NTRU software implementation for constrained devices

The NTRUEncrypt is a public-key cryptosystem based on the shortest vector problem. Its main characteristics are the low memory and computational requirements while providing a high security level. This document presents an implementation and optimization of the NTRU public-key cryptosys- tem for constrained devices. Speci cally the NTRU cryptosystem has been implemented on the ATMega128 and the ATMega163 microcontrollers. This has turned in a major e ort in order to reduce the consumption of memory and op- timize the computational resources. The di erent resulting optimizations have been compared and evaluated throught the AVR Studio 4 [1]. The nal outcome has also been compared with other published public-key cryptosystems as RSA or ECC showing the great performance NTRUEncrypt is able to deliver at a surprising very low cost

Enhancement of Nth degree truncated polynomial ring for improving decryption failure

Nth Degree Truncated Polynomial (NTRU) is a public key cryptosystem constructed in a polynomial ring with integer coefficients that is based on three main key integer parameters N; p and q. However, decryption failure of validly created ciphertexts may occur, at which point the encrypted message is discarded and the sender re-encrypts the messages using different parameters. This may leak information about the private key of the recipient thereby making it vulnerable to attacks. Due to this, the study focused on reduction or elimination of decryption failure through several solutions. The study began with an experimental evaluation of NTRU parameters and existing selection criteria by uniform quartile random sampling without replacement in order to identify the most influential parameter(s) for decryption failure, and thus developed a predictive parameter selection model with the aid of machine learning. Subsequently, an improved NTRU modular inverse algorithm was developed following an exploratory evaluation of alternative modular inverse algorithms in terms of probability of invertibility, speed of inversion and computational complexity. Finally, several alternative algebraic ring structures were evaluated in terms of simplification of multiplication, modular inversion, one-way function properties and security analysis for NTRU variant formulation. The study showed that the private key f and large prime q were the most influential parameters in decryption failure. Firstly, an extended parameter selection criteria specifying that the private polynomial f should be selected such that f(1) = 1, number of 1 coefficients should be one more or one less than -1 coefficients, which doubles the range of invertible polynomials thereby doubling the presented key space. Furthermore, selecting q 2:5754 f(1)+83:9038 gave an appropriate size q with the least size required for successful message decryption, resulting in a 33.05% reduction of the public key size. Secondly, an improved modular inverse algorithm was developed using the least squares method of finding a generalized inverse applying homomorphism of ring R and an (N x N) circulant matrix with integer coefficients. This ensured inversion for selected polynomial f except for binary polynomial having all 1 coefficients. This resulted in an increase of 48% to 51% whereby the number of invertible polynomials enlarged the key space and consequently improved security. Finally, an NTRU variant based on the ring of integers, Integer TRUncated ring (ITRU) was developed to address the invertiblity problem of key generation which causes decryption failure. Based on this analysis, inversion is guaranteed, and less pre-computation is required. Besides, a lower key generation computational complexity of O(N2) compared to O(N2(log2p+log2q)) for NTRU as well as a public key size that is 38% to 53% smaller, and a message expansion factor that is 2 to15 times larger than that of NTRU enhanced message security were obtained

NTRU software implementation for constrained devices

The NTRUEncrypt is a public-key cryptosystem based on the shortest vector problem. Its main characteristics are the low memory and computational requirements while providing a high security level. This document presents an implementation and optimization of the NTRU public-key cryptosys- tem for constrained devices. Speci cally the NTRU cryptosystem has been implemented on the ATMega128 and the ATMega163 microcontrollers. This has turned in a major e ort in order to reduce the consumption of memory and op- timize the computational resources. The di erent resulting optimizations have been compared and evaluated throught the AVR Studio 4 [1]. The nal outcome has also been compared with other published public-key cryptosystems as RSA or ECC showing the great performance NTRUEncrypt is able to deliver at a surprising very low cost

ITRU: NTRU-based cryptosystem using ring of integers

NTRU is a public key cryptosystem whose structure is based on the polynomial ring of integers. We present ITRU, an NTRU-like cryptosystem based on the ring of integers. We discuss the parameter selection procedure and provide an implementation of ITRU using an illustration. A comparison of the performance of ITRU and NTRU is provided which highlights the difference in parameter selection, invertibility and successful message decryption. We show that ITRU is an improvement of NTRU in that, it ensures successful message decryption upon implementation using the proposed parameter selection algorithm

A New Provably Secure Cryptosystem Using Dedekind Domain Direct Product Approach

We would like to prevent, detect, and protect communication and information systems' attacks, which include unauthorized reading of a message of file and traffic analysis or active attacks, such as modification of messages or files, and denial of service by providing cryptographic techniques. If we prove that an encryption algorithm is based on mathematical NP-hard problems, we can prove its security. In this paper, we present a new NTRU-Like public-key cryptosystem with security provably based on the worst-case hardness of the approximate lattice problems (NP-hard problems) in some structured lattices (ideal lattices) in order to attain the applicable objectives of preserving the confidentiality of communication and information system resources (includes hardware, software, firmware, information/data, and telecommunications). Our proposed scheme is an improvement of ETRU cryptosystem. ETRU is an NTRU-Like public-key cryptosystem based on the Eisenstein integers Z [f_3 ] where f_3 is a primitive cube root of unity. ETRU has heuristic security and it has no proof of security. We show that our cryptosystem has security stronger than that of ETRU, over cartesian product of dedekind domains and extended cyclotomic polynomials. We prove the security of our main algorithm from the R-SIS and R-LWE problems as NP-hard problems

