## TECHNOLOGY FOCUS

The research and practical results on Quantum computers in the recent years have given a major setback to classical and widely used cryptography schemes such as (Rivest‐Shamir‐Adleman) Algorithm and ECC (Elliptic Curve Cryptography). RSA and ECC depend on integer factorization problem and discrete logarithm problem respectively, which can be easily solved by Quantum Computers of sufficiently large size running the infamous Shor’s Algorithm. Therefore, cryptography schemes which are difficult to solve in both traditional as well as Quantum Computers need to be evaluated. **This course provides a detailed survey on Post‐Quantum Cryptography schemes and emphasizes their applicability to provide security in constrained devices.** A comprehensive insight is provided into the schemes which could possibly replace RSA and ECC for security in constrained devices.

While post‐quantum cryptography is an effort to develop novel classical cryptosystems which are robust to factorization and other quantum algorithms, which is certainly one option, this does not completely solve the problem. The point is that there may be undiscovered quantum algorithms (or undiscovered classical ones) that might easily break the security of the new cryptosystems. In other words, postquantum cryptography is likely to offer only a partial and temporary solution to the problem. By contrast, quantum key distribution (QKD), discussed also in this course, offers the ultimate solution: restoring security and confidentiality by resorting to unbreakable principles of nature, such as the uncertainty principle or the monogamy of entanglement. **So we cover in details in this course the quantum cryptography as well.**Even though QKD offers the ultimate solution to the security problem, its ideal implementation is hard to implement in practice and there are a number of open problems to be addressed. On one side, fully‐device independent QKD protocols provide the highest level of quantum security, but they are quite demanding to realize and are characterized by extremely low secret key rates. On the other hand, more practical QKD protocols assume some level of trust in their devices, an assumption that allows them to achieve reasonable rates, but this also opens the possibility of dangerous side‐channel attacks.

Besides a trade‐off between security and rate, there is also another important trade-off which is between rate and distance. Today, we know that there is a fundamental limit which restricts any point to point implementation of QKD. Given a lossy link with transmissivity , two parties cannot distribute more than the secret key capacity of the channel, which is i.e., scaling of secret bits per channel use at long distance. Ideal implementations of QKD protocols based on continuous‐variable systems and Gaussian states may approach this capacity while those based on discrete variables falls below by additional factors. To overcome this limit and enable long‐distance high‐rate implementations of QKD, we need to develop quantum repeaters and quantum networks In this way, we may achieve better long‐distance scaling and further boost the rates by resorting to more complex routing strategies. The study of quantum repeaters and secure QKD networks is one of the hottest topics today which is also covered in this course. The course aims at providing an overview of the most important and most recent advances in the field of quantum cryptography, both theoretically and experimentally.

In near term, we expect that quantum security and QKD will be competing with so called post quantum security solutions and for this reason in a separate segment of this course we discuss in details pros and cons of each technology.

## COURSE CONTENT

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## WHO SHOULD ATTEND

Participants with background in either quantum physics, networks planning, design, deployment and control or networks/internet economics should benefit from participation. This includes researchers, students and professors in academia as well as industry, networks operators, regulators and managers in this field.

**Monday ****1. INTRODUCTION**

Qubit

Entanglement

Quantum Gates and Quantum Computing

Quantum Teleportation and

Quantum Information Theory

Quantum algorithms

Quantum parallelism

Deutsch’s algorithm

The Deutsch–Jozsa algorithm**2. QSA ALGORITHMS**

The Deutsch Algorithm

Simon’s Algorithm

Shor’s Algorithm

Quantum Phase Estimation Algorithm

Grover’s Quantum Search Algorithm

Dürr-Høyer Quantum Search Algorithm

Quantum Counting Algorithm

Quantum Genetic Algorithm

Harrow-Hassidim-Lloyd Algorithm

Quantum Mean Algorithm

Quantum Weighted Sum Algorithm

** PHYSICS OF QUANTUM ALGORITHMS**

Implementation of Deutsch’s Algorithm

Implementation of Deutsch and Jozsa’s Algorithm

Ethan Bernstein and Umesh Vazirani Implementation

Implementation of Quantum Fourier Transform

Estimating Arbitrary Phases

Improving success probability when estimating phases

The Order‐Finding Problem

DESIGN EXAMPLE^{1)}: How quantum parallelism and interference work

DESIGN EXAMPLE^{2)}: Grover’s algorithm

DESIGN EXAMPLE^{3)}: Simon’s

DESIGN EXAMPLE^{4)} : Shor’s Algorithm

**Tuesday****3. POST‐QUANTUM CRYPTOGRAPHY**

3.1 Overview of Post-Quantum Cryptosystems

3.2 Rainbow

3.3 NTRU N-th degree Truncated polynomial Ring Units

3.4 LWE Cryptosystem

3.5 BLISS (Bimodal Lattice Signature Scheme (BLISS)

3.6 Variants of Merkle Signature Scheme

3.7 Lamport Signature

3.8 McEllice Cryptosystem: Code-based cryptography

3.9 Niederreiter Cryptosystem

Ex. 3.1 Key Generation for a SIS‐Based Scheme

**4. QUANTUM CRYPTOGRAPHY**

4.1 Discrete Variable Protocols

4.2 Device‐Independent QKD

4.3 Continuous‐Variable QKD

4.4 Theoretical Models of Security

4.5 Limits of Point‐to‐Point QKD

4.6 QKD Against a Bounded Quantum Memory

Ex : Formulas for Gaussian states

**Wednesday****5. QKD OVER SUBOPTICAL BANDS**

Fundamentals of CVQKD

Security of CVQKD protocols

Composable security proof for cv QKD

Multicarrier Quadrature Division Modulation QKD over THz Band

TERAHERTZ QKD: System Model

Secret Key Rates

The total von Neumann entropy

System performance in the Extended Terahertz range

**6. QUANTUM NETWORK PROTOCOLS**

Summary of the analytical tools

Quantum states

Fidelity

Separable and entangled states

Quantum measurements

Quantum channel

LOCC channels

Quantum Link Layer Protocol

Entanglement swapping protocol

GHZ entanglement swapping protocol

Graph state distribution protocol

Entanglement distillation

Reinforcement Learning-based quantum decision processes

Quantum Networks

Tensor network

Reduced/marginal states of the overall quantum state of the network

Practical network architecture

Elementary link generation

Quantum memories

Examples of transmission channels that are relevant in practice

Imperfections

Ideal quantum state