➿Quantum Computing Unit 11 – Quantum Cryptography

Quantum Basics Refresher

• Quantum mechanics describes the behavior of matter and energy at the atomic and subatomic scales
• Quantum states can exist in superposition, a combination of multiple states simultaneously until measured (Schrödinger's cat)
• Quantum entanglement occurs when two or more particles are correlated in such a way that measuring one instantly affects the others, regardless of distance
  • Entangled particles exhibit perfect correlations that cannot be explained by classical physics
  • Entanglement is a key resource in quantum cryptography and quantum computing
• Quantum bits, or qubits, are the fundamental unit of quantum information
  • Unlike classical bits, qubits can exist in a superposition of 0 and 1 states
• Quantum operations are performed using quantum gates, which manipulate qubits (Hadamard gate, CNOT gate)
• The no-cloning theorem states that an unknown quantum state cannot be perfectly copied, a crucial property for secure communication
• Quantum measurements collapse the quantum state, forcing it to take on a definite value (measuring the spin of an electron)

Classical vs. Quantum Cryptography

• Classical cryptography relies on computational complexity, assuming certain mathematical problems are hard to solve (factoring large numbers)
  • Classical encryption algorithms include RSA, AES, and DES
  • These algorithms are vulnerable to attacks by quantum computers using Shor's algorithm
• Quantum cryptography leverages the principles of quantum mechanics to ensure secure communication
  • Quantum cryptography is based on the inherent randomness and unclonability of quantum states
  • Quantum key distribution (QKD) allows for the secure exchange of encryption keys
• Quantum cryptography detects eavesdropping attempts, as measuring a quantum state disturbs it (intercepting photons in a QKD protocol)
• Quantum cryptography provides unconditional security, meaning it is secure against any attack allowed by the laws of physics
  • Classical cryptography offers computational security, which depends on the difficulty of solving mathematical problems
• Quantum cryptography is a symmetric key cryptosystem, where the same key is used for encryption and decryption
• Quantum cryptography complements classical cryptography, providing a secure means to distribute keys for classical encryption algorithms

Key Quantum Cryptography Protocols

• BB84 (Bennett-Brassard 1984) is the first and most widely used QKD protocol
  • Uses four quantum states (two bases) to encode information in photons
  • Sender and receiver randomly choose bases, discarding mismatched measurements to generate a shared key
• E91 (Ekert 1991) protocol uses entangled pairs of photons for QKD
  • Measures the violation of Bell's inequality to detect eavesdropping
  • Provides device-independent security, not relying on trusted hardware
• B92 (Bennett 1992) is a simplified version of BB84, using only two quantum states
  • Less efficient than BB84 but easier to implement experimentally
• SARG04 (Scarani-Acín-Ribordy-Gisin 2004) is a variant of BB84 resistant to photon number splitting attacks
  • Uses a different classical post-processing scheme to extract the key
• Decoy state protocols improve the security of QKD against photon number splitting and other attacks
  • Introduces decoy states with varying photon numbers to detect eavesdropping
• Continuous-variable QKD protocols encode information in the quadratures of light (amplitude and phase)
  • Enables higher key rates and compatibility with existing telecommunications infrastructure
• Measurement-device-independent (MDI) QKD protocols remove the need for trusted measurement devices
  • Performs Bell state measurements on photons from the sender and receiver to generate a key

Quantum Key Distribution (QKD)

• QKD is a method for securely distributing encryption keys using quantum communication channels
  • Enables two parties to produce a shared random secret key known only to them
  • The key can then be used to encrypt and decrypt messages using classical encryption algorithms (one-time pad)
• QKD relies on the quantum properties of photons, such as polarization or phase, to encode information
  • Photons are sent through a quantum channel (optical fiber or free space) from the sender to the receiver
• The security of QKD is based on the no-cloning theorem and the uncertainty principle
  • An eavesdropper cannot intercept and perfectly clone the photons without disturbing their quantum state
  • Measuring the photons in the wrong basis introduces detectable errors
• QKD consists of two main stages: quantum communication and classical post-processing
  • Quantum communication involves the transmission and measurement of quantum states
  • Classical post-processing includes sifting, error correction, and privacy amplification to extract a secure key
• QKD has been demonstrated over distances up to hundreds of kilometers using optical fibers and free-space links (satellite-based QKD)
• Challenges in QKD include the need for efficient single-photon sources and detectors, and the management of quantum channel imperfections (noise, loss)
• QKD networks have been established in various countries, enabling secure communication between multiple parties (DARPA Quantum Network, SECOQC Vienna)

