Day-22 Quantum Cryptography #Quantum30

Introduction

Quantum Cryptography is all about the keeping information secure from all types of adversaries using the effects of the quantum mechanics.

Let’s say we want to buy something online then for payment we may use the Credit/Debit Card Information or even UPI which uses the today’s practically possible existing cryptographic mechanism like public key crypto-systems.

These systems can’t be decrypted even if we have algorithm as well as ecryption text via classical computer. But as soon as quantum computers are developed these system no longer remains secure because they can be easly decrypted using quantum algorithms like shor’s algorithm, grover algorithm, quantum middle man attack etc.

Thus, these will be losts of fraud and loss of sensitive information means our today’s existing security system will totally be compromised by the adversaries.

What is a Public Key Cryptography ?

As we already studied upto 2 week all about the classical cryptography, public key cryptography is just the subfield.

What are the risks posed by Quantum Computer ?

Theoretically we have developed the algorithms that can break today’s existing approx all security mechanism but practically when we execute on classical computer, it take more and more time that expected but as soon as we developed the quantum computer it can easly execute those algorithm which lead to broke today’s existing all security mechanism.

Example : Shor’s Algorithm is used to factor any large Integer number into it’s prime factors thus we know that RSA, Diffie-Hellmann Key exchange, Elgmal etc. uses the prime factorization, discrete log problem, elliptic curves for encryption can be easly broken.

What is Quantum cryptography ?

Quantum cryptography is a science that applies quantum mechanics principles to data encryption and data transmission so that data cannot be accessed by hackers — even by those malicious actors that have quantum computing of their own. The broader application of quantum cryptography also includes the creation and execution of various cryptographic tasks using the unique capabilities and power of quantum computers. Theoretically, this type of computer can aid the development of new, stronger, more efficient encryption systems that are impossible using existing, traditional computing and communication architectures.

• While many areas of this science are conceptual rather than a reality today, several important applications where encryption systems intersect with quantum computing are essential to the immediate future of cybersecurity. Two popular, yet distinctly different cryptographic applications that are under development using quantum properties include:
• Quantum-safe cryptography: The development of cryptographic algorithms, also known as post-quantum cryptography, that are secure against an attack by a quantum computer and used in generating quantum-safe certificates.
• Quantum key distribution: The process of using quantum communication to establish a shared key between two trusted parties so that an untrusted eavesdropper cannot learn anything about that key.

How does Quantum Cryptography work?

Quantum Cryptography works on the principle of quantum entanglement, which is a phenomenon where two particles are correlated in a way that the state of one particle affects the state of the other particle, even when they are separated by a large distance. In quantum cryptography, the two parties, Alice and Bob, use a pair of entangled particles to establish a secure communication channel.

The process involves the following steps:

1. Alice sends a stream of photons (particles of light) to Bob.
2. Bob randomly selects a subset of photons and measures their polarization (direction of oscillation).
3. Bob sends the result of his measurements to Alice through a classical communication channel.
4. Alice and Bob compare a subset of their measurements to detect any eavesdropping.
5. If no eavesdropping is detected, they use the remaining photons to encode their message.
6. The encoded message is then sent over a classical communication channel.

Why is Quantum Cryptography secure?

The security of Quantum Cryptography relies on the fundamental laws of quantum mechanics. Any attempt to intercept or measure the photons during the transmission would disturb their state, and the disturbance would be detected by Alice and Bob, alerting them to the presence of an eavesdropper. This is known as the “no-cloning theorem,” which states that it is impossible to create an exact copy of an unknown quantum state. Therefore, the security of the communication channel is guaranteed by the laws of physics, making it impossible to hack.

What is Post Quantum Cryptography ?

Post-quantum cryptography, also known as quantum encryption, is the development of cryptographic systems for classical computers that can prevent attacks launched by quantum computers.

What is Quantum Key Distribution ?

Quantum key distribution (QKD) enables secure key exchange between parties using the principles of quantum mechanics. Key protocols include:

1. BB84 Protocol: Sender (Alice) encodes bits as polarizations of photons, receiver (Bob) measures in random bases. After public discussion of bases, they discard mismatched bits to form a shared key.
2. E91 Protocol (Entanglement-based QKD): Alice sends entangled photon pairs to Bob. They measure the photons in different bases and publicly compare a subset to detect eavesdropping.
3. B92 Protocol: Similar to BB84, but Alice encodes bits using two non-orthogonal states. Bob’s measurements reveal bits with a certain probability, and discrepancies signal eavesdropping.

What is Quantum Encryption ?

Quantum encryption leverages the principles of quantum mechanics to create unbreakable codes. It employs quantum bits (qubits) to encode information, using the uncertainty principle to detect any eavesdropping attempts. When an eavesdropper interacts with qubits, it disturbs their states, alerting the sender and receiver to potential compromise. This makes any interception detectable and ensures secure communication. Quantum key distribution (QKD), like the BB84 protocol, forms the basis of quantum encryption, enabling the exchange of secret keys between parties. Quantum encryption’s robustness against traditional hacking methods makes it a promising solution for ultra-secure communication, critical for protecting sensitive data in various applications, from finance to government communications.

What is One way functions ?

These functions are easy to compute forward but when we try to compute backward way then it became hard

Example : Multiplication of two prime number and reverse is factorization of the large number into two prime.

What is Quantum One Time Pad ?

The one-time pad is a classical encryption technique that involves using a random key to encrypt a message. In the context of quantum cryptography, a similar concept can be applied using quantum bits (qubits) and quantum operations. Here’s a brief mathematical description of the quantum one-time pad:

Key Preparation:

• The sender and receiver share a set of entangled qubits (e.g., photon pairs) using a quantum channel.
• The qubits are in a state such as |00⟩ + |11⟩, which is an entangled Bell state.

Message Preparation:

• The sender wants to send a binary message, represented by a string of bits: m = m_1 m_2 ... m_n, where each mi is either 0 or 1.
• For each bit mi in the message, the sender applies a quantum operation (X gate) to the corresponding qubit if mi = 1. Otherwise, if mi = 0, no operation is applied.

Encryption:

• The sender’s qubits (entangled with the receiver’s) are now in the state that encodes the encrypted message.

Decryption:

• The receiver measures each of their qubits, obtaining a sequence of outcomes: c = c1 c2 ... c_n, where each ci is either 0 or 1.
• For each outcome ci, if ci = 1, the receiver applies a quantum operation (X gate) to their corresponding qubit. Otherwise, if ci = 0, no operation is applied.

Result:

• After the receiver performs the operations, they will obtain the original message bits: m = c.

Conclusion

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