Commitments from Quantum One-Wayness
Dakshita Khurana, Kabir Tomer
TL;DR
The paper investigates quantum one-way hardness by introducing one-way state generators (OWSG) and proving that, when restricted to pure-state outputs, they suffice to realize quantum bit commitments and secure multi-party computation. A central technical device is the one-way puzzle, an intermediate, classically-output primitive derived from OWSG via shadow tomography, which is then leveraged to construct quantum weak pseudoentropy generators (WPEG) and, through PEGs and EFI, ultimately to quantum commitments. The authors develop a chain of implications—OWSG with pure states ⇒ one-way puzzles ⇒ quantum weak PEGs ⇒ quantum PEGs ⇒ imbalanced EFI ⇒ commitments—and use flavor-conversion results to obtain non-uniform and eventually uniform, statistically hiding and computationally binding quantum commitments. Their framework also highlights how classical-communication cryptography models (QCCC) naturally imply one-way puzzles, underscoring the broader relevance of the primitive. Overall, the work positions commitments as a minimal and central assumption for quantum cryptography, enabling secure MPC and other functionalities under comparatively weak hardness assumptions.
Abstract
One-way functions are central to classical cryptography. They are both necessary for the existence of non-trivial classical cryptosystems, and sufficient to realize meaningful primitives including commitments, pseudorandom generators and digital signatures. At the same time, a mounting body of evidence suggests that assumptions even weaker than one-way functions may suffice for many cryptographic tasks of interest in a quantum world, including bit commitments and secure multi-party computation. This work studies one-way state generators [Morimae-Yamakawa, CRYPTO 2022], a natural quantum relaxation of one-way functions. Given a secret key, a one-way state generator outputs a hard to invert quantum state. A fundamental question is whether this type of quantum one-wayness suffices to realize quantum cryptography. We obtain an affirmative answer to this question, by proving that one-way state generators with pure state outputs imply quantum bit commitments and secure multiparty computation. Along the way, we build an intermediate primitive with classical outputs, which we call a (quantum) one-way puzzle. Our main technical contribution is a proof that one-way puzzles imply quantum bit commitments.