Intro To Quantum Cryptology
An introduction to quantum cryptography, quantum key distribution (QKD), and the BB84 protocol, with a demonstration implemented in Go.
Introduction
Quantum cryptology combines quantum mechanics and mathematics to enable secure communication. This article will explain the Alice, Bob and Eve scenario commonly used to introduce quantum cryptography concepts.

1

Quantum Key Distribution (QKD)
We'll discuss how QKD works and implement an example using the Go programming language.

2

BB84 Protocol
We'll examine the BB84 protocol, one of the first and most well-known QKD protocols.

3

Golang Implementation
We chose Go for its strong mathematical foundation, type system, and readable syntax.
Key Terms and Concepts
Alice and Bob Scenario
A common example used to explain cryptographic concepts, where Bob sends Alice a secret message in a locked box.
Cryptography
The practice of securing communication from unauthorized access through encryption.
QKD
Quantum Key Distribution - a cryptographic algorithm using quantum mechanics to ensure key security.
Qubit
The quantum equivalent of a classical bit, able to exist in superposition of states.
Quantum Gates and States
Quantum Gates
Quantum equivalents of classical logic gates, represented by matrices. Examples include the Hadamard gate and CNOT gate.
Wave Functions
Mathematical descriptions of quantum states, used to describe properties like position and momentum of particles.
Superposition
The ability of a quantum system to exist in multiple states simultaneously until measured.
Quantum Computer Science and Cryptology
As cyber threats evolve, quantum cryptography offers new ways to secure communication. While not yet widely implemented, understanding QKD principles prepares us for future developments.

1

Classical Cryptography
Traditional methods like RSA encryption

2

Quantum Cryptography Research
Development of protocols like BB84

3

Current State
Experimental implementations and simulations

4

Future
Potential widespread adoption of quantum-safe cryptography
The BB84 Protocol
BB84, proposed by Bennett and Brassard in 1984, is a seminal QKD protocol. It allows two parties to generate a shared secret key using quantum properties of photons.
1
Qubit Preparation
Alice prepares qubits in random polarization states
2
Transmission
Qubits sent over quantum channel to Bob
3
Measurement
Bob measures qubits in random bases
4
Key Sifting
Alice and Bob compare measurement bases to determine shared key
Mathematical Foundations of BB84
The BB84 protocol relies on principles of quantum mechanics, particularly the use of non-orthogonal quantum states.
Hadamard Basis
Uses |+⟩ and |-⟩ states, superpositions of |0⟩ and |1⟩
Measurement
Measuring in the wrong basis gives a random result
No-Cloning Theorem
Prevents eavesdroppers from copying unknown quantum states
Implementing BB84 in Go
We'll create a simplified simulation of the BB84 protocol using Go. This demonstrates the key concepts without requiring actual quantum hardware.

1

Define Structures
Create QuantumBit and QuantumResult structs to represent qubits and protocol results

2

Implement Measurement
Simulate quantum measurement with classical randomness

3

Alice and Bob Functions
Create functions to simulate qubit preparation and measurement

4

Key Sifting
Compare measurement bases and extract the shared key
Go Code: Structures and Constants
package main

import (
    "fmt"
    "math/rand"
    "time"
)

const (
    BIT_0 = iota
    BIT_1 = iota
)

type QuantumBit struct {
    Polarization int
    ValueOfBit   int
}

type QuantumResult struct {
    AliceBitCounts []int
    AliceBaseCount []int
    BobBItCount    []int
    BobBaseCount   []int
    SharedBits     []int
}
Go Code: Variables and Initialization
var (
    QBIT        QuantumBit
    QRES        QuantumResult
    Qubit       = make([]*QuantumBit, 16)
    SharedQubit = make([]int, 0)
    Alices_Bits = make([]int, 16)
    Alices_Bases = make([]int, 16)
    Bobs_Bits   = make([]int, 16)
    Bobs_Bases  = make([]int, 16)
)

func init() {
    rand.Seed(time.Now().UnixNano())
}
Go Code: Quantum Measurement Simulation
func (Qubit *QuantumBit) Step_3_MeasurePolarization(pol int) int {
    if pol == Qubit.Polarization {
        return Qubit.ValueOfBit
    } else {
        return rand.Intn(2)
    }
}
This function simulates quantum measurement. If the measurement basis matches the qubit's polarization, it returns the qubit's value. Otherwise, it returns a random result.
Go Code: Alice's Setup Function
func Setup_Call_Alice() {
    for i := 0; i < 16; i++ {
        polarization := rand.Intn(2)
        value := rand.Intn(2)
        Qubit[i] = &QuantumBit{
            polarization,
            value,
        }
    }
    
    for idx, qubit := range Qubit {
        basis := rand.Intn(2)
        Alices_Bases[idx] = basis
        Alices_Bits[idx] = qubit.Step_3_MeasurePolarization(basis)
    }
    
