-processing; previously, constructing such puzzles required complex methods relying on classical shadows. The team conclusively proved that if Hamiltonian phase states underpin cryptography, then one-way functions must also exist, disproving earlier conjectures about Microcrypt’s potential independence from established mathematical concepts. This finding shifts focus towards utilising Hamiltonian phase states as a foundation for enhancing existing classical cryptographic systems rather than enabling entirely novel forms of encryption.

At Freie Universität Berlin alongside collaborators at multiple institutions, researchers have demonstrated a direct link between puzzle characteristics and verification methods within cryptography. They further established that assuming Hamiltonian phase states necessitates conventional one-way functions; this clarifies how to construct these puzzles without relying on complex techniques previously required, disproving hopes of creating new cryptographic systems independent of such foundations.

Quantum cryptography necessitates established computational assumptions

The pursuit of unbreakable encryption has long hinged on the difficulty of certain mathematical problems; however, researchers have now demonstrated a fundamental constraint within quantum approaches to cryptography. Their work reveals that building secure systems solely upon Hamiltonian phase states, specific patterns in quantum mechanics, requires the existence of conventional one-way functions, effectively dismantling hopes for an entirely new cryptographic model called Microcrypt. This finding doesn’t invalidate the potential of these quantum states but instead refocuses efforts towards integrating them with existing classical methods.

Recent work introduced the Hamiltonian phase state (HPS) assumptions, postulating they can instantiate pseudorandom and one-way state generators. A conjecture proposed these assumptions could hold even if one-way functions do not exist; this would provide a route to creating genuinely quantum cryptographic protocols termed ‘Microcrypt’. While this removes the possibility of instantiating Microcrypt cryptography using only Hamiltonian phase states, it reveals their potential in constructing classical cryptography with inherently quantum properties, technically stemming from building one-way puzzles from one-way state generators via custom “measure first, ask later” state certification protocols.

The research showed that realising secure systems based on Hamiltonian phase states necessitates the existence of conventional one-way functions. This means a completely new cryptographic system independent of established computational difficulty, known as Microcrypt, cannot be built solely upon these quantum states. However, the findings demonstrate Hamiltonian phase states can still contribute to classical cryptography by offering novel, inherently quantum assumptions for its construction. The authors achieved this result through developing methods to create one-way puzzles using specific state certification protocols and one-way state generators.

👉 More information
🗞 Instantiating Microcrypt: Obstacles and opportunities via tailored state certification
✍️ Jose Carrasco, Jens Eisert, Soumik Ghosh, Dominik Hangleiter, Nicky Kai Hong Li and Ryan Sweke
🧠 ArXiv: https://arxiv.org/abs/2609.15842

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