Oblivious transfer and quantum channels

Practical and unconditionally secure spacetime-constrained oblivious transfer

Spacetime-constrained oblivious transfer (SCOT) extends the fundamental primitive of oblivious transfer to Minkowski space. SCOT and location oblivious data transfer (LODT) are the only known cryptographic tasks with classical inputs and outputs for which unconditional security needs both quantum theory and relativity. We give an unconditionally secure SCOT protocol that, contrasting previous SCOT and LODT protocols, is practical to implement with current technology, where distant agents need only communicate classical information, while quantum communication occurs at a single location. We al…

使用两个纯态的量子Rabin不经意传输

Quantum Rabin oblivious transfer using two pure states

该研究针对Rabin不经意传输的密码学需求，提出使用两个纯态的量子协议，分析了双方最优作弊概率，证明其在部分$p_?$取值下优于无第三方经典协议，且混合态量子协议在部分场景下表现更优。

The physics of no-bit-commitment : Generalized quantum non-locality versus oblivious transfer

We show here that the recent work of Wolf and Wullschleger (quant-ph/0502030) on oblivious transfer apparently opens the possibility that non-local correlations which are stronger than those in quantum mechanics could be used for bit-commitment. This is surprising, because it is the very existence of non-local correlations which in quantum mechanics prevents bit-commitment. We resolve this apparent paradox by stressing the difference between non-local correlations and oblivious transfer, based on the time-ordering of their inputs and outputs, which prevents bit-commitment.

A Weak Quantum Oblivious Transfer

Due to the commonly known impossibility results, information theoretic security is considered impossible for oblivious transfer (OT) in both the classical and the quantum world. In this paper, we proposed a weak version of the all-or-nothing OT. In our protocol the honest parties do not need long term quantum memory, entanglements, or sophisticated quantum computations. We observe some difference between the classical and quantum OT impossibilities.

Quantum oblivious transfer protocols based on EPR states

We describe efficient protocols for quantum oblivious transfer and for one-out-of-two quantum oblivious transfer. These protocols, which can be implemented with present technology, are secure against general attacks as long as the cheater can not store the bit for an arbitrarily long period of time.

Oblivious transfer using quantum entanglement

Based on quantum entanglement, an all-or-nothing oblivious transfer protocol is proposed and is proven to be secure. The distinct merit of the present protocol lies in that it is not based on quantum bit commitment. More intriguingly, this OT protocol does not belong to a class of protocols denied by the Lo's no-go theorem of one-sided two-party secure computation, and thus its security can be achieved.

A novel application of probabilistic teleportation: p-Rabin qubit-oblivious transfer

All existing quantum oblivious transfer protocols are to realize the oblivious transfer of bit or bit-string. In this paper, p-Rabin quantum oblivious transfer of a qubit (abbr. p-Rabin qubit-OT) is achieved by using a probabilistic teleportation (abbr. PT) protocol. Here, this is the first time that the concept of qubit-OT is presented. As the PT protocol is able to transfer an (un)known pure state with a certain probability, this feature makes the PT protocol well fit for Rabin OT. Furthermore, the PT protocol can be used for OT of a bit by encoding classical bit with two pre-agreed orthogon…

Coin-Flipping-based Quantum Oblivious Transfer

When submitting ``Coin-Flipping-based Quantum Oblivious Transfer'' (quant-ph/0605027v4) to Indocrypt-2006, I received valuable reviews. Due to the attacks in these reviews, my major protocols, for cheat-sensitive and coin-flipping-based 2-1 oblivious transfers, are insecure. I would have withdrawn the paper. But I think I'd rather post the attacks made by the reviewer. Besides, as ``coin-flipping-based 2-1 OT'' is an important case-study in ``Two-party Models and the No-go Theorems'' (quant-ph/0608165), the paper is also touched by the attack. It will be reconsidered, and the case-study will b…

A device-independent protocol for XOR oblivious transfer

Oblivious transfer is a cryptographic primitive where Alice has two bits and Bob wishes to learn some function of them. Ideally, Alice should not learn Bob's desired function choice and Bob should not learn any more than what is logically implied by the function value. While decent quantum protocols for this task are known, many become completely insecure if an adversary were to control the quantum devices used in the implementation of the protocol. In this work we give a fully device-independent quantum protocol for XOR oblivious transfer.

