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Computational Intelligence and its Applications explores cutting-edge advancements in machine learning, data science, and their practical applications. This comprehensive guide caters to college students, researchers, and professionals equipping readers with the knowledge to navigate and leverage the latest trends in computational intelligence effectively. Key Features: - Emerging Technologies: Covers post-quantum cryptography, secure communication, and advancements in chatbot technology. - Practical Applications: Includes stock price prediction, cloud computing, and data-driven DNA sequencing. - Security and Detection: Enhances intrusion detection and analyzes crop disease using machine learning. - Natural Language Processing: Explores sentiment analysis and the impact of big data on natural language processing. - Advanced Techniques: Discusses blockchain technology, remote sensing, and depression detection on social media. Readership: Ideal for academia and industry alike.

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Veröffentlichungsjahr: 2025

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Table of Contents
BENTHAM SCIENCE PUBLISHERS LTD.
End User License Agreement (for non-institutional, personal use)
Usage Rules:
Disclaimer:
Limitation of Liability:
General:
PREFACE
List of Contributors
Emerging Frontiers: Post-Quantum Cryptography and Secure Communication
Abstract
Introduction
Key Concepts: Fundamental Techniques and Cryptography Protocols
Techniques/Challenges in Post-Quantum Cryptography
Lattice-based Cryptography
Code-based Cryptography (CBC)
Multivariate Polynomial Cryptography (MPC)
Hash-based Cryptography
Advantages of Hash-Based Cryptography
Supersingular Isogeny-Based Cryptography
Challenges in Post Quantum Cryptography
The Goal of PQC
Power and Performance of Supercomputers
CONCLUSION
REFERENCES
Chatbot with Machine Learning: Latest Advancements
Abstract
Introduction
Literature Review
Methodology
Techniques
Approaches
Latest Advances
Benefits, Challenges and Applications
Benefits
Challenges
Applications
Conclusion
Future Scope and Recommendations
Recommendations
REFERENCES
Stock Price Prediction: A Gateway to a Prosperous Future Using Data Science and Machine Learning
Abstract
Introduction
Data Science and Machine Learning: An Overview
Data Science
Machine Learning
Data Acquisition
Feature Engineering
Model Building
Evaluation
Deployment
Regression
Cross-validation
Proposed System
Input Data
Pre-processing
Algorithm Selection
Evaluation
Input Data
Pre-processing and Data Visualization
Algorithm Selection and Evaluation
Experimentation and Results
Simple Linear Regression
Support Vector Regression
Decision Tree Regression
Random Tree Regression
Analysis
Conclusion and Future Work
References
Cloud, Edge, and Fog Computing: A Study on their Broader Scope
Abstract
Introduction
Highlights of the Study
Scope of the Study
Literature Review
Overview of Cloud Computing
Overview of Fog Computing
Overview of Edge Computing
Comparison between Different Computing Techniques
Definition and Characteristics
Use Cases and Applications
Networking and Resource Management
Security and Privacy
Performance and Quality of Service (QoS)
Discussion
Definition and Characteristics
Applications and use cases
Networking and Resource Management
Security and Privacy
Results Analysis
Conclusion
Recommendations for future work
References
Data-Driven Approach of Species DNA Sequencing Based on Similar Patterns Using Machine Learning
Abstract
Introduction
Background
Role of ML and DL
Pattern Matching in DNA
DNA Sequence Encoding Specific Techniques
Structure of Paper
Related Work
Another View of Literature Survey: A Summary
Research Challenges
Problem Statements of Related Work
Recent Development in DNA Sequencing and Future Trends [17]
Application of Artificial Intelligence and Data Science in DNA Sequencing
Research Challenges in DNA Sequencing
Analysis of DNA Sequencing Error Correction
Exploring the Intersection of Genomic Medicine and ML: An Introspective Analysis of Computational Models
Deep Learning in Bioinformatics and its Applications in DNA Sequencing
Applications of DNA Sequencing in Healthcare and Disease Management [31]
Methodology
Dataset Description and Data Pre-Processing
General Procedure to Generate Uniform Vector Length of Given Sequence Input using K-Mer Concept
Component Used in General Framework
Results and Discussion
Conclusion and Future Scope
REFERENCES
Enhancing Intrusion Detection Performance with a Hybrid Module on KDD99 Dataset
Abstract
Introduction
Literature Review
Proposed Hybrid Design
What is Ensemble Learning
Ensemble Model (Hybrid)
Dataset Used
Methodology
Results
Conclusion
REFERENCES
A Comprehensive Study on Crop Disease Detection Using Machine Learning and Deep Learning Models
Abstract
INTRODUCTION
RESEARCH QUESTIONS
LITERATURE REVIEW
RESULT AND DISCUSSION
CONCLUSION
FUTURE SCOPE
REFERENCES
Machine Learning Approaches for Natural Language Processing and Sentiment Analysis
Abstract
Introduction
Machine Learning Algorithms for Sentiment Analysis
Support Vector Machines (SVM)
Linear Kernel
Polynomial Kernel
Radial Basis Function (RBF) Kernel
