Challenges
Datasets
Workspaces
Papers
Discussions
Leaderboard
Log inSign up
Challenges
Datasets
Workspaces
Papers
Discussions
Leaderboard
Blog
Job Board
Q3AS

© 2026 Aqora Quantum S.A.S.

TermsPrivacyLegal Notice

Jurnal Teknik Indonesia

Cryptography with the Ring-LWE (Learning With Errors) Algorithm

Hesty Sitohang, Roy Untung Pratama Saing, Agnes Selaras Osabela Sarahono, Joy Sofater Purba, Petrus Tebai, Paska Marto Hasugian

Published May 20, 2024• 0 citations
Publisher

Abstract

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.

DOI
10.58471/ju-ti.v3i01.653

Related papers

Cryptography with Ring Algorithm – LWE

Paramita Lumban Gaol, Stephen Buulolo, Aritmen Andreas L. Manurung +1 more

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.

Login Jurnal Teknologi Komputer•Jun 25, 2024•0 citations

An Enhanced Learning with Error-Based Cryptosystem: A Lightweight Quantum-Secure Cryptography Method

Mostefa Kara, Konstantinos Κarampidis, Giorgos M. Papadourakis +2 more

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.

J — Multidisciplinary Scientific Journal•Oct 13, 2024•3 citations

Applications of Ring Theory in Post-Quantum Cryptography

Dr. Muhammed Basheer

Post-quantum cryptography (PQC) aims to develop cryptographic protocols resistant to attacks by quantum computers, which threaten classical schemes based on integer factorization and discrete logarithm problems. Among various approaches, lattice-based cryptography has emerged as one of the most promising candidates for PQC. Within this domain, ring theory plays a foundational role by providing the algebraic structures—specifically polynomial rings modulo cyclotomic polynomials—used to define hard problems like Ring Learning With Errors (Ring-LWE). These problems underpin efficient and secure cryptographic primitives such as key exchange, encryption, digital signatures, and homomorphic encryption. This paper explores the theoretical background of ring theory relevant to PQC and discusses how it enables the construction of cryptosystems with strong security assumptions and practical efficiency. We also analyze specific schemes that utilize ring-based lattices, including New Hope, NTRUEncrypt, and Dilithium, highlighting the advantages of ring structures in reducing key sizes and improving computational speed. Furthermore, we review the implementation challenges and potential future directions for integrating ring theory into next-generation cryptographic protocols suitable for a post-quantum world.

International Journal for Research in Applied Science and Engineering Technology•Jun 5, 2025•0 citations

R-LWE-Based Distributed Key Generation and Threshold Decryption

Ferran Alborch Escobar, Ramiro Martínez, Paz Morillo

Ever since the appearance of quantum computers, prime factoring and discrete logarithm-based cryptography have been questioned, giving birth to the so-called post-quantum cryptography. The most prominent field in post-quantum cryptography is lattice-based cryptography, protocols that are proved to be as difficult to break as certain hard lattice problems like Learning with Errors (LWE) or Ring Learning with Errors (R-LWE). Furthermore, the application of cryptographic techniques to different areas, like electronic voting, has also nourished a great interest in distributed cryptography. In this work, we will give two original threshold protocols based in the lattice problem R-LWE: one for key generation and one for decryption. We will prove them both correct and secure under the assumption of hardness of some well-known lattice problems. Finally, we will give a rough implementation of the protocols in C to give some tentative results about their viability, in particular our model generates keys in the order of 103 ms and decrypts and encrypts in the order of 102 ms.

Mathematics•Feb 25, 2022•4 citations

Learning with Errors and Lattice-Based Post-Quantum Public-Key Cryptography

Jaskari, Mikko

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.

•Dec 5, 2025•0 citations

A Latticed-Based Public Key Encryption with KDM Security from R-LWE

Yan Fang Wu, Zheng Huang, Qiao Yan Wen

Since the introduction of the ring learning with errors (R-LWE) by Lyubashevsky, Peikert and Regev, many efficient and secure applications were founded in cryptography. In this paper, we mainly present an efficient public-key encryption scheme based on the R-LWE assumption. It is very simple to describe and analyze. As well as it can achieve security against certain key-dependent message (KDM) attacks. Namely, this efficient encryption scheme can securely encrypt its own secret key. The security of this scheme follows from the already proven hardness of the R-LWE problem since the R-LWE assumption is reducible to worst-case problems on the ideal lattice. Besides, the scheme enjoys a high level efficiency and low cost since the operations of the scheme are very simple and fast. The cost of both the encryption and decryption is only polylog(n) bit per message symbol.

Advanced engineering forum•Sep 1, 2012•0 citations
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.
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.
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.
Post-quantum cryptography (PQC) aims to develop cryptographic protocols resistant to attacks by quantum computers, which threaten classical schemes based on integer factorization and discrete logarithm problems. Among various approaches, lattice-based cryptography has emerged as one of the most promising candidates for PQC. Within this domain, ring theory plays a foundational role by providing the algebraic structures—specifically polynomial rings modulo cyclotomic polynomials—used to define hard problems like Ring Learning With Errors (Ring-LWE). These problems underpin efficient and secure cryptographic primitives such as key exchange, encryption, digital signatures, and homomorphic encryption. This paper explores the theoretical background of ring theory relevant to PQC and discusses how it enables the construction of cryptosystems with strong security assumptions and practical efficiency. We also analyze specific schemes that utilize ring-based lattices, including New Hope, NTRUEncrypt, and Dilithium, highlighting the advantages of ring structures in reducing key sizes and improving computational speed. Furthermore, we review the implementation challenges and potential future directions for integrating ring theory into next-generation cryptographic protocols suitable for a post-quantum world.
Ever since the appearance of quantum computers, prime factoring and discrete logarithm-based cryptography have been questioned, giving birth to the so-called post-quantum cryptography. The most prominent field in post-quantum cryptography is lattice-based cryptography, protocols that are proved to be as difficult to break as certain hard lattice problems like Learning with Errors (LWE) or Ring Learning with Errors (R-LWE). Furthermore, the application of cryptographic techniques to different areas, like electronic voting, has also nourished a great interest in distributed cryptography. In this work, we will give two original threshold protocols based in the lattice problem R-LWE: one for key generation and one for decryption. We will prove them both correct and secure under the assumption of hardness of some well-known lattice problems. Finally, we will give a rough implementation of the protocols in C to give some tentative results about their viability, in particular our model generates keys in the order of 103 ms and decrypts and encrypts in the order of 102 ms.
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.
Since the introduction of the ring learning with errors (R-LWE) by Lyubashevsky, Peikert and Regev, many efficient and secure applications were founded in cryptography. In this paper, we mainly present an efficient public-key encryption scheme based on the R-LWE assumption. It is very simple to describe and analyze. As well as it can achieve security against certain key-dependent message (KDM) attacks. Namely, this efficient encryption scheme can securely encrypt its own secret key. The security of this scheme follows from the already proven hardness of the R-LWE problem since the R-LWE assumption is reducible to worst-case problems on the ideal lattice. Besides, the scheme enjoys a high level efficiency and low cost since the operations of the scheme are very simple and fast. The cost of both the encryption and decryption is only polylog(n) bit per message symbol.