## 数学代写|密码学作业代写Cryptography代考|CS355

2023年3月30日

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## 数学代写|密码学作业代写Cryptography代考|Voting Protocol Security

To properly analyse security, we must consider an execution model for the election as a cryptographic protocol. This is described as one of our usual experiments, but we only sketch the technicalities.

The players in the protocol are the infrastructure players (ballot box, shuffle servers, counters and auditor), the voters and their devices. All players are modelled as interactive algorithms, managed by an experiment. The adversary may start pairs of voter and device instances. The adversary will specify the associated data the device uses. The adversary may have one voter cast multiple ballots in parallel. (This is required to model certain real-world attacks.)
The players communicate via a network that is authenticated, which means that the adversary may schedule the delivery of network messages, but cannot modify messages sent between parties, nor change the delivery order. Also, the voters and their devices communicate privately, meaning that the adversary cannot see the contents of network messages sent between voters and devices.
Remark. For voter-device communication, this models physical reality. For other communication, this is a very simplified model of messaging protocols as discussed in Chapter 13. We could easily include a suitable messaging protocol and public key infrastructure into the protocol, but for our purposes this would significantly complicate analysis at no gain to understanding.

The setup phase begins by starting the infrastructure players. Eventually, the adversary signals for setup to end, at which point the setup algorithm is run and the key material is distributed to the players.

The casting phase then starts. In this phase, the adversary provides a voter identity, associated data and a pair of ballots to the experiment, which starts an instance of the voter and a paired ballot casting device instance with the appropriate associated data and inputs either the left or the right ballot to the voter instance according to the challenge bit. The adversary then schedules network messages for delivery. The only infrastructure player active during the casting phase is the ballot box.

Finally, the adversary signals the end of the casting phase. Any network message that has not been delivered at the start of the phase is erased and any remaining voter or ballot casting device instances are halted. In the counting phase, the adversary schedules network messages for delivery.

## 数学代写|密码学作业代写Cryptography代考|CAST AS INTENDED

So far, we have assumed that a voter’s ballot casting device is corrupted if and only if the voter has been corrupted. In some settings the focus is on the voter defending against corrupt election authorities (or rather, not wanting to trust election authorities), which makes it reasonable to assume that the honest voter has some uncorruptible computational ability, in particular because it is hard to achieve anything otherwise. In many other settings we will find that the adversary is not the election authorities, but rather some external attacker (which may compromise one or more infrastructure players, of course). It is completely unreasonable to assume that these attackers will not corrupt an honest voter’s ballot casting device.

We have also assumed a personal ballot casting device. This need not be the case, and groups of voters may share a single physical ballot casting device. In this case corrupting a ballot casting device will have much greater effect, which means that adversaries will spend more effort doing so.

It follows that we may want to defend against a corrupt ballot casting device. This is often known as ensuring that the ballot was cast as intended, that is, that the encrypted ballot really is an encryption of the intended ballot.
Remark. There are concepts known as stored as cast and counted as stored which through composition ensure that the ballot was counted as intended.
Stored as cast essentially means that we should be able to check that the correct encrypted ballot was stored in the ballot box, which is in some sense trivial. Counted as stored would be ensured by the cryptographic machinery.
This is sometimes a useful mental model for thinking about some security properties. It is a reasonable approach for informal discussions of voting protocols with non-experts. It does not replace proper cryptographic definitions.
Cryptography in general is not able to force anyone to do anything. The entire goal of cryptography is instead to detect when someone is not doing what they are supposed to be doing. Given this detection ability, there are other mechanisms that incentivise or enforce proper behaviour.

Therefore, our goal is not forcing a device to cast the intended ballot, but to detect misbehaviour by corrupted devices. The detection need not be perfect, but the detection rate should be fairly robust. This also applies to an adversary trying to avoid detection. The avoidance need not be perfect and a relatively small detection rate can be survivable for a practical adversary.

# 密码学代写

## 数学代写|密码学作业代写Cryptography代考|CAST AS INTENDED

So far, we have assumed that a voter’s ballot casting device is corrupted if and only if the voter has been corrupted. 在某些情况下，重点在于选民抵御腐败的选举当局（或者更确切地说，不想信任选举当局），这使得假设诚实的选民具有一些廉洁的计算能力是合理的，特别是因为它很难实现否则。在许多其他设置中，我们会发现对手不是选举当局，而是一些外部攻击者（当然，这可能会危及一个或多个基础设施参与者）。假设这些攻击者不会破坏诚实选民的投票设备是完全不合理的。

Stored as cast 本质上意味着我们应该能够检查正确的加密选票是否存储在投票箱中，这在某种意义上是微不足道的。计算为已存储将由加密机制确保。

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## MATLAB代写

MATLAB 是一种用于技术计算的高性能语言。它将计算、可视化和编程集成在一个易于使用的环境中，其中问题和解决方案以熟悉的数学符号表示。典型用途包括：数学和计算算法开发建模、仿真和原型制作数据分析、探索和可视化科学和工程图形应用程序开发，包括图形用户界面构建MATLAB 是一个交互式系统，其基本数据元素是一个不需要维度的数组。这使您可以解决许多技术计算问题，尤其是那些具有矩阵和向量公式的问题，而只需用 C 或 Fortran 等标量非交互式语言编写程序所需的时间的一小部分。MATLAB 名称代表矩阵实验室。MATLAB 最初的编写目的是提供对由 LINPACK 和 EISPACK 项目开发的矩阵软件的轻松访问，这两个项目共同代表了矩阵计算软件的最新技术。MATLAB 经过多年的发展，得到了许多用户的投入。在大学环境中，它是数学、工程和科学入门和高级课程的标准教学工具。在工业领域，MATLAB 是高效研究、开发和分析的首选工具。MATLAB 具有一系列称为工具箱的特定于应用程序的解决方案。对于大多数 MATLAB 用户来说非常重要，工具箱允许您学习应用专业技术。工具箱是 MATLAB 函数（M 文件）的综合集合，可扩展 MATLAB 环境以解决特定类别的问题。可用工具箱的领域包括信号处理、控制系统、神经网络、模糊逻辑、小波、仿真等。