Sigmoid Kernel
Custom Kernels
Recurrent Neural Network (RNN)
Transformer Models
Pre-processing techniques for Sentiment Analysis
Tokenization
White Space Tokenization
Rule-based Tokenization
Statistical Tokenization
Tokenizers Designed Specifically for Social Media/Texting Language
Feature Engineering
Bag-of-Words (BoW)
N-grams
Word Embeddings
Word2Vec
GloVe
Comparative Evaluation of Machine Learning Approaches
Datasets for Evaluation
Stanford Sentiment Treebank (SST)
IMDb Movie Reviews
Amazon Product Reviews
Twitter Sentiment Analysis Dataset
Performance Metrics
Performance of different machine learning approaches in sentiment analysis
Support Vector Machines (SVM)
Strengths
Weaknesses
Recurrent Neural Networks (RNNs)
Strengths
Weaknesses
Transformer Models
Strengths
Weaknesses
Recent Advancements in NLP with Machine Learning
Transfer Learning
Explainable AI
Future Research Directions
Multilingual Sentiment Analysis
Fine-Grained Sentiment Classification using Deep Learning Architectures
Contextualized Word Representations
Ethical Considerations in NLP
Interdisciplinary Approaches
Conclusion
REFERENCES
From Data to Big Data: An Exploration of the Evolution and Impact of Large-Scale Data Analytics
Abstract
Introduction
Evolution of data
Impact of big data analytics across different domains
Finance
Manufacturing and Supply Chain
Transportation and Logistics
Applications of Big Data
Personalized Marketing
Fraud Detection
Supply Chain Optimization
Implications of big data for scientific research
Accelerated Discovery
Cross-Disciplinary Collaboration
Reproducible and Transparent Research
Data-Driven Hypothesis Generation
Challenges and Concerns
Data Quality and Integration
Data Privacy and Security
Computational Infrastructure and Resource Requirements
Ethical Considerations and Bias
Data Sharing and Collaboration
Conclusion
References
Analysis Study on Blockchain Technology
Abstract
Introduction
Literature Review
Blockchain Technologies
Types of Blockchain
1) Public Blockchain
2) Private Blockchain
3) Permission Blockchain
Blockchain-related Technologies
Encryption and Decryption
Digital signatures
Homomorphic Encryption
Security Concerns with Blockchain Systems
Network-level Security
Transaction-level Security
Associated Surround System Security
Smart Contract Security
Privacy Concerns with Blockchain Technology
Transactional Privacy
Unlinkability
Consensus Mechanisms in Blockchain
Proof of Work (Pow)
Proof of Stake (Pos)
Delegated Proof of Stake (Dpos)
Proof of Importance (Poi)
Proof of Activity (Poa)
Proof of Elapsed Time (PoET)
Practical Byzantine Fault Tolerance (PBFT)
Stellar Consensus
Ripple Consensus
Blockchain Use
Decentralized Exchanges
Distributed Cloud Storage
Digital Identity
Communication throughout the Supply Chain and Proof of Provenance
Smart Contracts
Digital Voting
Pros of Blockchain
Cons of Blockchain
Conclusion and Future Scope
REFERENCES
A Study on Remote Sensing Image Segmentation and Classification
Abstract
Introduction
Segmentation Fundamentals
Discontinuity-based Segmentation
First Order Derivatives (FOD)
Second Order Derivative (SOD)
Detection of Isolated Points
Line Detection
Edge Detection:
Edge Linking
Local Processing
Global Processing
Similarity-based Segmentation
Thresholding
Local Thresholding
Global Thresholding
Adaptive Thresholding
Region Growing
Region Splitting and Merging
Step-I Divide
Step-II Merge (conquer)
Step-I Divide
Step-II Conquer (merge)
Remote Sensing
Data Acquisition
Analysis of Acquired Data
Remote Sensing and Image Segmentation
Image Classification
Land Cover Classification Steps
Classification Criteria
Land use and Land Cover Classification System for use with Remote Sensor Data by the United States Geological Survey [18]
Training
Classification
Testing
Methods to implement supervised classification
Minimum distance to mean classifier
Algorithm
Parallelepiped Classification
Algorithm
Unsupervised Classification
Methods to Implement Unsupervised Classification
K-means
Algorithm
Conclusion
REFERENCES
Depression Detection on Social Media Using the CNN-LSTM Model
Abstract
Introduction
Related work
Proposed Methodology
DataSet
Preprocessing
Algorithm
LR
Bernoulli Naïve Bayes
CNN
SVM
XG-Boost
Ada-Boost
Proposed Model (CNN-LSTM)
Result
Conclusion
Future Work
References
Evaluating Twitter Sentiments via Natural Language Processing
Abstract
INTRODUCTION
COMMON BLOGGING PLATFORMS
Sentiments Analysis
Digital Social Networks
Twitter
E-commerce Microblogging
DOMINANT MACHINE LEARNING APPROACHES FOR ANALYZING SENTIMENT
Support Vector Machine
Natural Language Processing
Case-based Reasoning
Artificial Neural Network
Python
Application Programming Interface
TWITTER SENTIMENT ANALYSIS
RESULT ANALYSIS
Retrieval of Tweets
Analysis of Sentiments
DISCUSSION AND CONCLUSION
REFERENCES
Computational Intelligence and its Applications
Edited by
Vikash Yadav
Government Polytechnic Bighapur Unnao, Department of Technical Education, Uttar Pradesh, India
Vimal Kumar
Galgotias University, Greater Noida, Uttar Pradesh, India
Sonam Gupta
Ajay Kumar Garg Engineering College, Ghaziabad, Uttar Pradesh, India
&
Vandana Dixit Kaushik
Harcourt Butler Technical University, Kanpur, Uttar Pradesh, India

