In this paper we report a more secure and efficient encryption algorithm based on the NTRU cryptographic scheme.NTRU is lattice based scheme resistant to quantum computing, hence it falls under the class of post quantum cryptosystems.It is based on shortest vector problem (svp) [9].The main characteristics of the system are low memory and low computational requirements but it provides high level of security.We present modifications in the NTRU scheme for making it more secure and efficient particul arly for applications in wireless and constrained devices.In the original scheme, repetitions in the plaintext message lead to repetitions in the cipher text, which is a source of weakness in the system.To overcome this problem each byte of the input has been digested with different operations that produce different encrypted text even for repeated content of the Plain text message.The second modification is enhancing the public key scheme that makes this system more robust.These two modifications in the NTRU scheme makes it secure even for use in the Quantum Computing environment.
In this paper we report a more secure and efficient encryption algorithm based on the NTRU cryptographic scheme.NTRU is lattice based scheme resistant to quantum computing, hence it falls under the class of post quantum cryptosystems.It is based on shortest vector problem (svp) [9].The main characteristics of the system are low memory and low computational requirements but it provides high level of security.We present modifications in the NTRU scheme for making it more secure and efficient particul arly for applications in wireless and constrained devices.In the original scheme, repetitions in the plaintext message lead to repetitions in the cipher text, which is a source of weakness in the system.To overcome this problem each byte of the input has been digested with different operations that produce different encrypted text even for repeated content of the Plain text message.The second modification is enhancing the public key scheme that makes this system more robust.These two modifications in the NTRU scheme makes it secure even for use in the Quantum Computing environment.
Lattice-based cryptosystems rely on certain lattice problems for their socurity, such as the shortest vector and the closest vector probtems. NTRU is a kind of lattice based public key cryptosysytem gaining much attention because of its high efficiency. Its encryption and decryption use a mixing system suggested by polynomial algebra combined with a clustering principle based on elementary probability theory. With the availability of quantum computers, the security of cryptosystems based on classical mathematic problems needs to be reevaluated. Since lattice reduction is the main threat to lattice-based cryptosystems, lattice reduction using quantum search algorithms are analyzed to evaluate the security of NTRU in this paper. According to our results, original security paratneters proposed for NTRU should be increased in the event that Grover's quantum search algorithm is used for lattice reduction.
The advent of large-scale quantum computers poses an existential threat to the security of current public-key cryptosystems, such as RSA and Elliptic Curve Cryptography (ECC), which rely on the computational intractability of integer factorization and discrete logarithms. This paper explores lattice-based cryptography as a promising candidate for post-quantum security. We delve into the mathematical foundations of lattices, specifically focusing on hard problems like the Shortest Vector Problem (SVP), Closest Vector Problem (CVP), Small Integer Solution (SIS), and Learning With Errors (LWE) problems, which are believed to remain intractable even for quantum computers. We provide a comprehensive review of prominent lattice-based constructions, including NTRU, Kyber, and Dilithium, highlighting their security proofs, efficiency considerations, and suitability for various cryptographic primitives such as public-key encryption, key-exchange mechanisms, and digital signatures. Furthermore, we discuss the challenges and opportunities associated with their deployment, including parameter selection, resistance to side-channel attacks, and integration into existing cryptographic infrastructures. By examining the theoretical underpinnings and practical implications, this work aims to solidify understanding of lattice-based methods as a robust and essential component of the cryptographic landscape in the quantum era, moving beyond the traditional RSA frontier.
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.
In this work, a lightweight post-quantum cryptographic protocol specifically designed for resource-constrained IoT edge devices is presented, addressing the vulnerability of conventional encryption to quantum computing attacks. The proposed protocol employs a modified NTRU-based algorithm with reduced parameter sizes, achieving switch production in 12.4 ms, encryption in 8.2 ms, and total energy consumption of 4.2 mJ per exchange - 63% lower than standard post-quantum protocols. Experimental results demonstrate resistance against quantum attacks exceeding 1018 processes while maintaining response times under 50 ms, with a compression mechanism reducing message size to 186 bytes. The protocol achieves an optimal balance between post-quantum security and operational efficiency, offering a practical solution for narrow-bandwidth, battery-limited IoT environments.
The imminent threat of quantum computing poses a significant challenge to the security of current public-key cryptographic systems, most notably RSA. These classical algorithms rely on mathematical problems, such as integer factorization and discrete logarithms, which are efficiently solvable by Shor's algorithm on a sufficiently powerful quantum computer. This paper explores ideal lattices as a robust post-quantum foundation for asymmetric cryptography, offering a compelling alternative to traditional schemes. We delve into the mathematical underpinnings of ideal lattices, including the Ring Learning With Errors (RLWE) and Shortest Vector Problem (SVP), which are conjectured to be hard even for quantum computers. The advantages of ideal lattice-based cryptography, such as its quantum resistance, efficiency, and versatility in constructing various cryptographic primitives, are thoroughly discussed. We examine prominent examples like NTRU and CRYSTALS-Kyber, highlighting their design principles and performance characteristics. Furthermore, the paper addresses the ongoing standardization efforts by NIST and the practical considerations for migrating to lattice-based schemes. The objective is to present a comprehensive analysis demonstrating why ideal lattices are a leading candidate for securing digital communications in the quantum era, providing a secure and efficient pathway beyond the limitations of RSA.
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.