Quantum Entanglement in Cryptography

• Quantum entanglement is a key resource in various quantum cryptographic protocols
  • Entangled particles exhibit strong correlations that can be used to detect eavesdropping and ensure security
• The E91 protocol uses entangled pairs of photons for QKD
  • The sender and receiver perform measurements on their respective photons, choosing between three bases
  • The correlation between their measurements allows them to generate a shared key and detect any eavesdropping attempts
• Entanglement-based QKD provides device-independent security, not relying on the trustworthiness of the hardware
  • The security is based on the violation of Bell's inequality, a test of quantum nonlocality
• Quantum secret sharing protocols use multipartite entanglement to distribute a secret among multiple parties
  • The secret can only be reconstructed when a sufficient number of parties cooperate (threshold scheme)
• Quantum secure direct communication (QSDC) uses entanglement to directly transmit messages without prior key distribution
  • The security is based on the detection of eavesdropping through the disturbance of entanglement
• Entanglement swapping allows for the establishment of entanglement between distant parties without direct interaction (quantum repeaters)
• Challenges in entanglement-based quantum cryptography include the generation, distribution, and maintenance of high-quality entangled states over long distances

Security Proofs and Vulnerabilities

• Security proofs are essential to establish the theoretical security of quantum cryptographic protocols
  • Proofs are based on the laws of quantum mechanics and information theory
  • They provide bounds on the amount of information an eavesdropper can obtain without being detected
• The security of QKD has been proven against general attacks, including collective and coherent attacks
  • Collective attacks allow the eavesdropper to perform measurements on individual qubits and store the results
  • Coherent attacks allow the eavesdropper to perform joint operations on multiple qubits and postpone measurements
• Security proofs take into account imperfections in the quantum devices and channels (noise, loss, side-channels)
  • Device-independent security proofs remove the need for trusted devices, relying only on the violation of Bell's inequality
• Quantum hacking refers to the exploitation of vulnerabilities in the practical implementation of quantum cryptographic systems
  • Side-channel attacks exploit information leakage from the physical devices (detector blinding, timing attacks)
  • Trojan horse attacks introduce malicious signals into the quantum channel to gain information about the key
• Countermeasures against quantum hacking include the use of decoy states, measurement-device-independent protocols, and secure device designs
• Post-quantum cryptography aims to develop classical cryptographic algorithms that are secure against attacks by quantum computers
  • Examples include lattice-based cryptography, code-based cryptography, and multivariate cryptography

Real-World Applications and Challenges

• Quantum cryptography has been implemented in various real-world scenarios, including government, military, and commercial applications
  • ID Quantique and MagiQ Technologies offer commercial QKD systems for secure communication
  • Quantum cryptography has been used to secure elections, financial transactions, and critical infrastructure (power grids, water supply)
• Quantum cryptography can be integrated with existing classical cryptographic infrastructure
  • QKD can be used to distribute keys for classical encryption algorithms like AES
  • Post-quantum cryptography can be used to secure long-term data against future quantum attacks
• Challenges in the practical implementation of quantum cryptography include:
  • Scaling up quantum networks to cover larger distances and more users
  • Improving the efficiency and reliability of quantum devices (single-photon sources, detectors)
  • Integrating quantum and classical networks seamlessly
  • Standardization and certification of quantum cryptographic products
• Satellite-based QKD has been demonstrated as a means to establish global quantum communication networks
  • Micius satellite (China) has performed intercontinental QKD and entanglement distribution
• Quantum repeaters are being developed to extend the range of quantum communication networks
  • Quantum repeaters use entanglement swapping and quantum memory to relay quantum states over long distances without loss of fidelity

Future Directions in Quantum Cryptography

• Quantum internet is a vision for a global network of quantum devices, enabling secure communication and distributed quantum computing
  • Quantum internet would integrate quantum cryptography, quantum sensing, and quantum computing
  • Challenges include the development of quantum repeaters, quantum memories, and quantum error correction
• Quantum random number generation (QRNG) is an important primitive for various cryptographic applications
  • QRNG exploits the inherent randomness of quantum processes to generate true random numbers
  • QRNG can be used for key generation, authentication, and secure multi-party computation
• Quantum digital signatures provide secure authentication and non-repudiation in quantum communication
  • Quantum digital signatures use quantum one-way functions and quantum key distribution to sign and verify messages
• Quantum fingerprinting allows for the comparison of large datasets with minimal communication
  • Quantum fingerprints are exponentially smaller than classical fingerprints, enabling efficient equality testing
• Quantum-secured blockchain combines quantum cryptography with blockchain technology for enhanced security and privacy
  • Quantum key distribution can be used to secure the communication between blockchain nodes
  • Post-quantum cryptography can be used to secure the blockchain against future quantum attacks
• Quantum homomorphic encryption enables computation on encrypted data without revealing the underlying information
  • Quantum homomorphic encryption schemes are based on quantum error-correcting codes and quantum secret sharing
• Quantum-secure authentication protocols use quantum states to authenticate users and devices
  • Quantum-secure authentication can be based on quantum key distribution, quantum digital signatures, or quantum physical unclonable functions (PUFs)