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PREFACE

In the rapidly evolving landscape of technology, where the boundaries between the digital and physical worlds blur, computational intelligence stands as a beacon of innovation and problem-solving process. As the digital era continues to permeate every facet of our lives, the need for intelligent systems that can adapt, learn, and make decisions becomes increasingly vital. This book, “Computational Intelligence & its Applications”, delves deep into the heart of this transformative field, exploring its theoretical foundations and practical applications that are reshaping industries, societies, and the very nature of human-machine interaction.

Computational intelligence, an interdisciplinary domain drawing from computer science, mathematics, engineering, and cognitive sciences, encompasses a rich tapestry of techniques inspired by nature, evolution, and human cognition. From neural networks that emulate the workings of the human brain to evolutionary algorithms that mimic the process of natural selection, computational intelligence methodologies empower machines to solve complex problems, optimize processes, and learn from data in ways that were once deemed the exclusive realm of human intelligence.

From healthcare and finance to manufacturing and transportation, the impact of computational intelligence is profound and multifaceted. In the pages that follow, readers will encounter compelling case studies and examples showcasing how computational intelligence algorithms are revolutionizing medical diagnosis, enabling autonomous vehicles, predicting market trends, optimizing supply chains, and enhancing the overall quality of life. Each chapter is crafted to provide a balance between theoretical knowledge and practical insights, making this book an invaluable resource for students, researchers, and practitioners alike.