利用延迟测量在量子Rabin不经意传输中作弊

Cheating in quantum Rabin oblivious transfer using delayed measurements

本文研究Rabin量子不经意传输协议，提出利用延迟测量的攻击方法使作弊方获得额外信息并实现完美作弊，并给出降低作弊概率的协议修改建议。

Lower Bounds for Quantum Oblivious Transfer

Oblivious transfer is a fundamental primitive in cryptography. While perfect information theoretic security is impossible, quantum oblivious transfer protocols can limit the dishonest players' cheating. Finding the optimal security parameters in such protocols is an important open question. In this paper we show that every 1-out-of-2 oblivious transfer protocol allows a dishonest party to cheat with probability bounded below by a constant strictly larger than 1/2. Alice's cheating is defined as her probability of guessing Bob's index, and Bob's cheating is defined as his probability of guessin…

Continuous-Variable Protocol for Oblivious Transfer in the Noisy-Storage Model

Cryptographic protocols are the backbone of our information society. This includes two-party protocols which offer protection against distrustful players. Such protocols can be built from a basic primitive called oblivious transfer. We present and experimentally demonstrate here the first quantum protocol for oblivious transfer for optical continuous-variable systems, and prove its security in the noisy-storage model. This model allows to establish security by sending more quantum signals than an attacker can reliably store during the protocol. The security proof is based on new uncertainty re…

Simple Protocols for Oblivious Transfer and Secure Identification in the Noisy-Quantum-Storage Model

We present simple protocols for oblivious transfer and password-based identification which are secure against general attacks in the noisy-quantum-storage model as defined in [KWW09]. We argue that a technical tool from [KWW09] suffices to prove security of the known protocols. Whereas the more involved protocol for oblivious transfer from [KWW09] requires less noise in storage to achieve security, our "canonical" protocols have the advantage of being simpler to implement and the security error is easier control. Therefore, our protocols yield higher OT-rates for many realistic noise parameter…

Imperfect 1-out-of-2 quantum oblivious transfer: bounds, a protocol, and its experimental implementation

Oblivious transfer is an important primitive in modern cryptography. Applications include secure multiparty computation, oblivious sampling, e-voting, and signatures. Information-theoretically secure perfect 1-out-of 2 oblivious transfer is impossible to achieve. Imperfect variants, where both participants' ability to cheat is still limited, are possible using quantum means while remaining classically impossible. Precisely what security parameters are attainable remains unknown. We introduce a theoretical framework for studying semirandom quantum oblivious transfer, which is shown to be equiva…

Spacetime-constrained oblivious transfer

In 1-out-of-2 oblivious transfer (OT), Alice inputs numbers x_0, x_1, Bob inputs a bit b and outputs x_b. Secure OT requires that Alice and Bob learn nothing about b and x_{\bar{b}}, respectively. We define spacetime-constrained oblivious transfer (SCOT) as OT in Minkowski spacetime in which Bob must output x_b within R_b, where R_0 and R_1 are fixed spacelike separated spacetime regions. We show that unconditionally secure SCOT is impossible with classical protocols in Minkowski (or Galilean) spacetime, or with quantum protocols in Galilean spacetime. We describe a quantum SCOT protocol in Mi…

Asymptotically Secure Quantum Oblivious Transfer

Due to the commonly known impossibility results, unconditional security for oblivious transfer is seen as impossible even in the quantum world. In this paper, we try to overcome these impossibility results by proposing a protocol which is asymptotically secure. The protocol makes use of the basic properties of non-orthogonal quantum states. Apart from security, the advantages of our protocol include the fact that the honest players do not need to have quantum memory or create entanglement between individual qubits. The relation of our work to the known impossibility results is also discussed.

