Most of the current public key cryptosystems’ security is based on the integer factorization and the discrete logarithm, which are mathematical problems that are considered difficult to solve. However, the publication in 1994 of the Shor’s algorithm [1] was a major setback for the world of cryptography, since it provided a quantum algorithm capable of solving efficiently these mathematical problems. Therefore, in recent years many governments and technology companies have put a lot of effort into developing what is known as post-quantum cryptography, i.e. the science that studies cryptosystems that are resistant to quantum attacks. Along these lines, in 2016 the National Institute of Standards & Technology launched a competition with the aim of establishing and standardising the best performing post-quantum cryptosystems, being the NTRU (Nth Degree Truncated polynomial Ring Units) cryptosystem one of the candidates still on the table. The aim of this project is to study the quantum-resistant cryptosystem NTRU, both from a theoretical and practical point of view. Firstly, the mathematical results on which it is based are presented and the existing attacks against it are analyzed. Finally, a practical implementation of the cryptosystem and four of its attack is carried out, from which experimental results are extracted.
Most of the current public key cryptosystems’ security is based on the integer factorization and the discrete logarithm, which are mathematical problems that are considered difficult to solve. However, the publication in 1994 of the Shor’s algorithm [1] was a major setback for the world of cryptography, since it provided a quantum algorithm capable of solving efficiently these mathematical problems. Therefore, in recent years many governments and technology companies have put a lot of effort into developing what is known as post-quantum cryptography, i.e. the science that studies cryptosystems that are resistant to quantum attacks. Along these lines, in 2016 the National Institute of Standards & Technology launched a competition with the aim of establishing and standardising the best performing post-quantum cryptosystems, being the NTRU (Nth Degree Truncated polynomial Ring Units) cryptosystem one of the candidates still on the table. The aim of this project is to study the quantum-resistant cryptosystem NTRU, both from a theoretical and practical point of view. Firstly, the mathematical results on which it is based are presented and the existing attacks against it are analyzed. Finally, a practical implementation of the cryptosystem and four of its attack is carried out, from which experimental results are extracted.
The emergence of quantum computing is a serious threat to the principles of modern crypto-logical mathematics. The classical public-key cryptography, including Rivest-Shamir-Adleman (RSA), Elliptic Curve Cryptography (ECC), and Diffie-Hellman are very safe against classical adversaries yet become susceptible to quantum algorithms, including the Shor algorithm, which can easily solve the underlying mathematical problems. This weakness is jeopardizing confidentiality and integrity of the world-wide systems of communication, money transactions, and essential structures, and requires the immediate creation of safe alternatives. The current literature on post-quantum cryptography (PQC) has covered various classes of algorithm, such as lattice-based, code-based, multivariate schemes, and isogeny-based schemes. Although lattice-based approaches like Nth Degree Truncated Polynomial Ring Unit (NTRU) and FrodoKEM can be highly theoretically resistant, they can be computationally and memory-intensive. Cryptosystems based on code such as Classic McEliece are secure but not practicable because they have huge public key sizes. Multivariate schemes like Rainbow, and isogeny-based schemes like Super singular Isogeny Key Encapsulation (SIKE) have been attacked recently by cryptanalytic attacks, and broken completely. Such restrictions open the necessity to find more efficient and secure quantum-resistant solutions.This research study postulates a hybrid post-quantum cryptographic (PQC) system that combines CRYSTALS-Kyber for encryption with CRYSTALS-Dilithium for digital signatures both of which are approved through the National Institute of Standards and Technology (NIST) PQC standardization program. The model will be such that it ensures quantum resistance but at the same time it will be scalable, efficient and compatible with the existing infrastructures. The test outcomes indicate that the hybrid PQC model is 35-45 percent faster to encrypt and decrypt, signature performance is enhanced by up to 40 percent, and the throughput is 20 times higher (98.7 Mbps) than the same base PQC scheme including Nth Degree Truncated Polynomial Ring Unit (NTRU), McEliece and Rainbow. These enhancements affirm that the suggested model provides a viable trade-off between the security, speed, and efficiency in terms of key size, which makes it a viable and a sound base to ensure secure communication in the quantum age.