Additionally, this book explores the ethical dimensions of computational intelligence, addressing the societal implications of intelligent systems, including privacy concerns, bias in algorithms, and the ethical responsibility of AI developers. As we venture deeper into the era of artificial intelligence, understanding these ethical considerations is paramount to ensuring that computational intelligence serves humanity’s best interests.

We invite readers to embark on a journey through the realms of computational intelligence and witness firsthand the transformative power of intelligent algorithms. Whether you are a student eager to explore the frontiers of AI, a researcher seeking inspiration for your next project, or a practitioner aiming to harness the potential of computational intelligence in your industry, this book offers a wealth of knowledge and insights to guide you on your intellectual quest.

Vikash Yadav Government Polytechnic Bighapur Unnao, Department of Technical Education, Uttar Pradesh, IndiaVimal Kumar Galgotias University, Greater Noida, Uttar Pradesh, IndiaSonam Gupta Ajay Kumar Garg Engineering College, Ghaziabad, Uttar Pradesh, India &Vandana Dixit Kaushik Harcourt Butler Technical University, Kanpur, Uttar Pradesh, India

List of Contributors

AnshuAmity Institute of Information Technology, Uttar pradesh, IndiaAditya VermaAmity Institute of Information Technology, Uttar pradesh, IndiaAnil Kumar YadavVIT Bhopal University, Madhya Pradesh, IndiaAshok Kumar RaiGalgotias University, Greater Noida, IndiaAyushi PrakashAjay Kumar Garg Engineering College, Ghaziabad, IndiaAbdul AleemGalgotias University, Uttar pradesh, IndiaBably DollyIntegral University, Lucknow, UP, IndiaBosco Paul AlapattChrist (Deemed to be University), Delhi NCR Campus, Ghaziabad, IndiaGurpreet KaurAmity Institute of Information Technology, Uttar pradesh, IndiaLakshay Singh MahurRaj Kumar Goel Institute of Technology, Ghaziabad, IndiaMayur RahulCSJM University, Kanpur, Uttar pradesh, IndiaManoj KumarVIT Bhopal University, Madhya Pradesh, IndiaManish Kumar GuptaBuddha Institute of Technology, Gorakhpur, IndiaMartand RatnamAKTU, Lucknow, UP, IndiaNamita TiwariCSJM University, Kanpur, Uttar pradesh, IndiaNidhi SindhwaniAmity Institute of Information Technology, Uttar pradesh, IndiaPankaj SinghKIET group of Institutions, Uttar pradesh, IndiaPradeep GuptaAjay Kumar Garg Engineering College, Ghaziabad, IndiaRohit AnandG. B pant DSEU, Okhla Campus 1, New Delhi, IndiaRohit VashishtKIET group of Institutions, Uttar pradesh, IndiaRadhey ShyamDepartment of Information Technology SRMCEM, Lucknow, IndiaSonia DeshmukhKIET group of Institutions, Uttar pradesh, IndiaSonam GuptaAjay Kumar Garg Engineering College, Ghaziabad, IndiaShivani SaxenaAjay Kumar Garg Engineering College, Ghaziabad, IndiaSneha MauryaAjay Kumar Garg Engineering College, Ghaziabad, IndiaSandhya AvasthiABES Engineering College, Ghaziabad, IndiaShilpi KhannaDepartment of Information Technology SRMCEM, Lucknow, IndiaSmita SinghDepartment of Information Technology SRMCEM, Lucknow, IndiaTarun JaiswalNational Institute of Technology, Raipur, IndiaTanvi JaiswalDepartment of Information Technology SRMCEM, Lucknow, IndiaUtkarsh DixitABES Engineering College, Ghaziabad, IndiaVivek KumarKoneru Lakshmaiah Education Foundation, Vijayawada, Andhra Pradesh, IndiaVikash YadavGovernment Polytechnic Bighapur, Unnao, Department of Technical Education, Uttar Pradesh, IndiaVikash Kumar MishraGalgotias University, Uttar pradesh, IndiaVimal KumarGalgotias University, Uttar pradesh, India

