Classical Binding for Quantum Commitments

Dominique Unruh

Dominique Unruh

Rahul Jain

Marcel Dall’Agnol, Nicholas Spooner

Collapse binding and collapsing were proposed by Unruh (Eurocrypt '16) as post-quantum strengthenings of computational binding and collision resistance, respectively. These notions have been very successful in facilitating the "lifting" of classical security proofs to the quantum setting. A basic and natural question remains unanswered, however: are they the weakest notions that suffice for such lifting? In this work we answer this question in the affirmative by giving a classical commit-and-open protocol which is post-quantum secure if and only if the commitment scheme (resp. hash function) used is collapse binding (resp. collapsing). We also generalise the definition of collapse binding to quantum commitment schemes, and prove that the equivalence carries over when the sender in this commit-and-open protocol communicates quantum information. As a consequence, we establish that a variety of "weak" binding notions (sum binding, CDMS binding and unequivocality) are in fact equivalent to collapse binding, both for post-quantum and quantum commitments. Finally, we prove a "win-win" result, showing that a post-quantum computationally binding commitment scheme that is not collapse binding can be used to build an equivocal commitment scheme (which can, in turn, be used to build one-shot signatures and other useful quantum primitives). This strengthens a result due to Zhandry (Eurocrypt '19) showing that the same object yields quantum lightning.

André Chailloux, Iordanis Kerenidis, Bill Rosgen

Claude Crépeau, Paul Dumais, Dominic Mayers +1 more

Quantum 2-party cryptography differs from its classical counterpart in at least one important way: Given black-box access to a perfect commitment scheme there exists a secure 1-2 quantum oblivious transfer. This reduction proposed by Crépeau and Kilian was proved secure against any receiver by Yao, in the case where perfect commitments are used. However, quantum commitments would normally be based on computational assumptions. A natural question therefore arises: What happens to the security of the above reduction when computationally secure commitments are used instead of perfect ones? In this paper, we address the security of 1-2 QOT when computationally binding string commitments are available. In particular, we analyse the security of a primitive called Quantum Measurement Commitment when it is constructed from unconditionally concealing but computationally binding commitments. As measuring a quantum state induces an irreversible collapse, we describe a QMC as an instance of ``computational collapse of a quantum state''. In a QMC a state appears to be collapsed to a polynomial time observer who cannot extract full information about the state without breaking a computational assumption. We reduce the security of QMC to a weak binding criteria for the string commitment. We also show that secure QMCs implies QOT using a straightforward variant of the reduction above.