Practical quantum oblivious transfer with a single photon

Quantum oblivious transfer (QOT) is an essential cryptographic primitive. But unconditionally secure QOT is known to be impossible. Here we propose a practical QOT protocol, which is perfectly secure against dishonest sender without relying on any technological assumption. Meanwhile, it is also secure against dishonest receiver in the absence of long-term quantum memory and complicated collective measurements. The protocol is extremely feasible, as it can be implemented using currently available Mach-Zehnder interferometer, and no quantum memory, collective measurements nor entanglement are ne…

An Experimental Implementation of Oblivious Transfer in the Noisy Storage Model

Cryptography's importance in our everyday lives continues to grow in our increasingly digital world. Oblivious transfer (OT) has long been a fundamental and important cryptographic primitive since it is known that general two-party cryptographic tasks can be built from this basic building block. Here we show the experimental implementation of a 1-2 random oblivious transfer (ROT) protocol by performing measurements on polarization-entangled photon pairs in a modified entangled quantum key distribution system, followed by all of the necessary classical post-processing including one-way error co…

基于与经典部分同态加密兼容的XOR不经意传输的量子线性多项式求值

Quantum linear polynomial evaluation based on XOR oblivious transfer compatible with classical partially homomorphic encryption

该研究提出基于XOR不经意传输的量子线性多项式求值方案，结合经典同态加密或量子计算实现不同安全级别的模2线性多项式求值，还探讨了经典后处理方法。

量子通用可组合不经意线性求值

Quantum Universally Composable Oblivious Linear Evaluation

本文提出首个不依赖量子不经意传输的量子不经意线性求值协议，利用高维量子态和互无偏基在素数及素数幂维伽罗瓦域上实现计算，并推广到向量情形，证明其在量子通用可组合框架下具有静态安全性。

Statistically Secure Quantum Oblivious Transfer

This paper has been withdrawn.

具有完美单边安全性的不完全量子不经意传输

Incomplete quantum oblivious transfer with perfect one-sided security

针对2选1量子不经意传输，研究不完全协议下的作弊概率界限，提出基于四个对称纯量子态的最优非交互协议，证明其性能优于经典协议且无需纠缠与量子存储器。

Quantum oblivious transfer: a short review

Quantum cryptography is the field of cryptography that explores the quantum properties of matter. Its aim is to develop primitives beyond the reach of classical cryptography or to improve on existing classical implementations. Although much of the work in this field is dedicated to quantum key distribution (QKD), some important steps were made towards the study and development of quantum oblivious transfer (QOT). It is possible to draw a comparison between the application structure of both QKD and QOT primitives. Just as QKD protocols allow quantum-safe communication, QOT protocols allow quant…

Secure quantum weak oblivious transfer against individual measurements

In quantum weak oblivious transfer, Alice sends Bob two bits and Bob can learn one of the bits at his choice. It was found that the security of such a protocol is bounded by $2P_{Alice}^{\ast }+P_{Bob}^{\ast }\geq 2$, where $P_{Alice}^{\ast }$ is the probability with which Alice can guess Bob's choice, and $P_{Bob}^{\ast }$ is the probability with which Bob can guess both of Alice's bits\ given that he learns one of the bits with certainty. Here we propose a protocol and show that as long as Alice is restricted to individual measurements, then both $P_{Alice}^{\ast }$ and $P_{Bob}^{\ast }$ can…

Quantum Key Distribution and String Oblivious Transfer in Noisy Channels

We prove the unconditional security of a quantum key distribution (QKD) protocol on a noisy channel against the most general attack allowed by quantum physics. We use the fact that in a previous paper we have reduced the proof of the unconditionally security of this QKD protocol to a proof that a corresponding Quantum String Oblivious Transfer (String-QOT) protocol would be unconditionally secure against Bob if implemented on top of an unconditionally secure bit commitment scheme. We prove a lemma that extends a security proof given by Yao for a (one bit) QOT protocol to this String-QOT protoc…

噪声存储模型中的容错不经意传输

Error-tolerant oblivious transfer in the noisy-storage model

本文利用熵不确定性关系，推导了在可信与不可信噪声并存下oblivious transfer安全性的紧致界限，解决了实验设备噪声可能被作弊者利用的安全隐患。

量子Rabin不经意传输中的混合态

Mixed States in Quantum Rabin Oblivious Transfer

本文研究混合量子态在Rabin不经意传输中的应用，提出三种混合态协议，通过扩展纯态方案和概率方法，在不同参数下实现优于经典和量子纯态协议的性能。

非交互式XOR量子不经意传输：最优协议及其实验实现

Non-interactive XOR quantum oblivious transfer: optimal protocols and their experimental implementations

