Cryptography presentation graduate level

Applications of Neural
Network-Based AI in
Cryptography
Authors: Abderrahmane Nitaj, Tajjeeddine Rachidi
Source: Cryptography, 2023, Volume 7, Article 39
Published: 11 August 2023

Introduction to AI and Cryptography
Artificial Intelligence (AI): A modern technology that
mimics human intelligence in tasks like prediction,
classification, and automation.
Cryptography: A critical field ensuring secure
communication by protecting data against adversaries. The
importance of AI in Cryptography is:
• Enhances the security of cryptographic protocols.
• Detects vulnerabilities in cryptosystems.
• Improves efficiency in encryption and decryption.
Core Objective of the Study: Exploring the applications of
neural networks in advancing cryptographic algorithms. Figure 1. A multi-layer perceptron forming a 4-layer
neural net with 3 input units, 5 units in the first hidden layer,
4 units in the second hidden layer, and 2 output units.

Why AI is Crucial for Cryptography
Artificial Intelligence enhances cryptographic systems
by improving security, identifying vulnerabilities, and optimizing
operations. Its applications provide faster encryption and better
resistance against advanced cyber threats, crucial for modern
digital systems. The key benefits of AI in cryptography are:
• Strengthens data security in communication and storage.
• Accelerates key generation and encryption processes.
• Adapts to evolving cyber threats and vulnerabilities.
AI is essential for enabling secure online transactions,
protecting communication networks, and advancing blockchain
technology.
Figure 2. Basic unit of artificial neural networks: the
perceptron.

Symmetric vs. Asymmetric Cryptography
Cryptography is the foundation of secure
communication, enabling data protection and privacy. It is
categorized into two main types:
1. Symmetric Cryptography:
• Uses the same key for both encryption and
decryption.
• Example: Advanced Encryption Standard (AES).
• Applications: Securing communication channels and
sensitive data.
2. Asymmetric Cryptography:
• Utilizes a pair of keys: public for encryption and
private for decryption.
• Example: Rivest-Shamir-Adleman (RSA).
• Applications: Digital signatures and secure key
exchange.
Figure 3. Working of Symmetric and Asymmetric Cryptography

Key Differences
Feature Symmetric Cryptography Asymmetric Cryptography
Key Type Single shared key Public and private key pair
Key Distribution Requires secure channel Public key can be distributed openly
Encryption/Decryption Speed Faster Slower
Key Management
More complex, as the same key is used for both
encryption and decryption
Simpler, as different keys are used for encryption
and decryption
Digital Signatures Not directly supported Directly supported
Common Use Cases Data confidentiality, file encryption
Secure communication, digital signatures, public key
infrastructure (PKI)
Examples AES, DES, 3DES RSA, DSA, ECC

Neural Networks in Cryptanalysis
Neural networks bring a transformative approach to
cryptography, particularly in analyzing and enhancing the security of
encryption systems. The applications in cryptanalysis are:
Modeling S-Box Nonlinearities:
Nonlinear transformations where M and c are matrix and
constant parameters, respectively.
Neural networks can approximate cryptographic transformations, and it
can optimize their resistance to attacks.
Cryptographic Attacks Using Neural Networks:
Known-plaintext attack: Reconstruct the key K using observed
ciphertext C and plaintext P.
Differential cryptanalysis: Predict the differential uniformity of S-boxes.
Figure 4. Learning the nonlinear line that
separates the green dots from the red dots
using 2 hidden layers with 20 neurons each.

Key Cryptographic Systems
There are four prominent cryptographic systems (AES, RSA, LWE, and Ascon) , each addressing
specific needs for data security and encryption.
Advanced Encryption Standard (AES): It is a symmetric block cipher with 128-bit block size and variable
key lengths. It is widely used for securing sensitive data in real-time applications.
Rivest–Shamir–Adleman (RSA): It is an asymmetric encryption system relying on prime factorization. It is
Used for secure key exchange and digital signatures.
Learning With Errors (LWE): It is a lattice-based cryptographic system resistant to quantum attacks. It is
foundation for post-quantum cryptography standards.
Ascon Cipher: It is a lightweight cryptographic system for resource-constrained devices. It ensures
authenticated encryption and hashing with 128-bit security.