Emerging Frontiers: Post-Quantum Cryptography and Secure Communication

Namita Tiwari1,*,Mayur Rahul1,Vikash Yadav2
1 CSJM University, Kanpur, Uttar pradesh, India
2 Government Polytechnic Bighapur, Unnao, Department of Technical Education, Uttar Pradesh, India

Abstract

The field of cryptography is facing a significant challenge due to fast updates in computer history. This chapter explores the key concepts, techniques, and challenges associated with post-quantum cryptography (PQC). The chapter begins by introducing the fundamental principles of quantum computing and the threats it poses to traditional cryptography systems. Each family is examined in detail, highlighting its underlying mathematical foundations, security assumptions, and implementation considerations. The chapter also discusses the ongoing standardization efforts in post-quantum cryptography led by organizations such as the “National Institute of Standards and Technology” (NIST). Furthermore, the chapter explores the challenges and open research questions in the field, such as the efficient implementation of post-quantum algorithms, the impact on existing protocols and systems, and the integration of post-quantum cryptography into real-world applications.

Keywords: Cryptography protocols, Message authentication codes (MACs), NIST, Post-quantum cryptography, Post-quantum algorithms, Quantum computers.
*Corresponding author Namita Tiwari: CSJM University, Kanpur, Uttar pradesh, India; E-mail: [email protected]

Introduction

PQC is a field of study and research focusing on cryptography protocols that can withstand quantum computers. Quantum computers can potentially solve the underlying mathematical problems upon which current encryption algorithms are based, rendering them ineffective. PQC's goal is to develop new cryptography algorithms that can resist attacks by quantum computers. These algorithms are designed to provide security against both classical and quantum computers, ensuring that encrypted data remains protected in a post-quantum computing era. Secure communication involves protecting the content of the communication from unauthorized access, preventing any unauthorized modifications or tampering with the data, and verifying the identity of the communicating parties. To achieve secure communication, various cryptography techniques and protocols are employed. These techniques involve the use of encryption, which transforms the original message into an unintelligible form, making it difficult for eavesdroppers

to understand. Only authorized recipients with the necessary decryption keys can decipher the encrypted message and retrieve the original information. Secure communication protocols also address the issue of data integrity. They ensure that the message remains unaltered during transit by employing message authentication codes (MACs) or digital signatures. These techniques verify the integrity of the data by attaching a small piece of information that is computed using cryptography algorithms [1].

Furthermore, secure communication involves establishing the authenticity of the communicating parties. This is achieved through techniques like digital certificates and public key infrastructure (PKI), where each participant is issued a unique digital certificate that binds their identity to a public key. By verifying the digital certificate, the recipient can be assured of the sender's identity and establish a secure channel for communication. Secure communication is crucial in various contexts, including online banking, e-commerce, government communications, and sensitive data exchanges. It protects against eavesdropping, data tampering, impersonation attacks, and other forms of cyber threats, ensuring that sensitive information remains confidential and trustworthy throughout the communication process.

Key Concepts: Fundamental Techniques and Cryptography Protocols

There are several fundamental techniques and cryptography protocols used to achieve secure communication [2]. Here are some commonly employed techniques:

Encryption: It is the process of coding plaintext (original message) into ciphertext (encrypted message) using an encryption algorithm and a secret key. It ensures that even if intercepted, the message cannot be understood without the corresponding decryption key. Popular encryption algorithms include AES and RSA.Symmetric Key Cryptography: It uses the common key for both coding and decoding, and the key must be shared through the proper channel. This approach is efficient for encrypting big data. Examples are AES, DES, and Blowfish.Asymmetric Key Cryptography: It involves a public and private key for encryption and decryption, respectively. It is used in secure key exchange and digital signatures. Examples are RSA, ECC, and Diffie-Hellman key exchange.Hash Functions: It converts the input of an arbitrary string to an output of a fixed string known as a message digest. Popular hash function algorithms are SHA-2, SHA-3, and message digest algorithm (MD5).Digital Signatures: These use asymmetric key cryptography to provide data integrity and non-repudiation. The sender uses its private key to make a unique digital signature, and the verifier verifies it using the corresponding public key.Transport-Layer Security TLS or Secure-Sockets Layer (SSL): These protocols provide secure communication over the Internet. SSL/TLS is commonly used in web browsing, email, etc.Virtual Private Networks (VPNs): VPNs create secure communication over public networks. VPNs are widely used for remote access, securing Wi-Fi connections, and maintaining privacy online.

These techniques and protocols can be combined and tailored to specific communication needs, providing layers of security to protect sensitive information and ensure secure communication between parties [3].

The following section examines the techniques and challenges associated with post quantum cryptography [4-7].

Techniques/Challenges in Post-Quantum Cryptography

Researchers are exploring various mathematical problems and cryptographic primitives believed to be intractable against quantum computers. Some of the promising approaches include:

Lattice-based Cryptography: It includes Learning with Errors (LWE) and Ring Learning with Errors (RLWE) schemes, which offer security against attacks by both classical and quantum computers.Code-based Cryptography: It employs error-correcting codes to provide security. Schemes like McEliece and Niederreiter cryptosystems utilize the difficulty of decrypting the linear codes to achieve resistance against quantum attacks.Multivariate Cryptography: It is based on the hardness of solving multivariate polynomial equations. It involves schemes like Rainbow and the Unbalanced Oil and Vinegar (UOV) cryptosystems.Hash-based Cryptography: It employs cryptographic hash functions to construct digital signatures and key exchange protocols. Merkle trees and the Lamport signature scheme are examples of hash-based post-quantum cryptographic techniques.Supersingular isogeny-based cryptography: These schemes are based on elliptic curves and isogenies, and security relies on the hardness of certain isogeny problems.

Lattice-based Cryptography

It offers a promising alternative to traditional cryptographic systems, such as those based on number theory or elliptic curves, which may be vulnerable to quantum attacks.

The main advantages of lattice-based cryptography include:

Security: Lattice-based schemes are provable and secure based on the hardness of lattice problems, even against quantum computers.Post-quantum resistance: Lattice-based cryptography is considered a leading candidate for post-quantum cryptography, as the underlying lattice problems are not efficiently solvable by quantum algorithms.Versatility: Lattice-based techniques can be applied to various cryptographic primitives, including encryption, digital signatures, key exchange protocols, and secure multiparty computation.Efficiency: While lattice-based cryptography typically involves larger key sizes compared to traditional cryptographic systems, advances in lattice reduction algorithms and optimization techniques have improved the efficiency of lattice-based schemes.

Some commonly used lattice-based cryptographic primitives include:

Lattice-based encryption schemes (e.g., Learning With Errors Encryption, Ring-Learning With Errors Encryption).Lattice-based signature schemes (e.g., BLISS, Dilithium).Lattice-based key exchange protocols (e.g., New Hope, Frodo).Lattice-based fully homomorphic encryption (e.g., TFHE).

As with any cryptographic system, it is essential to stay up to date with the latest advancements and rely on standardized and vetted implementations for secure deployment.

Code-based Cryptography (CBC)

It relies on error-correcting codes for providing security. The security of code-based cryptographic schemes is based on the hardness of certain decoding problems associated with error-correcting codes.

In code-based cryptography, encryption, digital signatures, and key exchange protocols are constructed using error-correcting codes. These codes introduce redundancy into the transmitted data to detect and correct errors caused by noise or interference during transmission.

Advantages of code-based cryptography include:

Post-quantum resistance: CBC is considered a promising post-quantum alternative as the decoding problem used in these schemes.Well-studied and understood: Error-correcting codes have been extensively studied and used in various engineering applications, making the theoretical foundations of code-based cryptography well-developed.Relatively efficient: Code-based schemes can provide a good balance between security and efficiency, with practical implementations available.Compatibility with existing systems: Code-based cryptography can be implemented using existing infrastructure and protocols without major modifications, making it easier to integrate into existing systems.