该研究确定了非交互式量子XOT协议的最小欺骗概率，提出并光学实现了优于经典协议的最优及反转协议，确保双方欺骗概率不变。

Oblivious transfer and quantum non-locality

Oblivious transfer, a central functionality in modern cryptography, allows a party to send two one-bit messages to another who can choose one of them to read, remaining ignorant about the other, whereas the sender does not learn the receiver's choice. Oblivious transfer the security of which is information-theoretic for both parties is known impossible to achieve from scratch. - The joint behavior of certain bi-partite quantum states is non-local, i.e., cannot be explained by shared classical information. In order to better understand such behavior, which is classically explainable only by com…

实用量子盲目键分发的性能

Performance of Practical Quantum Oblivious Key Distribution

本研究提出一种基于对称密码学的实用量子盲目传输方案，展示了其在安全性和性能上的优势，相较于现有基于噪声存储模型和公钥密码学的解决方案。

Can relativistic bit commitment lead to secure quantum oblivious transfer?

While unconditionally secure bit commitment (BC) is considered impossible within the quantum framework, it can be obtained under relativistic or experimental constraints. Here we study whether such BC can lead to secure quantum oblivious transfer (QOT). The answer is not completely negative. On one hand, we provide a detailed cheating strategy, showing that the "honest-but-curious adversaries" in some of the existing no-go proofs on QOT still apply even if secure BC is used, enabling the receiver to increase the average reliability of the decoded value of the transferred bit. On the other hand…

Impossibility of composable Oblivious Transfer in relativistic quantum cryptography

We study the cryptographic primitive Oblivious Transfer; a composable construction of this resource would allow arbitrary multi-party computation to be carried out in a secure way, i.e. to compute functions in a distributed way while keeping inputs from different parties private. First we review a framework that allows us to analyze composability of classical and quantum cryptographic protocols in special relativity: Abstract Cryptography implemented with Causal Boxes. We then (1) explore and formalize different versions of oblivious transfer found in the literature, (2) prove that their equiv…

Quantum oblivious transfer and bit commitment protocols based on two non-orthogonal states coding

Oblivious transfer protocols (R-OT and OT$_{1}^{2}$) are presented based on non-orthogonal states transmission, and the bit commitment protocols on the top of OT$_{1}^{2}$ are constructed. Although these OT protocols are all unconditional secure, the bit commitment protocols based on OT protocols are not secure against attack similar to that presented by no-go theorem.

基于有界量子存储模型和计算假设的设备无关不经意传输

Device-Independent Oblivious Transfer from the Bounded-Quantum-Storage-Model and Computational Assumptions

提出一种基于有界量子存储和计算假设的设备无关不经意传输协议，通过单设备自测试实现设备无关性，放宽非通信假设且具有永恒安全性。

On Bit Commitment and Oblivious Transfer in Measurement-Device Independent settings

Among the most studied tasks in Quantum Cryptography one can find Bit Commitment (BC) and Oblivious Transfer (OT), two central cryptographic primitives. In this paper we propose for the first time protocols for these tasks in the measurement-device independent (MDI) settings and analyze their security. We analyze two different cases: first we assume the parties have access to perfect single photon sources (but still in the presence of noise and losses), and second we assume that they only have imperfect single photon sources. In the first case we propose a protocol for both BC and OT and prove…

A simple quantum oblivious transfer protocol

A simple and efficient protocol for quantum oblivious transfer is proposed. The protocol can easily be implemented with present technology and is secure against cheaters with unlimited computing power provided the receiver does not have the technology to store the particles for an arbitrarily long period of time. The proposed protocol is a significant improvement over the previous protocols. Unlike the protocol of Crépeau and Kilian which is secure if only if the spin of the particle is measured along the $x$ or the $y$ axis, the present protocol is perfectly secure no matter along which axes …

Asymptotically secure All-or-nothing Quantum Oblivious Transfer

We present a device independently secure quantum scheme for p-threshold all-or-nothing oblivious transfer. Novelty of the scheme is that, its security does not depend -- unlike the usual case -- on any quantum bit commitment protocol, rather it depends on Hardy's argument for two-qubit system. This scheme is shown to be unconditionally secure against any strategy allowed by quantum mechanics. By providing a secure scheme for all-or-nothing quantum oblivious transfer, we have answered a long standing open problem, other than the quantum key distribution, whether there is any two-party quantum c…

Generation and Distribution of Quantum Oblivious Keys for Secure Multiparty Computation

