This paper presents the NTRU (N-th degree Truncated Polynomial Ring)encryption algorithm and extends the encryption and decryption processes using polynomials. Theencryption and decryption algorithms work by generating random polynomials and convertingmessages into polynomials. The paper discusses the quantum-resistant properties of the NTRUalgorithm and how it differs from classical RSA or elliptic curve algorithms.
This paper presents the NTRU (N-th degree Truncated Polynomial Ring)encryption algorithm and extends the encryption and decryption processes using polynomials. Theencryption and decryption algorithms work by generating random polynomials and convertingmessages into polynomials. The paper discusses the quantum-resistant properties of the NTRUalgorithm and how it differs from classical RSA or elliptic curve algorithms.
This article presents the NTRU (N-th degree Truncated Polynomial Ring) encryption algorithm and extends the encryption and decryption processes using polynomials. The operation of the encryption and decryption algorithms is carried out by generating random polynomials and converting messages into polynomials. The article discusses the quantum-resistant properties of the NTRU algorithm and how it differs from the classical RSA or elliptic curve algorithms. The importance of the NTRU algorithm and its stability against quantum algorithms for ensuring cryptographic security in the post-quantum era are emphasized. These approaches show the possibilities of countering the threats that arise, especially behind the development of quantum computers. The program shows how encryption works in the Python programming language and using polynomials.
The quantum-resistant qualities of various encryption methods, such as N-th degree Truncated polynomial Ring Units (NTRU) Encrypt, NTRU Sign, Ring-Lizard, and Kyber protocols are becoming more important in light of the ever-evolving nature of digital threats. An-depth analysis of the mathematical derivation of these algorithms, as well as a determination of their computing efficiency and resistance to quantum assaults is discussed in this paper. Techniques of the Ring-Lizard and Kyber algorithms to lattice-based encryption are analyzed. The study gives an overview of quantum-resistant capabilities of these algorithms and their performance measures. Strengths and weaknesses of the NTRU Encrypt, NTRU Sign, Ring-Lizard, and Kyber algorithms are discussed. The results give useful insights for cybersecurity practitioners, academics, and policymakers, aiding them in making educated choices to protect digital infrastructures against quantum attacks.
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.
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.
Cryptographic design and analysis play a key role in securing communication through untrusted channels.This need is even more pronounced with the advent of cloud-centric environments.Symmetric encryption techniques can deliver high computational efficiencies only if the distribution and management of keys are secured.Public key cryptographic systems such as RSA and Elliptic Curve Cryptography (ECC), which have been the mainstay, are at risk due to arrival of quantum computers that can solve the integer factorization and discrete logarithm problems efficiently.Although post-quantum cryptography has made some breakthroughs, the lattice-based schemes still have to contend with difficulties such as heavy computation requirements, difficulty in choosing parameters, high power consumption, and low security-performance tradeoff.If lattices parameters are not properly set, they may not withstand lattice attacks and computational efficiency will also be degraded, limiting factor for their use in cloud environments.This study, in the quest for a solution, recommends the usage of N-th degree Truncated Polynomial Ring Units (NTRU) cryptosystem which is optimized by adjusting key parameters like lattice dimension (N), modulus (q), and small modulus (p) determining a Hermite factor (𝛿)-based approach.A metaheuristic optimization technique, Electric Eel Foraging Optimization (EEFO), is used to effectively balance security strength, correctness, and computational efficiency.Also, a new cryptographically strong and quantum-resistant key exchange capability is provided by the Improved Supersingular Isogeny Diffie-Hellman (ISIDH) protocol.The experiments have shown method to have an encryption strength of 0.95, an average success rate of 93.47%, and reduced energy consumption of 0.00085, thereby proving its efficiency.
As quantum computing technology evolves, it poses greater risks to current cryptography schemes such as RSA and Elliptic Curve Cryptography (ECC), widely used to secure digital communications These classical algorithms are based on mathematical problems that quantum algorithms such as Shore-Grover deal with. Both, can resolve much faster, making them vulnerable to quantum attack This has given rise to post-quantum cryptography (PQC), which focuses on developing quantum-resistant algorithms to protect data in the future of quantum computers classical cryptography Can Break This paper aims to provide a comprehensive insight into quantum-resistant cryptographic algorithms, including lattice-based, hash-based, code-based, and multivariable polynomial methods. It examines the efficiency, benefits, and challenges associated with implementing these algorithms in real-world applications. By comparing key parameters such as key size, encryption/decryption speed, and signature size, this study examines the relative strengths and limitations of post-quantum algorithms to their classical counterparts The results show that lattice-based algorithms , such as NTRU and Kyber, offer promising solutions with relative efficiency and manageable key sizes, making them potential candidates for quantum-resistant cryptography but other approaches , such as SPHINCS+ (hash-based) and McEliece (code-based), large -Face challenges of key size and slow encryption speed, which may limit their usefulness in some applications Despite these challenges, quantum post-cryptography is necessary to secure the future of digital communications.