However, there are also some challenges and limitations associated with code-based cryptography:

Key size: Code-based schemes typically require larger key sizes compared to traditional cryptographic systems, which may impact the efficiency and performance of the cryptographic operations.Key management: Key management in code-based cryptography can be more complex due to the large key sizes and potential vulnerabilities if key update procedures are not properly implemented.Limited deployment: Despite its post-quantum security, code-based cryptography has not yet been widely deployed, and the adoption of code-based schemes in real-world applications is still limited.

Some well-known code-based cryptographic schemes include:

McEliece cryptosystem.Niederreiter cryptosystem.RQC (Ring-LWE-based Quasi-Cyclic) cryptosystem.

Multivariate Polynomial Cryptography (MPC)

It relies on the computational hardness of solving systems of multivariate polynomial equations. Unlike traditional cryptographic systems that are based on number theory or elliptic curves, MPC utilizes the algebraic properties of polynomials to provide security.

In MPC, algorithms are based on the evaluation of multivariate polynomial equations. These equations involve multiple variables and coefficients, and the security of the system depends on the difficulty of solving these equations to recover the original input.

Solving systems of multivariate polynomial equations is a computationally difficult problem, even for powerful computers.

There are several constructions and schemes within MPC, each with its own strengths and characteristics. Two notable examples of MPC schemes are:

Rainbow: This scheme is a multivariate polynomial signature scheme. It uses a layered structure of polynomial equations and employs specific techniques to increase security while maintaining efficiency. Rainbow signatures are resistant to forgery and tampering attacks.Unbalanced Oil and Vinegar (UOV): This is another multivariate polynomial signature scheme. It is based on the concept of oil and vinegar mixing, where the polynomials are divided into two types: the “oil” polynomials that provide security and the “vinegar” polynomials that act as public information. UOV signatures offer high resistance against known attacks.

The main challenge in implementing MPC is the efficiency and scalability of the cryptographic operations. Multivariate polynomial systems tend to have large equation sizes and require computationally intensive operations. Therefore, optimizing the performance of MPC schemes is an ongoing area of research.

It is worth noting that while MPC has shown promising resistance against attacks, it may have some limitations compared to other post-quantum cryptography approaches. For example, MPC may be vulnerable to certain algebraic attacks or advancements in solving multivariate polynomial systems. Therefore, ongoing research and analysis are crucial to ensure the security of MPC in the face of evolving attacks and computational advancements.

Hash-based Cryptography

It is also known as hash-based digital signatures or one-time signatures. It is based on the computational hardness of finding collisions or per-image resistance in hash functions [3].

In hash-based cryptography, a one-way hash function is used to derive a short fixed-length digest or hash value from an arbitrary-sized input message. The security of hash-based schemes is based on the assumption that finding collisions (two different inputs producing the same hash) or inverting the hash function (finding the original input from a given hash value) is computationally difficult.

The main idea behind hash-based cryptography is to use a one-time signature scheme, where a different key pair is used for each signature. The public key is derived from the private key using the hash function, and the signature is generated by including the hash value of the message along with the private key. Verification is performed by hashing the received message and comparing it with the derived public key and the signature.

Advantages of Hash-Based Cryptography

Post-quantum resistance: Hash-based schemes are considered post-quantum secure, as their security is based on the hardness of finding collisions or inverting hash functions, which is believed to be resistant to quantum algorithms.

Simplicity and efficiency: Hash functions are widely available, well-studied, and efficient cryptography primitives, making hash-based schemes relatively simple and efficient.Compatibility with existing systems: Hash-based cryptography can be integrated into existing protocols and systems with minimal modifications, as hash functions are already widely used in various applications.Minimal key management: In hash-based cryptography, the key management is relatively simple since new key pairs are generated for each signature. This eliminates the need for complex key distribution or revocation mechanisms.