The oblivious transfer primitive is sufficient to implement secure multiparty computation. However, secure multiparty computation based only on classical cryptography is severely limited by the security and efficiency of the oblivious transfer implementation. We present a method to efficiently and securely generate and distribute oblivious keys by exchanging qubits and by performing commitments using classical hash functions. With the presented hybrid approach, quantum and classical, we obtain a practical and high-speed oblivious transfer protocol, secure even against quantum computer attacks.…

Rabin不经意传输的量子协议

Quantum protocols for Rabin oblivious transfer

本文针对Rabin不经意传输提出安全性改进的量子协议设计，并证明任何量子协议均存在常数下界，同时引入作弊优势概念以量化非对称作弊场景下的安全性。

用于量子消息的双服务器不经意传输

Two-Server Oblivious Transfer for Quantum Messages

针对现有双服务器不经意传输仅支持经典消息的局限，本文提出可处理量子消息的双服务器不经意传输协议，以支持量子网络中的量子信息处理。

One-out-of-two Quantum Oblivious Transfer based on Nonorthogonal States

This study proposes a simple and efficient one-out-of-two quantum oblivious transfer (QOT) protocol based on nonorthogonal states. The nonorthogonal property grants quantum bit immunity to some operations in order to achieve the irreversible goal of discarding a message, resulting in a one-out-of-two selection effect. In addition, it can also prevent entangled cheating from an illegal agent. The resulting QOT protocol is therefore built directly on quantum resources, rather than on a two-level structure which must first create two classical keys using the quantum resources (all-or-nothing QOT)…

Oblivious transfer based on single-qubit rotations

We present a bit-string quantum oblivious transfer protocol based on single-qubit rotations. Our protocol is built upon a previously proposed quantum public-key protocol and its practical security relies on the laws of Quantum Mechanics. Practical security is reflected in the fact that, due to technological limitations, the receiver (Bob) of the transferred bit-string is restricted to performing only "few-qubit" coherent measurements. We also present a single-bit oblivious transfer based on the proposed bit-string protocol. The protocol can be implemented with current technology based on optic…

Quantum m-out-of-n Oblivious Transfer

In the m-out-of-n oblivious transfer (OT) model, one party Alice sends n bits to another party Bob, Bob can get only m bits from the n bits. However, Alice cannot know which m bits Bob received. Y.Mu[MJV02]} and Naor[Naor01] presented classical m-out-of-n oblivious transfer based on discrete logarithm. As the work of Shor [Shor94], the discrete logarithm can be solved in polynomial time by quantum computers, so such OTs are unsafe to the quantum computer. In this paper, we construct a quantum m-out-of-n OT (QOT) scheme based on the transmission of polarized light and show that the scheme is ro…

Optimal bounds for semi-honest quantum oblivious transfer

Oblivious transfer is a fundamental cryptographic primitive in which Bob transfers one of two bits to Alice in such a way that Bob cannot know which of the two bits Alice has learned. We present an optimal security bound for quantum oblivious transfer protocols under a natural and demanding definition of what it means for Alice to cheat. Our lower bound is a smooth tradeoff between the probability B with which Bob can guess Alice's bit choice and the probability A with which Alice can guess both of Bob's bits given that she learns one of the bits with certainty. We prove that 2B + A is greater…

Oblivious Transfer is in MiniQCrypt

MiniQCrypt is a world where quantum-secure one-way functions exist, and quantum communication is possible. We construct an oblivious transfer (OT) protocol in MiniQCrypt that achieves simulation-security in the plain model against malicious quantum polynomial-time adversaries, building on the foundational work of Bennett, Brassard, Crépeau and Skubiszewska (CRYPTO 1991). Combining the OT protocol with prior works, we obtain secure two-party and multi-party computation protocols also in MiniQCrypt. This is in contrast to the classical world, where it is widely believed that one-way functions al…

基于单向函数的量子不经意传输实用协议

A Practical Protocol for Quantum Oblivious Transfer from One-Way Functions

提出一种基于单向函数的量子不经意传输协议，在普通模型中实现模拟安全性，并通过改进效率和提供错误校正分析，促进实验实现。

A generic construction of quantum-oblivious-key-transfer-based private query with ideal database security and zero failure

