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arXiv:2606.29007

Quantum Primitive for Output-Hiding Function Sharing: Strategic Settings

Olivia R. Hartzell

quant-phSubmitted Jun 27, 2026• Announced Jun 30, 2026• 0 citations
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Abstract

Applications of the proposed primitive: Quantum Primitive for Output-Hiding Function Sharing are discussed for environments in which the parties may have strategic considerations over the generated function value, and therefore may not be mutually trusted. We show that in environments in which the measurement may not be reliably controlled by either party, the primitive permits the parties to generate private, unbiased coins.

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Applications of the proposed primitive: Quantum Primitive for Output-Hiding Function Sharing are discussed for environments in which the parties may have strategic considerations over the generated function value, and therefore may not be mutually trusted. We show that in environments in which the measurement may not be reliably controlled by either party, the primitive permits the parties to generate private, unbiased coins.
A quantum information-theoretic primitive is introduced for determining a discrete-valued function that depends on multiple parties' local private inputs. The primitive permits the parties to mutually learn each others' local inputs, and thereby determine function values, while their individual systems remain independent of these inputs. The resulting function values are shared among the parties, but may remain information-theoretically hidden from any external observer, as well as from adversarial state-preparation or measurement processes within the quantum system, in every iteration. In particular, while classically producing a shared function with these information-theoretic properties requires the use of private keys or hidden randomness, in the proposed setting it is achieved using quantum resources alone. I outline the primitive's general properties while applications across a broad range of secure quantum communication and computation settings including: quantum key distribution, multi-party coordination and decision schemes, function evaluation, and in some settings, protocols for fairly generated private coins, are relegated to further publications.
Applications of the proposed primitive: Quantum Primitive for Output-Hiding Function Sharing, are discussed for secure quantum communications and computation protocols. In particular, QKD applications provide notable enhanced security and efficiency properties relative to status-quo protocols. Additionally, we provide examples when parties may wish to encode joint functions, or decisions, which remain information-theoretically hidden from external parties and those internal to the quantum system, without additional private keys, hidden randomness, or classical communication. In particular these applications may be useful in domains such as; financial transactions, joint signaling or coordination decisions, and navigation systems, among others.
A secure Multi-Party Computation (MPC) is one of the distributed computational methods, where it computes a function over the inputs given by more than one party jointly and keeps those inputs private from the parties involved in the process. Randomization in secret sharing leading to MPC is a requirement for privacy enhancements; however, most of the available MPC models use the trust assumptions of sharing and combining values. Thus, randomization in secret sharing and MPC modules is neglected. As a result, the available MPC models are prone to information leakage problems, where the models can reveal the partial values of the sharing secrets. In this paper, we propose the first model of utilizing a random function generator as an MPC primitive. More specifically, we analyze our previous development of the Symmetric Random Function Generator (SRFG) for information-theoretic security, where the system is considered to have unconditional security if it is secure against adversaries with unlimited computing resources and time. Further, we apply SRFG to eradicate the problem of information leakage in the general MPC model. Through a set of experiments, we show that SRFG is a function generator that can generate the combined functions (combination of logic GATEs) withn/2n/2n/2-private tonnn-private norms. As the main goal of MPC is privacy preservation of the inputs, we analyze the applicability of SRFG properties in secret sharing and MPC and observe that SRFG is eligible to be a cryptographic primitive in MPC developments. We also measure the performance of our proposed SRFG-based MPC framework with the other randomness generation-based MPC frameworks and analyze the comparative attributes with the state-of-the-art models. We observe that our posed SRFG-based MPC is$\approx$30% better in terms of throughput and also shows 100% privacy attainment.