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International Journal of Quantum Information

Randomized quantum oblivious transfer with application in hacker-resistant computation

Xiaogang Cheng, Ren Guo, Yonghong Chen

Published Jun 1, 2018• 1 citation
Publisher

Abstract

OT (Oblivious transfer) is a fundamental primitive in cryptography. But it is well known that in quantum cryptography, unconditionally secure OT is impossible. A variant of OT, i.e. randomized OT, is presented. We then show how to realize this variant in quantum cryptography with some security relaxations, which is inevitable because of the well-known impossible result in quantum cryptography. We also present a new secure computational model, namely HRC (Hacker-Resistant Computation) model. Since on today’s Internet there are more and more hackers and increased cyber threat, knowing how to protect the information and privacy stored on our computer and on cloud servers is very important, even when the computer or server has been breached by hackers. Finally, some interesting applications of the randomized OT variant to HRC are discussed.

DOI
10.1142/s0219749918500399

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OT (Oblivious transfer) is a fundamental primitive in cryptography. But it is well known that in quantum cryptography, unconditionally secure OT is impossible. A variant of OT, i.e. randomized OT, is presented. We then show how to realize this variant in quantum cryptography with some security relaxations, which is inevitable because of the well-known impossible result in quantum cryptography. We also present a new secure computational model, namely HRC (Hacker-Resistant Computation) model. Since on today’s Internet there are more and more hackers and increased cyber threat, knowing how to protect the information and privacy stored on our computer and on cloud servers is very important, even when the computer or server has been breached by hackers. Finally, some interesting applications of the randomized OT variant to HRC are discussed.
Oblivious transfer (OT) is a fundamental primitive in cryptography. It is known that unconditionally secure OT is impossible, even with the help of quantum mechanics. Furthermore, no classical OT scheme has been proven to offer computational security in the usual super-polynomial model, and there is evidence that such schemes cannot be based on one-way permutations. Nevertheless, inspired by Ralph Merkle's 1974 key distribution scheme, we offer a novel classical OT scheme based on one-way permutations and prove its polynomial security: the effort to cheat it scales as t3/2, where t is the legitimate effort needed to implement it. Unfortunately, our scheme melts down under the onslaught of a quantum adversary after an effort merely in the order of t5/6, so that it is actually easier to subvert it than to use it legitimately! By allowing the honest parties to use quantum computation as well, however, it may be that our OT scheme can be repaired so as to resist modest quantum attacks.
Oblivious transfer (OT) is an essential building block for secure multiparty computation. Up to now, one- and two-server OT protocols have been investigated. It has been proven that unconditionally secure one-server OT is impossible even with the quantum system. Recently, Hayashi and Song proposed the first two-server OT protocol for quantum messages [Adv. Quantum Technol. 7, 2300184 (2024)], which is the only one for two-server OT for quantum messages to our knowledge. This protocol has the assumption that two quantum servers do not communicate with each other. However, it is unrealistic to make such an assumption. In addition, an equation error occurs in the protocol description. To tackle these issues, we first point out the equation error existent in the protocol of Hayashi and Song and correct it. Then, we propose a two-server OT protocol for quantum messages by using entanglement swapping. Security analysis shows that the user privacy holds even if the two quantum servers communicate mutually.
Motivated by the applications of secure multi-party computation as a privacy-protecting data analysis tool, and identifying oblivious transfer as one of its main practical enablers, we propose a practical realization of randomized quantum oblivious transfer. By using only symmetric cryptography primitives to implement commitments, we construct computationally secure randomized oblivious transfer without the need for public-key cryptography or assumptions imposing limitations on the adversarial devices. We show that the protocol is secure under an indistinguishability-based notion of security and demonstrate an experimental implementation to test its real-world performance. Its security and performance are then compared to both quantum and classical alternatives, showing potential advantages over existing solutions based on the noisy storage model and public-key cryptography.
Oblivious transfer (OT) is one of the most fundamental primitives in cryptography and is widely used in protocols for secure two-party and multi-party computation. As secure com-putation becomes more practical, the need for practical large scale oblivious transfer protocols is becoming more evident. Oblivious transfer extensions are protocols that enable a relatively small number of “base-OTs ” to be utilized to compute a very large number of OTs at low cost. In the semi-honest setting, Ishai et al. (CRYPTO 2003) presented an OT extension protocol for which the cost of each OT (beyond the base-OTs) is just a few hash function operations. In the malicious setting, Nielsen et al. (CRYPTO 2012) presented an efficient OT extension protocol for the setting of active adversaries, that is secure in the random oracle model. In this work, we present an OT extension protocol for the setting of malicious adversaries that is more efficient and uses less communication than previous works. In addition, our protocol can be proven secure in both the random oracle model, and in the standard model with a type of correlation robustness. Given the importance of OT in many secure computation protocols, increasing the efficiency of OT extensions is another important step forward to making secure
Quantum cryptography is the field of cryptography that explores the quantum properties of matter. Generally, it aims to develop primitives beyond the reach of classical cryptography and to improve existing classical implementations. Although much of the work in this field covers quantum key distribution (QKD), there have been some crucial steps towards the understanding and development of quantum oblivious transfer (QOT). One can show the similarity between the application structure of both QKD and QOT primitives. Just as QKD protocols allow quantum-safe communication, QOT protocols allow quantum-safe computation. However, the conditions under which QOT is fully quantum-safe have been subject to intense scrutiny and study. In this review article, we survey the work developed around the concept of oblivious transfer within theoretical quantum cryptography. We focus on some proposed protocols and their security requirements. We review the impossibility results that daunt this primitive and discuss several quantum security models under which it is possible to prove QOT security.
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.