The Advanced Encryption
Standard (AES)
AES is a symmetric block cipher that relies on mathematical
transformations to secure data that performs encryption in rounds with distinct
mathematical operations. Block size of AES is 128 bits, and the key lengths
are 128, 192, or 256 bits. There are 10 rounds for 128-bit keys, 12 rounds for
192-bit keys, and 14 rounds for 256-bit keys.
Key Equation (Encryption Process):
1. AddRoundKey: Where S is the current state, and K is
the round key.
2. SubBytes: Nonlinear byte substitution using an S-box.
3. ShiftRows: Row-wise circular shifts for diffusion.
4. MixColumns: Matrix multiplication for enhancing diffusion.
Table 1: AddRoundKey operation Xors state with key.

AES Encryption and
Decryption
AES encryption involves a series of well-defined transformations across multiple
rounds. The decryption process reverses these transformations.
Encryption Steps:
1. Initial Round:
(Plaintext XORed with initial key).
2. Main Rounds:
• SubBytes: Byte substitution with S-box transformation.
• ShiftRows: Circular shifts for diffusion.
• MixColumns: Matrix multiplication for data diffusion: S′=M⋅S
• AddRoundKey: XORing state with round key.
3. Final Round: Includes all operations except MixColumns.
Decryption Steps:
Inverse Operations:
1. Inverse SubBytes, ShiftRows, and MixColumns.
2. AddRoundKey applied in reverse order.
Table 2: MixColumns operation yielding a new state.

Applications of AI in AES Security
Artificial intelligence enhances the security and analysis of AES by automating vulnerability detection and
improving cryptographic components. Here are the applications of AI:
1. Resistance Testing: AI models test S-box properties like nonlinearity and differential uniformity. Example: Using neural
networks to evaluate cryptographic strength against differential and linear attacks.
2. Side-Channel Attack Mitigation: AI analyzes power consumption and timing data to detect and mitigate vulnerabilities.
3. Fault Injection Analysis: Advanced ANNs simulate fault attacks to identify weaknesses in AES implementations.
4. Optimization of S-box Design: AI-generated S-boxes exhibit improved resistance to algebraic and statistical attacks.

RSA Cryptosystem
RSA is a cornerstone of asymmetric cryptography,
enabling secure key exchange and digital signatures.
Key Components:
• Public Key (N,e): N=p⋅q, where p and q are large primes.
• Private Key (d): Derived using e d 1 (mod
⋅ ≡ ϕ(N)).
Encryption:
Where M is the plaintext, and C is the ciphertext.
Decryption:
Applications: Secure communications (e.g., HTTPS), Digital signatures
for authenticity and integrity, and Key exchange in hybrid encryption
systems.
Figure 5: Algorithms to factor an integer n with running times.

RSA Key Generation and Encryption
RSA relies on mathematical principles for generating secure keys
and encrypting data.
Key Generation Steps:
1.Select two large prime numbers, p and q.
2.Compute N=p⋅q (modulus).
3. Calculate Euler's totient function: (
ϕ N)=(p−1)(q−1)
4. Choose a public exponent e, where 1 < e < (N) and
ϕ
gcd(e, (N))=1.
ϕ
5. Compute the private key d using:
e d≡1(mod (N))
⋅ ϕ

AI Applications in RSA Security
AI techniques significantly enhance the security and robustness of the RSA
cryptosystem by identifying vulnerabilities and optimizing performance.
Applications of AI in RSA:
1.Resistance to Side-Channel Attacks: AI models analyze timing and power consumption
data to detect potential leaks during decryption.
2.Fault Attack Mitigation: Neural networks simulate fault injection scenarios to identify
vulnerabilities in RSA implementations.
3.Prime Selection Optimization: AI ensures the selection of secure prime numbers p and q to
resist factorization attacks.
4.Factorization Resistance Testing: Advanced AI algorithms analyze moduli N to test
resistance against known factorization methods.
5.Partial Key Recovery Testing: AI predicts private key dd from exposed bits, ensuring
robust key design.
Figure 6: Side-channel attack analysis

Learning with Errors (LWE)
LWE is a lattice-based cryptographic scheme resistant to quantum attacks, forming the basis for many post-quantum
cryptographic systems.
Key Concepts:
1.LWE Problem:
•Given a matrix A, vector b, and error e, find the secret vector ss such that: b=A⋅s+e(mod q)
•A: Public matrix, s: Secret vector, e: Small error vector.
2. Core Parameters: q: Prime modulus, (n,m): Dimensions of the matrix and vectors, and χ: Error distribution
(typically Gaussian).
Applications:
•Foundation for post-quantum encryption standards (e.g., CRYSTALS-Kyber).
•Used in homomorphic encryption and digital signatures.
Figure 7: Learning with errors