Higher security and lower failure probability have always been people's pursuits in quantum-oblivious-key-transfer-based private query (QOKT-PQ) protocols since Jacobi \emph{et al}. [Phys. Rev. A 83, 022301 (2011)] proposed the first protocol of this kind. However, higher database security generally has to be obtained at the cost of a higher failure probability, and vice versa. Recently, based on a round-robin differential-phase-shift quantum key distribution protocol, Liu \emph{et al}. [Sci. China-Phys. Mech. Astron.58, 100301 (2015)] presented a private query protocol (RRDPS-PQ protocol) uti…

Towards Communication-Efficient Quantum Oblivious Key Distribution

Oblivious Transfer, a fundamental problem in the field of secure multi-party computation is defined as follows: A database DB of N bits held by Bob is queried by a user Alice who is interested in the bit DB_b in such a way that (1) Alice learns DB_b and only DB_b and (2) Bob does not learn anything about Alice's choice b. While solutions to this problem in the classical domain rely largely on unproven computational complexity theoretic assumptions, it is also known that perfect solutions that guarantee both database and user privacy are impossible in the quantum domain. Jakobi et al. [Phys. Re…

从零知识证明中获得隐含转移，或如何实现最优轮次的量子隐含转移和量子状态的零知识证明

Oblivious Transfer from Zero-Knowledge Proofs, or How to Achieve Round-Optimal Quantum Oblivious Transfer and Zero-Knowledge Proofs on Quantum States

本文提出了一种将经典零知识证明转换为量子隐含转移协议的通用方法，实现了最优轮次的量子隐含转移，并引入了新的复杂度类ZKstatesQIP和ZKstatesQMA。

基于比特承诺的量子不经意传输实现实验性安全多方计算

Experimental Secure Multiparty Computation from Quantum Oblivious Transfer with Bit Commitment

本文实验实现了基于比特承诺的量子不经意传输协议，并首次将其应用于私有集合交集，证明了两家银行可在不泄露其他数据的情况下识别共同可疑账户，展示了其实际商业价值。

One-out-of-$m$ spacetime-constrained oblivious transfer

In one-out-of-$m$ spacetime-constrained oblivious transfer (SCOT), Alice and Bob agree on $m$ pairwise spacelike separated output spacetime regions $R_0,R_1,\ldots, R_{m-1}$ in an agreed reference frame in a spacetime that is Minkowski, or close to Minkowski; Alice inputs a message $x_i$ in the causal past of a spacetime point $Q_i$ of $R_i$, for $i\in\{0,1,\ldots,m-1\}$; Bob inputs $b\in\{0,1,\ldots,m-1\}$ in the intersection of the causal pasts of $Q_0,Q_1,\ldots,Q_{m-1}$ and outputs $x_b$ in $R_b$; Alice remains oblivious to $b$ anywhere in spacetime; and Bob is unable to obtain $x_i$ in $R…

Resource requirements of private quantum channels and consequence for oblivious remote state preparation

Shannon in celebrated works had shown that n bits of shared key is necessary and sufficient to transmit n-bit classical information in an information-theoretically secure way. Ambainis, Mosca, Tapp and de Wolf in quant-ph/0003101 considered a more general setting, referred to as Private quantum channels, in which instead of classical information, quantum states are required to be transmitted and only one-way communication is allowed. They show that in this case 2n bits of shared key is necessary and sufficient to transmit an n-qubit state. We consider the most general setting in which we allow…

1-out-of-2 Oblivious transfer using flawed Bit-string quantum protocol

Oblivious transfer (OT) is an important tool in cryptography. It serves as a subroutine to other complex procedures of both theoretical and practical significance. Common attribute of OT protocols is that one party (Alice) has to send a message to another party (Bob) and has to stay oblivious on whether Bob did receive the message. Specific (OT) protocols vary by exact definition of the task - in the all-or-nothing protocol Alice sends a single bit-string message, which Bob is able to read only with 50% probability, whereas in 1-out-of-2 OT protocol Bob reads one out of two messages sent by Al…

Oblivious transfer based on quantum state computational distinguishability

Oblivious transfer protocol is a basic building block in cryptography and is used to transfer information from a sender to a receiver in such a way that, at the end of the protocol, the sender does not know if the receiver got the message or not. Since Shor's quantum algorithm appeared, the security of most of classical cryptographic schemes has been compromised, as they rely on the fact that factoring is unfeasible. To overcome this, quantum mechanics has been used intensively in the past decades, and alternatives resistant to quantum attacks have been developed in order to fulfill the (poten…