However, there are some challenges and limitations associated with hash-based cryptography:

Signature size: Hash-based signatures can be significantly larger than traditional digital signatures, which may impact the efficiency and bandwidth requirements for signature generation and verification.Limited signature reuse: Hash-based signatures are generally designed for one-time use and cannot be reused for multiple messages. This can be impractical in scenarios where frequent signing is required.Migration challenges: Adopting hash-based cryptography may require significant changes in existing cryptography systems and protocols, which can be challenging to deploy and integrate.

Some well-known hash-based signature schemes include:

Lamport signatures.Winternitz signatures.Merkle signatures.

Supersingular Isogeny-Based Cryptography

It is based on the computational hardness of the isogeny problem in supersingular elliptic curves. It offers an alternative to traditional cryptography systems that may be vulnerable to attacks by quantum computers. In supersingular isogenyl- based cryptography, the security of the cryptographic schemes is based on the difficulty of finding the isogeny between two given elliptic curves. The main idea behind supersingular isogeny-based cryptography is to use the isogeny function as a trapdoor function. By starting with a known base curve and applying a sequence of isogenies, a public key is derived from the private key. The security lies in the computational hardness of computing the isogeny in the reverse direction, i.e., finding the private key from the public key.

Advantages of supersingular isogeny-based cryptography include:

Post-quantum resistance: Supersingular isogeny-based cryptography is designed to be resistant to attacks by both classical and quantum computers, as the underlying computational problem is believed to be hard even for quantum algorithms.Smaller key sizes: Supersingular isogeny-based cryptographic schemes often have smaller key sizes compared to some other post-quantum alternatives, which can be advantageous in terms of efficiency and storage requirements.Potential for efficient implementations: Advances in algorithmic techniques and efficient arithmetic on elliptic curves have led to more practical and efficient implementations of supersingular isogeny-based schemes.Compatibility with existing systems: Supersingular isogeny-based cryptography can be integrated into existing protocols and systems with proper modifications, allowing for compatibility and interoperability.

However, there are also challenges and considerations in supersingular isogeny-based cryptography:

Relatively new and ongoing research: Supersingular isogeny-based cryptography is still an active and new research area, and further analysis and scrutiny are needed to ensure its security and practicality.Performance trade-offs: While improvements in efficiency have been made, supersingular isogeny-based cryptography generally involves more computational overhead compared to some traditional cryptography systems.Standardization and adoption: Standardization efforts are underway to evaluate and establish the security and practicality of supersingular isogeny-based schemes. Adoption may depend on widespread acceptance and interoperability.

Some well-known supersingular isogeny-based cryptographic schemes include:

Supersingular-Isogeny Key Encapsulation (SIKE).Supersingular-Isogeny Diffie-Hellman (SIDH).Commutative-Supersingular-Isogeny Diffie-Hellman (CSIDH).

As supersingular isogeny-based cryptography is a rapidly evolving field, it is essential to refer to the latest research and standardized specifications for the most up-to-date information on implementations and best practices.

Challenges in Post Quantum Cryptography

Security Analysis: Designing and analyzing secure post-quantum cryptographic algorithms is a significant challenge. It requires demonstrating resistance against attacks from both classical and quantum computers, ensuring provable security under various mathematical assumptions, and assessing the impact of algorithmic optimizations on security.Efficiency and Performance: Post-quantum cryptographic algorithms typically involve complex mathematical operations, which can be computationally expensive and require significant computational resources. Balancing security and efficiency is crucial to ensure the practical adoption of post-quantum cryptography.Standardization and Interoperability: Standardization plays a vital role in post-quantum cryptography to ensure interoperability and compatibility across different systems and platforms. Establishing standardized algorithms, protocols, and evaluation criteria requires collaboration among researchers, industry stakeholders, and standardization bodies.Integration into Existing Systems: Integrating post-quantum cryptographic algorithms into existing systems presents challenges, particularly in cases where legacy systems or protocols rely on classical cryptographic primitives. Ensuring backward compatibility, migration strategies, and seamless integration without compromising security is a key consideration.