Cryptanalysis of an NTRU-based Proxy Encryption Scheme from ASIACCS\u2715

In ASIACCS 2015, Nuñez, Agudo, and Lopez proposed a proxy re-encryption scheme, NTRUReEncrypt, based on NTRU, which allows a proxy to translate ciphertext under the delegator\u27s public key into a re-encrypted ciphertext that can be decrypted correctly by delegatee\u27s private key. In addition to its potential resistance to quantum algorithm, the scheme was also considered to be efficient. However, in this paper we point out that the re-encryption process will increase the decryption error, and the increased decryption error will lead to a reaction attack that enables the proxy to recover the private key of the delegator and the delegatee. Moreover, we also propose a second attack which enables the delegatee to recover the private key of the delegator when he collects enough re-encrypted ciphertexts from a same message. We reevaluate the security of NTRUReEncrypt, and also give suggestions and discussions on potential mitigation methods

New Security Definitions, Constructions and Applications of Proxy Re-Encryption

La externalización de la gestión de la información es una práctica cada vez más común, siendo la computación en la nube (en inglés, cloud computing) el paradigma más representativo. Sin embargo, este enfoque genera también preocupación con respecto a la seguridad y privacidad debido a la inherente pérdida del control sobre los datos. Las soluciones tradicionales, principalmente basadas en la aplicación de políticas y estrategias de control de acceso, solo reducen el problema a una cuestión de confianza, que puede romperse fácilmente por los proveedores de servicio, tanto de forma accidental como intencionada. Por lo tanto, proteger la información externalizada, y al mismo tiempo, reducir la confianza que es necesario establecer con los proveedores de servicio, se convierte en un objetivo inmediato. Las soluciones basadas en criptografía son un mecanismo crucial de cara a este fin. Esta tesis está dedicada al estudio de un criptosistema llamado recifrado delegado (en inglés, proxy re-encryption), que constituye una solución práctica a este problema, tanto desde el punto de vista funcional como de eficiencia. El recifrado delegado es un tipo de cifrado de clave pública que permite delegar en una entidad la capacidad de transformar textos cifrados de una clave pública a otra, sin que pueda obtener ninguna información sobre el mensaje subyacente. Desde un punto de vista funcional, el recifrado delegado puede verse como un medio de delegación segura de acceso a información cifrada, por lo que representa un candidato natural para construir mecanismos de control de acceso criptográficos. Aparte de esto, este tipo de cifrado es, en sí mismo, de gran interés teórico, ya que sus definiciones de seguridad deben balancear al mismo tiempo la seguridad de los textos cifrados con la posibilidad de transformarlos mediante el recifrado, lo que supone una estimulante dicotomía. Las contribuciones de esta tesis siguen un enfoque transversal, ya que van desde las propias definiciones de seguridad del recifrado delegado, hasta los detalles específicos de potenciales aplicaciones, pasando por construcciones concretas

Методи розв’язання задачі LPN над скінченними кільцями для оцінювання стійкості симетричних постквантових шифросистем

Дисертація на здобуття наукового ступеня кандидата технічних наук за спеціальністю 05.13.21 – Системи захисту інформації. – Харківський національний університет імені В. Н. Каразіна, Міністерства освіти і науки України. – Харків, 2021. У дисертації розв’язано актуальну наукову задачу розробки більш ефективних (в порівнянні з перебірним) методів розв’язання задачі LPN над скінченними кільцями для оцінювання стійкості симетричних постквантових шифросистем. Вперше отримано аналітичні оцінки обсягу матеріалу, достатнього для розв’язання із заданою достовірністю задачі LPN над довільним скінченним кільцем, які дозволяють визначити часову складність узагальненого алгоритму BKW. Розроблено два методи підвищення ефективності розв’язання задачі LPN за допомогою ММП. Вперше розроблено метод побудови нових алгоритмів розв’язання СР над кільцем за довільною скінченною сукупністю вхідних таких алгоритмів. Наведено аналітичні вирази оцінок достовірності та часової складності алгоритмів розв’язання СР, які будуються за допомогою розробленого методу, через відповідні характеристики вхідних алгоритмів. Головним практичним результатом роботи є можливість оцінювати стійкість симетричних шифросистем, які будуються над скінченними кільцями та базуються на складності розв’язання задачі LPN

Modified Mclaren-marsaglia Pseudo-random Number Generator and Stochastic Key Agreement

A discussion of problems in cryptographic applications, with a brief survey of pseudo-random number generators (PRNG) used as synchronous stream ciphers, leads to a discussion of the McClaren-Marsaglia shuffling PRNG, and some means of altering its structure to both provide a more secure PRNG and to provide effective means by which to inject aperiodicity into a modified form of McClaren-Marsaglia. A discussion of two closely related protocols using this modified form of McClaren-Marsaglia as means by which correspondents may agree upon a set of random bits in a manner suitable for use in cryptographic applications is then presented, with implementation in the C programming language of the second protocol. Analysis of the protocols concludes that a reasonable expectation of confidentiality and cryptographic strength in the agreed bit-sequence is obtained.Computer Science Departmen