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Paper 1
Non-Interactive Oblivious Transfer and One-Time Programs from Noisy Quantum Storage
Ricardo Faleiro, Manuel Goulão, Leonardo Novo, Emmanuel Zambrini Cruzeiro
- Year
- 2024
- Journal
- arXiv preprint
- DOI
- arXiv:2410.08367
- arXiv
- 2410.08367
Few primitives are as intertwined with the foundations of cryptography as Oblivious Transfer (OT). Not surprisingly, with the advent of quantum information processing, a major research path has emerged, aiming to minimize the requirements necessary to achieve OT by leveraging quantum resources, while also exploring the implications for secure computation. Indeed, OT has been the target of renewed focus regarding its newfound quantum possibilities (and impossibilities), both towards its computation and communication complexity. For instance, non-interactive OT, known to be impossible classically, has been strongly pursued. In its most extreme form, non-interactive chosen-input OT (one-shot OT) is equivalent to a One-Time Memory (OTM). OTMs have been proposed as tamper-proof hardware solutions for constructing One-Time Programs -- single-use programs that execute on an arbitrary input without revealing anything about their internal workings. In this work, we leverage quantum resources in the Noisy-Quantum-Storage Model to achieve: 1. Unconditionally-secure two-message non-interactive OT -- the smallest number of messages known to date for unconditionally-secure chosen-input OT. 2. Computationally-secure one-shot OT/OTM, with everlasting security, assuming only one-way functions and sequential functions -- without requiring trusted hardware, QROM, or pre-shared entanglement. 3. One-Time Programs without the need for hardware-based solutions or QROM, by compiling our OTM construction with the [GKR08, GIS+10] compiler.
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Quantum Calculus of Fibonacci Divisors and Fermion-Boson Entanglement for Infinite Hierarchy of N = 2 Supersymmetric Golden Oscillators
Oktay K. Pashaev
- Year
- 2024
- Journal
- arXiv preprint
- DOI
- arXiv:2410.04169
- arXiv
- 2410.04169
The quantum calculus with two bases, as powers of the Golden and the Silver ratio, relates Fibonacci divisor derivative with Binet formula of Fibonacci divisor number operator, acting in Fock space of quantum states.It provides a tool to study the hierarchy of Golden oscillators with energy spectrum in form of Fibonacci divisor numbers. We generalize this model to supersymmetric number operator and corresponding Binet formula for supersymmetric Fibonacci divisor number operator. The operator determines the Hamiltonian of hierarchy of supersymmetric Golden oscillators, acting in fermion-boson Hilbert space and belonging to N=2 supersymmetric algebra. The eigenstates of the super Fibonacci divisor number operator are double degenerate and can be characterized by a point on the super-Bloch sphere. By the supersymmetric Fibonacci divisor annihilation operator, we construct the hierarchy of supersymmetric coherent states as eigenstates of this operator. Entanglement of fermions with bosons in these states is calculated by the concurrence, represented by the Gram determinant and hierarchy of Golden exponential functions. We show that the reference states and corresponding von Neumann entropy, measuring fermion-boson entanglement, are characterized completely by the powers of the Golden ratio. The simple geometrical classification of entangled states by the Frobenius ball and meaning of the concurrence as double area of parallelogram in Hilbert space are given.
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