The only known threat to some symmetric cryptographic schemes like DES is Grover’s algorithm that proposes a square root speed-up over classical brute force algorithms. NIST [14] points out that if the key sizes are sufficient, symmetric cryptographic schemes (specifically the Advanced Encryption Standard-AES) are resistant to quantum computers. The development of quantum computer is on full pace, hopefully it might be available in a decade. Thus, it is necessary to develop efficient quantum secure public key cryptosystems to provide safe key exchange in quantum era. In this paper we presented an efficient implementation of a Ring-Learning with errors public key cryptosystem whose security is based on intractability of hard problem on lattices. And comparative analysis of proposed cryptosystem with RSA, ECDH and LWE based key exchange protocols is presented.
The only known threat to some symmetric cryptographic schemes like DES is Grover’s algorithm that proposes a square root speed-up over classical brute force algorithms. NIST [14] points out that if the key sizes are sufficient, symmetric cryptographic schemes (specifically the Advanced Encryption Standard-AES) are resistant to quantum computers. The development of quantum computer is on full pace, hopefully it might be available in a decade. Thus, it is necessary to develop efficient quantum secure public key cryptosystems to provide safe key exchange in quantum era. In this paper we presented an efficient implementation of a Ring-Learning with errors public key cryptosystem whose security is based on intractability of hard problem on lattices. And comparative analysis of proposed cryptosystem with RSA, ECDH and LWE based key exchange protocols is presented.
Ring Learning With Errors (Ring-LWE) is one of the basic schemes used to develop cryptographic algorithms that are resistant to quantum attacks, offering better computational efficiency compared to standard Learning With Errors (LWE). Ring-LWE uses the algebraic characteristics of polynomial rings to create a robust and fast encryption system. This study implements and evaluates the Ring-LWE algorithm in the context of public key exchange and encryption. Simulations are performed with various security parameters, including modulus size and error rate, to test the resistance to brute force attacks and lattice-based attacks. The experimental results show that the Ring-LWE algorithm can achieve a balance between security and computational efficiency, with shorter processing time than conventional LWE while maintaining a high level of security even in the face of quantum computers. From this study, it can be concluded that Ring-LWE is an excellent choice for application in post-quantum security systems, especially in encrypted communication and digital authentication applications. The next step can be directed at optimizing resource utilization and testing against various types of attacks.
With the possibility of quantum computers making an appearance, possibly capable of breaking several well established and widespread crytposystems (especially those that implement public key cryptography), necessity has arisen to create new cryptographic algorithms which remain safe even against adversaries using quantum computers. Several algorithms based on different mathematical problems have been proposed which are considered to be hard to solve with quantum computers. In recent years, a new lattice-based mathematical problem called Learning With Errors (and its variant Ring - Learning With Errors) was introduced, and several cryptosystems based on this problem were introduced, some of which are becoming practical enough to compete with traditional schemes that have been used for decades. The primary focus in this work is the implementation of two Ring - Learning With Errors based schemes (one key exchange mechanism and one digital signature scheme) on the TLS protocol via the OpenSSL library as a way of checking their overall viability in real-world scenarios, by comparing them to classical schemes implementing the same functionalities.
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 imminent threat posed by cryptographically relevant quantum computers necessitates a paradigm shift in public-key cryptography. Traditional schemes like RSA and Elliptic Curve Cryptography (ECC), the bedrock of modern secure communication, are vulnerable to quantum algorithms such as Shor's. This paper explores Module-LWE (Learning With Errors) cryptosystems as a compelling post-quantum replacement for RSA. We delve into the foundational mathematical properties of Module-LWE, highlighting its security rooted in the presumed intractability of hard lattice problems. A key focus is the concept of "tightly reduced hardness," which signifies that the security of a cryptographic scheme based on Module-LWE can be directly and efficiently linked to the worst-case hardness of an underlying lattice problem. This tight reduction allows for more aggressive parameter choices, leading to improved efficiency, smaller key and ciphertext sizes, and enhanced performance compared to generic LWE or other post-quantum candidates, without compromising security. We analyze the advantages of Module-LWE in terms of provable security, performance characteristics, and its suitability for key encapsulation mechanisms and digital signatures. The discussion encompasses its practical implications, implementation considerations, and its strong position within the NIST Post-Quantum Cryptography standardization effort, ultimately presenting Module-LWE as a robust, efficient, and future-proof alternative to RSA in a post-quantum world.
Among the different cryptosystems, the Public Key Cryptosystems (PKCS) are of great usage and are used in many applications. Most of the current PKCS are based on a hard problem making the cryptanalysis of such cipher infeasible given the current computing and memory availability. However, Quantum Computing threatens all the current PKCS as they offer a new model that can solve those hard problems, e.g. the factorization problem of RSA or the discrete logarithm problem of ELGAMAL algorithm. Lattice Based PKCS are a promising filed to introduce an immune cipher system against quantum cryptanalysis. This paper presents a summary of recent progress in the field of lattice-based cryptography, by focusing on the recent advancement in lattice-based public key cryptosystems and key exchange mechanisms based on the learning with errors (LWE) problem and its ring variant Ring-LWE.
The rapid development of quantum computers poses a significant threat to the majority of current authenticated key exchang protocols, designed on the hardness of large integer factorization and discrete logarithm problems. Therefore, it is imperative to develop secure and efficient quantum-resistant authenticated key exchang protocols. This paper designs a new public-key cryptographic scheme for identity authentication based on Ring Learning With Errors (RLWE) problem and error reconciliation mechanism. Based on the scheme, we further design a quantum-resistant authenticated key exchange protocol (AKE). This protocol is provably secure under the standard eCK model and achieves forward secrecy. Compared with other classic key exchange protocols based on the RLWE problem, our protocol shows comprehensive advantages in terms of security, computational complexity, and communication complexity.