NTRU is one of the important lattice-based post-quantum cryptography methods, offering resistance against quantum computing attacks. However, a drawback of NTRU lies in its relatively low efficiency in generating key pairs. Therefore, this study proposes an NTRU-based key expansion method that enables efficient public key expansion. Furthermore, the proposed method is applied to an anonymous certificate scheme, allowing an end entity to generate a key pair only once, after which the certificate authority can expand multiple distinct public keys for anonymity. The experimental results demonstrate that the proposed key expansion method achieves significantly higher efficiency than key pair generation.
NTRU is one of the important lattice-based post-quantum cryptography methods, offering resistance against quantum computing attacks. However, a drawback of NTRU lies in its relatively low efficiency in generating key pairs. Therefore, this study proposes an NTRU-based key expansion method that enables efficient public key expansion. Furthermore, the proposed method is applied to an anonymous certificate scheme, allowing an end entity to generate a key pair only once, after which the certificate authority can expand multiple distinct public keys for anonymity. The experimental results demonstrate that the proposed key expansion method achieves significantly higher efficiency than key pair generation.
Abstract. Public key exchange protocol is identified as an important application in the field of public-key cryptography. Most of the existing public key exchange schemes are Diffie-Hellman (DH)-type, whose security is based on DH problems over different group-s. Note that there exists Shor’s polynomial-time algorithm to solve these DH problems when a quantum computer is available, we are therefore motivated to seek for a non-DH-type and quantum resistant key exchange protocol. To this end, we turn our attention to lattice-based cryptography. The higher methodology behind our roadmap is that in anal-ogy to the link between ElGamal, DSA, and DH, one should expect a NTRU lattice-based key exchange primitive in related to NTRU-ENCRYPT and NTRU-SIGN. However, this excepted key exchange protocol is not presented yet and still missing. In this paper, this missing key exchange protocol is found, hereafter referred to as NTRU-KE, which is stud-ied in aspects of security and key-mismatch failure. In comparison with ECDH (Elliptic Curve-based Diffie-Hellman), NTRU-KE features faster computation speed, resistance to quantum attack, and more communication overhead. Accordingly, we come to the conclu-sion that NTRU-KE is currently comparable with ECDH. However, decisive advantage of NTRU-KE will occur when quantum computers become a reality.
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.
Although the current lattice-based ring signcryption scheme resists quantum attacks,it has large key storage and high encryption/decryption time.The linkable lattice ring signcryption scheme not only can protect signer anonymity,but also can determine whether two signatures are generated by the same signer.Thus,based on the compact Gaussian sampling algorithm and rejection sampling technique,the identity-based linkable ring signcryption scheme is constructed on the NTRU lattice.Firstly,the system master key is generated using the trapdoor generation algorithm on the NTRU lattice.Then private keys of ring members are obtained based on the compact Gaussian sampling algorithm.Finally,the user signature is generated using rejection sampling,and the key encapsulation mechanism encrypts the signature.Security proof in the random oracle model (ROM) that DRLWE and NTRU small integer solutions are difficult to solve ensures confidentiality,unforgeability,unconditional anonymity,and linkability.Performance analysis shows that compared to the lattice-based ring signcryption and linkable ring signature schemes on NTRU,the proposed scheme has a smaller public key and lower encryption/decryption cost,greatly improving efficiency.
Wireless sensor networks (WSNs) are pervasively employed in critical domains such as smart healthcare, industrial automation, and environmental surveillance, where secure access control is essential. User authentication protocols are vital for thwarting unauthorized intrusions, yet the vast majority of existing schemes rely on conventional public-key cryptography (such as ECC, RSA), which is provably insecure in the post-quantum era due to Shor's algorithm. This motivates the design of post-quantum authentication that is also lightweight for resource-limited sensors. To address this challenge, we propose an efficient authentication and key agreement protocol based on Number Theory Research Unit (NTRU), a lattice-based cryptosystem offering proven resistance to quantum attacks. We have proven the correctness and security of our scheme through BAN logic and random oracle model and demonstrated through informal analysis that our scheme can resist various attack methods and possesses high security features. Moreover, we thoroughly evaluate our protocol against the most recent state-of-the-art schemes. The results indicate that our scheme has the lowest computational cost, and its communication cost is superior to that of most other schemes. Overall, our proposed protocol provides a robust, efficient, and future-proof authentication solution for WSNs, well-suited for deploying WSNs environments.
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.