    QRES.AliceBaseCount = Alices_Bases
    QRES.AliceBitCounts = Alices_Bits
}
Go Code: Bob's Setup Function
func Setup_Call_Bob() {
    for idx, qubit := range Qubit {
        basis := rand.Intn(2)
        Bobs_Bases[idx] = basis
        Bobs_Bits[idx] = qubit.Step_3_MeasurePolarization(basis)
    }
    
    QRES.BobBItCount = Bobs_Bits
    QRES.BobBaseCount = Bobs_Bases
}
Go Code: Key Sifting
func FinalCallCheckAndVerifyBits() {
    for i := 0; i < 16; i++ {
        if Alices_Bases[i] == Bobs_Bases[i] {
            fmt.Println("[+]-[QSTAT]-[+] => Found equal bit...")
            SharedQubit = append(SharedQubit, Alices_Bits[i])
        }
    }
    QRES.SharedBits = SharedQubit
}
Go Code: Main Function
func main() {
    Setup_Call_Alice()
    Setup_Call_Bob()
    FinalCallCheckAndVerifyBits()
    fmt.Println("Alice's bits:", QRES.AliceBitCounts)
    fmt.Println("Alice's bases:", QRES.AliceBaseCount)
    fmt.Println("Bob's bits:", QRES.BobBItCount)
    fmt.Println("Bob's bases:", QRES.BobBaseCount)
    fmt.Println("Shared bits:", QRES.SharedBits)
}
Running the BB84 Simulation
When you run this Go program, you'll see output similar to:
[+]-[QSTAT]-[+] => Found equal bit...
[+]-[QSTAT]-[+] => Found equal bit...
[+]-[QSTAT]-[+] => Found equal bit...
Alice's bits: [0 0 0 0 0 0 0 1 1 0 0 0 0 1 1 0]
Alice's bases: [0 0 1 0 1 1 0 0 0 1 1 1 0 1 1 0]
Bob's bits: [1 1 0 0 0 1 0 1 1 1 1 1 1 1 0 1]
Bob's bases: [1 0 1 0 1 0 0 1 0 0 0 1 1 0 1 0]
Shared bits: [0 0 0]
Interpreting the Results
Equal Bits Found
The "[+]-[QSTAT]-[+] => Found equal bit..." messages indicate when Alice and Bob used the same measurement basis.
Bits and Bases
The output shows the random bits and bases generated for Alice and Bob.
Shared Key
The "Shared bits" are the secret key Alice and Bob have successfully generated.
Limitations of the Simulation
While this Go implementation demonstrates the basic principles of BB84, it has some key limitations:

1

Classical Randomness
Uses classical random number generation instead of true quantum randomness

2

No Quantum Superposition
Doesn't truly represent quantum states in superposition

3

Simplified Measurement
Doesn't capture the full complexity of quantum measurement

4

No Eavesdropper Detection
Doesn't implement methods to detect potential eavesdroppers
Advantages of Quantum Key Distribution
Unconditional Security
Based on laws of physics, not computational complexity
Eavesdropper Detection
Any interception attempt can be detected
Forward Secrecy
New keys generated for each communication session
Challenges in Implementing QKD
Distance Limitations
Quantum states degrade over long distances, limiting range
Specialized Hardware
Requires quantum devices, not compatible with classical networks
Cost
Current QKD systems are expensive to implement and maintain
Speed
Key generation rates are typically slower than classical methods
Other QKD Protocols

1

E91 (Ekert91)
Uses entangled particle pairs, proposed by Artur Ekert in 1991

2

B92
Simplified version of BB84, uses only two quantum states

3

SARG04
Designed to be more efficient and practical than BB84

4

Continuous-Variable QKD
Uses quantum states with continuous spectra, like coherent states
Quantum Cryptography in the Real World
While still largely experimental, QKD has seen some real-world implementations:
QKD Networks
Experimental networks have been set up in various countries to test QKD over fiber optic networks.
Satellite QKD
China's Micius satellite has demonstrated intercontinental quantum key distribution.
Financial Sector
Some banks have tested QKD for securing financial transactions.
The Future of Quantum Cryptography

