Quantum-secure cryptography is a dynamic field due to its crucial role in various domains. This field aligns with the ongoing efforts in data security. Post-quantum encryption (PQE) aims to counter the threats posed by future quantum computers, highlighting the need for further improvement. Based on the learning with error (LWE) system, this paper introduces a novel asymmetric encryption technique that encrypts entire messages of n bits rather than just 1 bit. This technique offers several advantages including an additive homomorphic cryptosystem. The robustness of the proposed lightweight public key encryption method, which is based on a new version of LWE, ensures that private keys remain secure and that original data cannot be recovered by an attacker from the ciphertext. By improving encryption and decryption execution time—which achieve speeds of 0.0427 ms and 0.0320 ms, respectively—and decreasing ciphertext size to 708 bits for 128-bit security, the obtained results are very promising.
Quantum-secure cryptography is a dynamic field due to its crucial role in various domains. This field aligns with the ongoing efforts in data security. Post-quantum encryption (PQE) aims to counter the threats posed by future quantum computers, highlighting the need for further improvement. Based on the learning with error (LWE) system, this paper introduces a novel asymmetric encryption technique that encrypts entire messages of n bits rather than just 1 bit. This technique offers several advantages including an additive homomorphic cryptosystem. The robustness of the proposed lightweight public key encryption method, which is based on a new version of LWE, ensures that private keys remain secure and that original data cannot be recovered by an attacker from the ciphertext. By improving encryption and decryption execution time—which achieve speeds of 0.0427 ms and 0.0320 ms, respectively—and decreasing ciphertext size to 708 bits for 128-bit security, the obtained results are very promising.
In this work, we introduce a novel post-quantum public key encryption scheme over integers, leveraging a hybrid approach that combines large random numbers with the Learning With Errors (LWE) system. The scheme addresses the security challenges posed by quantum computing advancements, aiming to provide a robust solution resistant to quantum-based attacks. By using the unknown random number hardness assumption with enhancements to the traditional LWE framework and operating directly on integers, this approach ensures a high level of cryptographic security while maintaining computational efficiency. Extensive theoretical and experimental analyses demonstrate that the proposed encryption system achieves state-of-the-art performance: encryption execution time as low as2.45×10−5seconds, decryption time of4.47×10−5seconds, and an integrity check time of5.30×10−5seconds. Moreover, the ciphertext size is reduced to only 1330 bits while maintaining a 256 -bit security level, representing a significant reduction in storage requirements compared to conventional lattice-based approaches. These results confirm that our scheme not only provides strong quantum-resistant security guarantees but also delivers excellent efficiency and scalability, making it a viable candidate for secure communications in bandwidth-limited and resource-constrained environments in the quantum era.
Ring-LWE (Ring Learning With Errors) is a post-quantum cryptography algorithm based on mathematical problems in number theory and algebra. It is an extension of LWE (Learning With Errors) first introduced by Oded Regev and is used for secure data encryption from quantum computer attacks. The process consists of three main steps: key generation, encryption, and decryption. Key generation uses random polynomials and noise to create public and private keys. While encryption produces ciphertext in the form of polynomial pairs, decryption uses the private key to return the ciphertext to the original message. To conduct the experiment, the modulus value q = 17, the modulus polynomial f(x) = x2 + 1, and the private key and random polynomial have been determined. The results of the experiment show that the message can be accurately decrypted using the private key, thus proving the success of this algorithm in maintaining data security. With its security properties that are resistant to quantum attacks, Ring-LWE is a promising alternative for future cryptography.
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.
The swift advancement of quantum computing devices holds the potential to create robust machines that can tackle an extensive array of issues beyond the scope of conventional computers. Consequently, quantum computing machines create new risks at a velocity and scale never seen before, especially with regard to encryption. Lattice-based cryptography is regarded as post-quantum cryptography’s future and a competitor to a quantum computer attack. Thus, there are several advantages to lattice-based cryptographic protocols, including security, effectiveness, reduced energy usage and speed. In this work, we study the learning with errors (LWE) problem and the cryptosystems that are based on the LWE problem and, in addition, we present a new efficient variant of LWE cryptographic scheme.
Due to the threat of future quantum computers, it is necessary to develop cryptographic schemes that are resistant to quantum attacks. Lattice based cryptographic schemes have resistance to quantum attacks and security under worst-case assumptions that are difficult to solve. To solve the problems of large size of public and private keys, low encryption efficiency, and large noise growth in identity based encryption schemes, an adaptive secure identity based all homomorphic encryption scheme based on Learning with Errors (LWE) is constructed. This scheme uses {0,1} matrices to store plaintext, significantly improving encryption efficiency compared to single bit encryption schemes. It uses key conversion technology to achieve homomorphic operations and modulus conversion technology to reduce noise. It also converts IDs into bit sequences to construct an encryption scheme for adaptive security. Compared to selective security that only provides security guarantees for specific types of attacks, adaptive security is suitable for general scenarios, providing higher security guarantees and being able to cope with more challenging attack situations. It has been proven through the LWE problem that the security of our proposed scheme satisfies IND-ID-CPA. Finally, the experimental results indicate that this scheme introduces less noise, and has higher encryption efficiency and performance.
The security of conventional public-key cryptography schemes is based on mathematical problems which are considered to be infeasible to solve by classical computers in a reasonable amount of time. However, the rise of quantum computers might break this security in the future. Post-quantum cryptography (PQC) aims to achieve secure schemes which are resistant against attacks assisted by quantum computers. Public-key cryptography refers to asymmetric cryptography in which encryption is done with a public key and decryption is done with a private key. Characteristic properties of public-key cryptography include the possibility to derive the private key from public information by solving some presumably hard problem. The hardness of the problem constitutes the basis for the system's security. In the post-quantum era, the security must be based on problems that are too hard to solve even for quantum computers. In this thesis, we will study lattice-based cryptography which is believed to serve as a good candidate for secure post-quantum public-key cryptography. Our main attention is in the problem of learning with errors, which is in the base of some lattice-based schemes and is linked to the hard problem of finding short vectors in a lattice.