Exploring Quantum-Resistant Encryption

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UniAPT's focus on quantum-resilient encryption stems from the need to prepare for the advent of quantum computing, which poses a significant threat to conventional cryptographic algorithms. Our project incorporates research and implementation of cryptographic methods that are believed to be resistant to quantum computing attacks.

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Key Aspects of Quantum-Resilient Encryption

Post-Quantum Cryptography (PQC) Algorithms

Focusing on cryptographic algorithms that are considered secure against quantum computer attacks.

Lattice-Based Cryptography

One of the leading candidates for PQC, due to its complexity and resistance to quantum attacks.

Hash-Based Cryptography

Another PQC method, leveraging the security of hash functions, which are currently not susceptible to quantum attacks.

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Implementation Strategy

Algorithm Selection

Evaluating and selecting suitable quantum-resistant algorithms based on security and performance.

Integration

Implementing these algorithms into our existing security infrastructure.

Testing and Validation

Rigorous testing to ensure the resilience of these algorithms against quantum attacks.

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Quantum-Resilient Encryption Implementation Table

Encryption Type	Description	Implementation Challenges	Use Case in UniAPT Project
Lattice-Based	Based on the hardness of lattice problems.	Requires higher computational resources.	Protecting sensitive user data.
Hash-Based	Utilizes secure hash functions.	Larger key sizes needed.	Securing transaction data.
Code-Based	Based on error-correcting codes.	Complexity in implementation.	Internal data encryption.

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Core Problem (Shortest Vector Problem - SVP)

• Definition: Given a lattice $L$, defined as a set of points in $�n$-dimensional space with a basis $B={b 1 ​ ,b 2 ​ ,...,b n ​ },$, the SVP is to find the shortest non-zero vector in $�L$.
• Mathematical Representation:

  • A lattice point $�v$ can be represented as $v=∑ i=1 n ​ x i ​ b i$ where $x i ​$ are integers.
  • The Euclidean norm (length) of a vector $v$ is $∣∣v∣∣= ∑v i 2 ​ ​ .$.
  • The SVP is to minimize $∣∣v∣∣$ for $v≠0v=0$.
• Quantum Resistance: The complexity of solving SVP scales exponentially with lattice dimension, making it infeasible for quantum computers.

Security of Hash Functions

• Definition: A hash function $�H$ maps data of arbitrary size to data of fixed size. Properties of a secure hash function include preimage resistance, second preimage resistance, and collision resistance.
• Mathematical Representation:

  • Given a hash function $H$, finding a message $m$ such that $H(m)=h$ for a given hash output $h$ should be computationally infeasible (preimage resistance).
  • For any given message $m 1$, it should be hard to find a different message $m 2 ​$ such that $H(m 1 ​ )=H(m 2 ​ )$ (second preimage resistance).
  • It should be hard to find any two distinct messages $m 1$ and $m 2$ such that $H(m 1 ​ )=H(m 2 ​ )$ (collision resistance).
• Quantum Resistance: Hash functions are considered quantum-resistant because finding a collision requires a brute-force search, which, even with a quantum computer, would only be quadratically faster than classical computers.

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Mathematical Background

• Lattice-Based Cryptography: The security of lattice-based systems often relies on the hardness of the Shortest Vector Problem (SVP) or the Closest Vector Problem (CVP).

  • SVP Calculation: Given a lattice $L$, find the shortest non-zero vector in $L$. The difficulty increases with the lattice dimension, making it quantum-resistant.
• Hash-Based Cryptography: Uses cryptographic hash functions to create one-time signatures.

  • Security Parameter Example: A hash function with output length $n$ bits offers $2n$ possible output values, creating a large enough space to resist quantum attacks.

The diagram above represents the Quantum-Resilient Encryption Workflow in UniAPT’s project. It visually outlines the sequential stages of how data is processed using quantum-resilient encryption methods. The workflow can be described as follows:

1. Data Input: The initial stage where raw or plaintext data is received as input.

2. Lattice-Based Encryption: In this stage, the data undergoes encryption using lattice-based cryptographic methods. This step ensures that the data is secured against potential quantum computing threats by leveraging the hardness of lattice problems.

3. Hash-Based Encryption: Following lattice-based encryption, the data is further processed with hash-based cryptographic methods, adding an additional layer of security and ensuring the integrity of the data.

4. Encrypted Data Storage: Once encrypted, the data is stored securely. This storage is designed to be safe from both conventional and quantum decryption attempts.

5. Data Use/Transmission: The encrypted data is either used within the system or transmitted to its intended destination. The encryption ensures that the data remains secure during transmission or usage.

6. Decryption Process: At the receiving end or when the data needs to be used, it undergoes a decryption process. This step reverses the encryption using the corresponding decryption algorithms, ensuring that only authorized parties can access the original data.

7. Data Output: The final stage where the decrypted data is output for authorized use, completing the encryption-decryption cycle.

import matplotlib.pyplot as plt
import numpy as np

# Creating a diagram for Quantum-Resilient Encryption Workflow

# Define the stages of the encryption workflow
stages = ['Data Input', 'Lattice-Based\nEncryption', 'Hash-Based\nEncryption', 'Encrypted\nData Storage', 'Data Use/Transmission', 'Decryption\nProcess', 'Data Output']

# Define the connections between stages
connections = [1, 1, 1, 1, 1, 1, 1]  # Each stage is connected to the next

fig, ax = plt.subplots()

# Create horizontal bar graph
y_pos = np.arange(len(stages))
ax.barh(y_pos, connections, align='center')
ax.set_yticks(y_pos)
ax.set_yticklabels(stages)
ax.invert_yaxis()  # labels read top-to-bottom
ax.set_xlabel('Workflow Progression')
ax.set_title('Quantum-Resilient Encryption Workflow in UniAPT')

plt.show()

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This workflow demonstrates UniAPT's commitment to data security, particularly in preparing for the era of quantum computing, by implementing advanced quantum-resilient encryption techniques. ​​