The standard public-key cryptosystems used today relies mathematical problems that require a lot of computing force to solve, so much that, with the right parameters, they are computationally unsolvable. But there are quantum algorithms that are able to solve these problems in much shorter time. These quantum algorithms have been known for many years, but have only been a problem in theory because of the lack of quantum computers. But with recent development in the building of quantum computers, the cryptographic world is looking for quantum-resistant replacements for today’s standard public-key cryptosystems. Public-key cryptosystems based on lattices are possible replacements. This thesis presents several possible candidates for new standard public-key cryptosystems, mainly NTRU and ring-LWE-based systems. The latticebased cryptosystems are shown to be very fast and have strong, provable security against quantum computers, but are a lot more complicated than RSA and Diffie-Hellman.
The security of current public-key cryptosystems relies on the hardness of factoring large integers or solving discrete logarithm problems. However, these mathematical problems can be solved in polynomial time using a quantum computer. This vulnerability has prompted research into post-quantum cryptography using alternative mathematical problems that are secure in the era of quantum computers. In this regard, the National Institute of Standards and Technology (NIST) began to standardize post-quantum cryptography in 2016. In this expository article, we give an overview of recent research on post-quantum cryptography. In particular, we describe the construction and security of multivariate polynomial cryptosystems and lattice-based cryptosystems, which are the main candidates of post-quantum cryptography.
In the medical field, images play a crucial role in patient monitoring, treatment planning, and diagnosis. Since the digital healthcare revolution, a large number of medical images are being transmitted and stored, making security essential. Any breach in data confidentiality can lead to misdiagnosis of patients. The traditional encryption techniques, like McEliece, have been used to shield medical data. However, the rise of quantum computers poses a threat to the prevailing encryption techniques, as they can easily break and expose medical data to quantum attacks. To overcome these attacks, post-quantum cryptography (PQC) has been introduced. Nth degree truncated polynomial ring unit (NTRU) is a lattice-based PQC algorithm that uses complex mathematical concepts that cannot be solved by quantum computers. Harnessing NTRU's lattice-based security ensures the robustness and resilience of medical data. The proposed system implements the PQC-based NTRU algorithm to protect medical data against quantum attacks.
The advent of quantum computing poses a significant threat to the security of current asymmetric cryptographic systems, which underpin much of modern digital communication and security. These systems, predominantly RSA and Elliptic Curve Cryptography (ECC), rely on the computational hardness of mathematical problems such as integer factorization and the discrete logarithm problem. Shor's algorithm, a quantum algorithm, demonstrates the ability to efficiently solve these problems, rendering classical public-key cryptography vulnerable to attacks by sufficiently powerful quantum computers. This paper argues for and thoroughly examines the strategic imperative of transitioning from these classical cryptographic foundations to a new paradigm based on lattices, which are believed to be resistant to quantum attacks. We delve into the fundamental mathematical problems underlying lattice-based cryptography, such as the Shortest Vector Problem (SVP) and the Learning With Errors (LWE) problem, whose worst-case hardness is leveraged to achieve cryptographic security. A comprehensive literature review is provided, tracing the evolution of quantum threats and the emergence of lattice-based schemes. The methodology details the construction principles of prominent lattice-based cryptosystems. Results demonstrate their theoretical security against quantum adversaries and highlight their practical attributes, including compact key sizes and competitive performance. The discussion section contextualizes lattice-based cryptography within the broader landscape of post-quantum candidates, examining their strengths, weaknesses, and the ongoing standardization efforts by organizations like NIST. We conclude that lattice-based cryptography offers a robust and promising foundation for building resilient asymmetric cryptographic systems in the post-quantum era, ensuring the long-term security of digital information through a necessary re-architecture of cryptographic primitives.
In the evolving landscape of quantum computing, the security of conventional cryptosystems is increas- ingly compromised. This requires innovative data protection strategies, leading to the exploration of Post-Quantum Cryptography (PQC) techniques. This research aims to address these challenges, focusing on the integration of Nth- Degree Truncated Polynomial Ring (NTRU) encryption - known for its quantum resistivity - and Shamir’s Secret Sharing (SSS) for secure and quantum-secured key distribution, particularly in resource-constrained environments. Despite their effectiveness, NTRU ciphers face obstacles in public key distribution due to significant computational and memory requirements. Leveraging SSS, a scheme to distribute the NTRU public key to multiple shares, providing enhanced security while mitigating resource limitations is proposed. Recognizing the potential for security breaches like Man-in-the-Middle (MitM) and Distributed Denial of Service (DDoS) attacks, the proposed work seeks to fortify defenses against these threats. The findings of the proposed method are intended to offer a significant contribution to strengthening cryptographic practices in the face of emerging quantum technologies.