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arXiv:2502.09201 · Entropy

Commitment Schemes from OWFs with Applications to Quantum Oblivious Transfer

Thomas Lorünser, Sebastian Ramacher, Federico Valbusa

Published Jul 15, 2025• 2 citations
arXivHTMLPDF

Abstract

Commitment schemes (CSs) are essential to many cryptographic protocols and schemes with applications that include privacy-preserving computation on data, privacy-preserving authentication, and, in particular, oblivious transfer protocols. For quantum oblivious transfer (qOT) protocols, unconditionally binding commitment schemes that do not rely on hardness assumptions from structured mathematical problems are required. These additional constraints severely limit the choice of commitment schemes to random oracle-based constructions or Naor's bit commitment scheme. As these protocols commit to individual bits, the use of such commitment schemes comes at a high bandwidth and computational cost. In this work, we investigate improvements to the efficiency of commitment schemes used in qOT protocols and propose an extension of Naor's commitment scheme requiring the existence of one-way functions (OWFs) to reduce communication complexity for 2-bit strings. Additionally, we provide an interactive string commitment scheme with preprocessing to enable the fast and efficient computation of commitments.

DOI
10.3390/e27070751

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Commitment schemes (CSs) are essential to many cryptographic protocols and schemes with applications that include privacy-preserving computation on data, privacy-preserving authentication, and, in particular, oblivious transfer protocols. For quantum oblivious transfer (qOT) protocols, unconditionally binding commitment schemes that do not rely on hardness assumptions from structured mathematical problems are required. These additional constraints severely limit the choice of commitment schemes to random oracle-based constructions or Naor's bit commitment scheme. As these protocols commit to individual bits, the use of such commitment schemes comes at a high bandwidth and computational cost. In this work, we investigate improvements to the efficiency of commitment schemes used in qOT protocols and propose an extension of Naor's commitment scheme requiring the existence of one-way functions (OWFs) to reduce communication complexity for 2-bit strings. Additionally, we provide an interactive string commitment scheme with preprocessing to enable the fast and efficient computation of commitments.
Commitment schemes are essential to many cryptographic protocols and schemes with applications that include privacy-preserving computation on data, privacy-preserving authentication, and in particular also in oblivious transfer protocols. For quantum oblivious transfer (qOT) protocols, unconditionally binding commitment schemes that do not rely on hardness assumptions from structured mathematical problems are required. These additional constraints severely limit the choice of commitment schemes to random oracle-based constructions or Naor’s bit commitment scheme. As these protocols commit to individual bits, the use of such commitment schemes comes at a high bandwidth and computational cost.In this work, we investigate improvements to the efficiency of commitment schemes used in qOT protocols and propose an extension of Naor’s commitment scheme requiring the existence of one-way functions (OWF) to reduce communication complexity for 2-bit strings. Additionally, we provide an interactive string commitment scheme with preprocessing to enable a fast and efficient computation of commitments.
We present a new simulation-secure quantum oblivious transfer (QOT) protocol based on one-way functions in the plain model. With a focus on practical implementation, our protocol surpasses prior works in efficiency, promising feasible experimental realization. We address potential experimental errors and their correction, offering analytical expressions to facilitate the analysis of the required quantum resources. Technically, we achieve simulation security for QOT through an e q u i v o c a l and r e l a x e d − e x t r a c t a b l e quantum bit commitment.
Abstract Oblivious transfer (OT) is one of the cornerstones of secure multiparty computation. It is clear that unconditionally secure OT is impossible. Any protocol for OT requires computational assumptions, such as number‐theoretic cryptographic assumptions or the assumptions of existence of one‐way functions. On the other hand, it is broadly believed that one‐way functions alone do not promise secure OT. However, in this paper, a novel computationally secure quantum oblivious transfer (QOT) protocol is proposed with the help of quantum channels under the minimum assumption requirements: the existence of one‐way functions.
We propose an efficient quantum protocol performing quantum bit commitment, which is a simple cryptographic primitive involved with two parties, called a committer and a verifier. Our protocol is non-interactive, uses no supplemental shared information, and achieves computational concealing and statistical binding under a natural complexity-theoretical assumption. An earlier protocol in the literature relies on the existence of an efficient quantum one-way function. Our protocol, on the contrary, exploits a seemingly weaker assumption on computational difficulty of distinguishing two specific ensembles of reduced quantum states. This assumption is guaranteed by, for example, computational hardness of solving the graph automorphism problem efficiently on a quantum computer.
Oblivious transfer (OT) and bit commitment (BC) are two-party cryptographic protocols which play crucial roles in the construction of various cryptographic protocols. We propose three practical quantum cryptographic protocols in this paper. We first construct a practical quantum random oblivious transfer (R-OT) protocol based on the fact that non-orthogonal states cannot be reliably distinguished. Then, we construct a fault-tolerant one-out-of-two oblivious transfer ( O T 1 2 ) protocol based on the quantum R-OT protocol. Afterwards, we propose a quantum bit commitment (QBC) protocol which executes the fault-tolerant O T 1 2 several times. Mayers, Lo and Chau (MLC) no-go theorem proves that QBC protocol cannot be unconditionally secure. However, we find that computing the unitary transformation of no-go theorem attack needs so many resources that it is not realistically implementable. We give a definition of physical security for QBC protocols and prove that the practical QBC we proposed is physically secure and can be implemented in the real world.
Secure multiparty computation enables collaborative computations across multiple users while preserving individual privacy, which has a wide range of applications in finance, machine learning and healthcare. Secure multiparty computation can be realized using oblivious transfer as a primitive function. In this paper, we present an experimental implementation of a quantum-secure quantum oblivious transfer (QOT) protocol using an adapted quantum key distribution system combined with a bit commitment scheme, surpassing previous approaches only secure in the noisy storage model. We demonstrate the first practical application of the QOT protocol by solving the private set intersection, a prime example of secure multiparty computation, where two parties aim to find common elements in their datasets without revealing any other information. In our experiments, two banks can identify common suspicious accounts without disclosing any other data. This not only proves the experimental functionality of QOT, but also showcases its real-world commercial applications.