Lattice Problems and LWE
The security of LWE is grounded in the hardness of lattice-based computational problems, making it resistant to both
classical and quantum attacks.
Key Lattice Problems:
1.Shortest Vector Problem (SVP): Find the shortest non-zero vector v in a lattice L such that:
2. Closest Vector Problem (CVP): Given a vector t not in L, find the lattice vector v closest to t:
3. GapSVP: Approximation version of SVP with a factor γ.
Reduction from LWE to Lattice Problems:
•Solving LWE is as hard as solving lattice problems like GapSVP and SIVP in the worst case.
•The reduction relies on the error term e following a Gaussian distribution.
Figure 7: Lattice based cryptography

AI and LWE Security
Artificial Intelligence provides valuable tools to analyze and strengthen LWE-based cryptosystems by
testing their resistance against potential vulnerabilities.
Applications of AI in LWE:
1.Parameter Optimization: AI helps fine-tune parameters q,n,m,χ to ensure security while maintaining efficiency.
2.Hardness Testing: Advanced neural networks simulate GapSVP and CVP scenarios to validate the resilience of
LWE implementations.
3.Error Distribution Analysis: AI verifies the Gaussian distribution of the error vector e, crucial for LWE’s
security.
4.Key Recovery Testing: AI evaluates the feasibility of recovering the secret vector ss under known-plaintext
attacks.

The Ascon Cipher Family
Ascon is a lightweight cryptographic family designed for efficiency in resource-
constrained environments, ensuring authenticated encryption and hashing.
Key Features:
•Designed For: Internet of Things (IoT) and other low-power devices.
•Security Level: 128-bit.
•Core Components:
• Authenticated Encryption: Ascon-128 and Ascon-128a.
• Hashing: Ascon-Hash and Ascon-XOF (extendable output function).
State Representation: Operates on a 320-bit state divided into:
• Inner State (Sr
): Variable rate.
• Outer State (Sc
): Capacity component.
Figure 8: Ascon’s Authenticated
Encryption

Ascon Encryption Process
Ascon provides a lightweight solution for
authenticated encryption with integrity checks,
optimized for low-resource environments.
Steps in the Ascon Encryption Process:

Applications of AI in Ascon Security
AI plays a significant role in testing the resilience of the Ascon cipher against various attacks and
optimizing its cryptographic operations.
Applications of AI:
1. Resistance to Side-Channel Attacks: Neural networks analyze power consumption, electromagnetic radiation,
and timing variations to detect vulnerabilities in Ascon implementations.
2.Fault Injection Testing: AI simulates fault attacks to evaluate how Ascon responds to errors or disruptions in the
encryption process.
3. S-box and Permutation Optimization: AI models test and optimize the S-box and permutation layers used in
Ascon for better resistance against cryptanalysis.
4.Key Generation and Attack Resistance: AI helps generate more secure keys and analyze the cipher’s resistance
to brute force and cryptanalysis attacks.

Machine Learning Techniques in
Cryptography
Machine learning (ML) techniques, particularly neural networks, are
increasingly used to improve cryptographic algorithms, identify weaknesses,
and strengthen security.
Key Machine Learning Techniques:
1.
Supervised Learning: Training models on known data (e.g., plaintext and
ciphertext pairs) to predict key generation or detect vulnerabilities.
2.
Unsupervised Learning: Identifying hidden patterns or anomalies in
cryptographic systems without labeled training data.
3.
Reinforcement Learning: Optimizing cryptographic parameters and designs
through iterative testing, where AI receives feedback from its success or
failure.
4.
Deep Learning: Using deep neural networks to approximate complex
cryptographic functions and improve resistance to attacks like differential and
linear cryptanalysis.
Figure 9: Feedforward Neural Network (FFNN)

Key Challenges and Future Prospects

Comparative Table of Cryptographic Systems

Conclusion
1.AI in Cryptography:
AI offers advanced techniques for automating cryptanalysis and
optimizing cryptographic operations.
AI's applications range from enhancing S-box design in AES to testing
the resilience of RSA and LWE systems against various attacks.
2.Quantum Resistance:
With the advent of quantum computing, lattice-based schemes like LWE
are positioned as foundational to future cryptography. AI plays a crucial
role in testing and optimizing these post-quantum systems.
3.Future Prospects:
The future of cryptography will involve deep integration of AI,
particularly in optimizing lightweight cryptographic solutions like
Ascon and in making cryptographic systems more efficient and secure
against quantum threats.
Figure 10: Hybrid Cryptographic Management for secure data

Cryptography presentation graduate level

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