1

2

3

4

1

Quantum Internet
Global quantum communication networks

2

Post-Quantum Cryptography
Classical algorithms resistant to quantum attacks

3

Quantum-Safe Hybrid Systems
Combining quantum and classical methods

4

Current QKD Systems
Limited deployments and experiments
Quantum Computing Threats to Classical Cryptography
While quantum cryptography offers new security paradigms, quantum computers also pose threats to existing cryptographic systems.
Shor's Algorithm
Can efficiently factor large numbers, breaking RSA encryption
Grover's Algorithm
Provides quadratic speedup for searching unstructured databases
Symmetric Key Vulnerability
Grover's algorithm could weaken AES and other symmetric ciphers
Post-Quantum Cryptography
To address quantum computing threats, researchers are developing new classical algorithms believed to be resistant to quantum attacks.

1

Lattice-based Cryptography
Based on the hardness of certain lattice problems

2

Hash-based Signatures
Uses hash functions to create digital signatures

3

Code-based Cryptography
Relies on the difficulty of decoding certain error-correcting codes

4

Multivariate Cryptography
Based on the difficulty of solving systems of multivariate polynomial equations
Quantum Random Number Generation
Quantum processes can be used to generate truly random numbers, which are crucial for cryptography.
Benefits
  • True randomness based on quantum uncertainty
  • Impossible to predict or reproduce
  • Can generate high-quality keys for encryption
Methods
  • Measuring quantum states of photons
  • Vacuum fluctuations in optical systems
  • Radioactive decay processes
Quantum Entanglement in Cryptography
Entanglement is a quantum phenomenon where particles become correlated in such a way that the quantum state of each particle cannot be described independently.
E91 Protocol
Uses entangled particle pairs to generate secure keys
Quantum Teleportation
Could enable secure transfer of quantum states
Entanglement Swapping
Allows extension of quantum networks
Quantum Key Distribution in Space
Extending QKD to satellite-based systems could enable global quantum-secure networks.

1

2016
China launches Micius, the first quantum communication satellite

2

2017
First satellite-to-ground quantum key distribution demonstrated

3

2018
Intercontinental video call secured by satellite QKD

4

Future
Planned global quantum communication networks
Quantum Cryptography Standards
As quantum cryptography matures, standards are being developed to ensure interoperability and security.

1

ETSI
European Telecommunications Standards Institute is working on QKD standards

2

ISO/IEC
Developing standards for quantum technologies, including cryptography

3

NIST
U.S. National Institute of Standards and Technology is evaluating post-quantum cryptography algorithms
Quantum Cryptography Research Centers
Ethical Considerations in Quantum Cryptography
Privacy Implications
Quantum-secure communication could enhance privacy but also enable unbreakable encryption for malicious actors
National Security
Quantum cryptography could impact intelligence gathering and cyber warfare capabilities
Digital Divide
Access to quantum technologies may create new inequalities in cybersecurity
Dual-Use Concerns
Quantum cryptography research could have both civilian and military applications
Learning Quantum Cryptography
For those interested in diving deeper into quantum cryptography, here are some resources:

1

Online Courses
Platforms like Coursera and edX offer introductory quantum computing and cryptography courses

2

Textbooks
"Quantum Cryptography" by Sergienko and "Introduction to Quantum Cryptography" by Katz are good starting points

3

Research Papers
Follow publications in journals like Physical Review A and Quantum Information & Computation

4

Quantum Programming
Learn quantum circuit design with tools like Qiskit, Cirq, or Q#
Quantum Cryptography Companies
ID Quantique
Swiss company offering commercial QKD systems and quantum random number generators
Quintessence Labs
Australian firm developing quantum key and random number generation technologies
MagiQ Technologies
US-based company working on quantum-enhanced security solutions
Conclusion
Quantum cryptography represents a paradigm shift in secure communication, leveraging the principles of quantum mechanics to achieve unprecedented levels of security. While challenges remain in its practical implementation, ongoing research and development are bringing quantum cryptographic systems closer to widespread adoption.

1

Current State
Experimental systems and limited deployments demonstrate the potential of quantum cryptography

2

Challenges
Distance limitations, cost, and integration with existing infrastructure remain hurdles

3

Future Prospects
Continued advances may lead to quantum-secured global communication networks
Further Reading
Academic Papers
"Quantum Cryptography: Public Key Distribution and Coin Tossing" by Bennett and Brassard (1984)
Books
"Quantum Cryptography and Secret-Key Distillation" by Gilles Van Assche
Online Resources
NIST Post-Quantum Cryptography Standardization
Research Groups
Centre for Quantum Technologies (CQT) in Singapore