NTWE: A Natural Combination of NTRU and LWE

Gärtner, Joel

doi:10.1007/978-3-031-40003-2_12

Cited by 3 publications

(3 citation statements)

References 17 publications

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“…The implementation of algorithms in strict accordance with Formula (5) also practically prevents attacks based on known signatures; however, using Formula (9) allows you to include multipliers equal to various degrees of the secret vector P in formulas for calculating elements of the public key, the presence of which is aimed at ensuring resistance to attacks using the search for potential equivalent keys. At the same time, the security level to a direct attack (calculation of secret vectors based on public-key elements) increases due to the appearance of additional square vector equations in the system of equations written in accordance with Formulas (7) and (8). The system of square vector equations considered in a direct attack has the following form:…”

Section: Discussionmentioning

confidence: 99%

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A Method for Specifying Complete Signature Randomization and an Algebraic Algorithm Based on It

Moldovyan,

Moldovyan

et al. 2024

Mathematics

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To eliminate the limitations of signature randomization in known algebraic algorithms with a hidden group, the security of which is based on the computational complexity of solving large systems of power equations, a method for ensuring complete randomization is proposed. Based on this method, a new algorithm of the indicated type was developed, using a four-dimensional finite non-commutative associative algebra as an algebraic basis. We obtained estimates of the security of algorithms to direct attacks as well as from attacks based on known signatures, which confirm the effectiveness of the proposed signature randomization method. Due to the relatively small size and signature of the public and private keys, the developed algorithm is of interest as a potential practical post-quantum digital signature scheme.

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Section: Discussionmentioning

confidence: 99%

“…Thus, the post-quantum cryptography should be based on computationally complex problems other than DLP and FP. For example, post-quantum public-key cryptographic algorithms on groups [7], algebraic lattices [8], codes [9], and hash functions [10] have been proposed.…”

Section: Introductionmentioning

confidence: 99%

A Method for Specifying Complete Signature Randomization and an Algebraic Algorithm Based on It

Moldovyan,

Moldovyan

et al. 2024

Mathematics

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“…Известны постквантовые двухключевые алгоритмы на группах [3], кодах [4,5], алгебраических решетках [6,7], хеш-функциях [8], булевых функциях [9], трудно обратимых отображениях [10,11] и некоммутативных алгебрах [12,13]. Обращают на себя внимание алгоритмы, основанные на трудно обратимых нелинейных отображениях с секретной лазейкой.…”

Section: Introductionunclassified

Algebraic Signature Algorithms With Complete Signature Randomization

2024

Cybersecurity Issues

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Цель работы: устранение потенциального снижения стойкости алгоритмов ЭЦП на некоммутативных алгебрах с увеличением числа подписанных электронных документов.Метод исследования: обеспечение полной рандомизации подписи путем включения в формулу генерации подгоночного элемента подписи случайного обратимого вектора как одного из множителей. Использование двух проверочных уравнений с вхождение одного и того же подгоночного элемента подписи. Формирование открытого ключа в виде набора векторов, вычисляемых в зависимости от векторов, содержащихся в скрытой (секретной) коммутативной группе конечной некоммутативной ассоциативной алгебры, используемой в качестве алгебраического носителя алгоритма ЭЦП.Результаты исследования: показана ограниченность рандомизации подписи, приводящая к снижению стойкости при увеличении числа подписанных документов, в ранее предложенных алгебраических алгоритмах ЭЦП со скрытой группой, стойкость которых основана на вычислительной трудности решения большой системы степенных уравнений. Разработан способ обеспечения полной рандомизации подписи в алгебраических алгоритмах указанного типа. Показано, что результаты изучения строения конечных некоммутативных алгебр (с точки зрения декомпозиции на множество коммутативных подалгебр), используемых в качестве алгебраического носителя, имеют существенное значение как для выбора параметров разрабатываемого алгоритма ЭЦП, так и для оценки его стойкости. Разработан новый алгебраический алгоритм ЭЦП, представляющий интерес как практичная постквантовая криптосхема благодаря достаточно малым размерам открытого ключа и подписи.Научная и практическая значимость результатов статьи состоит в разработке и апробации способа обеспечения полной рандомизации подписи и обоснования необходимости реализации последней в алгоритмах ЭЦП на некоммутативных ассоциативных алгебрах. Разработанный новый алгоритм ЭЦП является достаточно практичным и представляет интерес как прототип для разработки постквантовых алгоритмов ЭЦП, ориентированных на применение в условиях ограниченности доступных вычислительных ресурсов.

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Post-Quantum Public-Key Cryptoschemes on Finite Algebras

Moldovyan,

Moldovyan

2024

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One direction in the development of practical post-quantum public-key cryptographic algorithms is the use of finite algebras as their algebraic carrier. Two approaches in this direction are considered: 1) construction of electronic digital signature algorithms with a hidden group on non-commutative associative algebras and 2) construction of multidimensional cryptography algorithms using the exponential operation in a vector finite field (in a commutative algebra, which is a finite field) to specify a nonlinear mapping with a secret trapdoor. The first approach involves the development of two types of cryptoschemes: those based on the computational difficulty of a) the hidden discrete logarithm problem and b) solving a large system of quadratic equations. For the second type, problems arise in ensuring complete randomization of the digital signature and specifying non-commutative associative algebras of large dimension. Ways to solve these problems are discussed. The importance of studying the structure of finite non-commutative algebras from the point of view of decomposition into a set of commutative subalgebras is shown. Another direction is aimed at a significant (10 or more times) reduction in the size of the public key in multivariate-cryptography algorithms and is associated with the problem of developing formalized, parameterizable, unified methods for specifying vector finite fields of large dimensions (from 5 to 130) with a sufficiently large number of potentially implementable types and modifications each type (up to 2500 or more). Variants of such methods and topologies of nonlinear mappings on finite vector fields of various dimensions are proposed. It is shown that the use of mappings that specify the exponential operation in vector finite fields potentially eliminates the main drawback of known multivariate-cryptography algorithms, which is associated with the large size of the public key.

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NTWE: A Natural Combination of NTRU and LWE

Cited by 3 publications

References 17 publications

A Method for Specifying Complete Signature Randomization and an Algebraic Algorithm Based on It

A Method for Specifying Complete Signature Randomization and an Algebraic Algorithm Based on It

Algebraic Signature Algorithms With Complete Signature Randomization

Post-Quantum Public-Key Cryptoschemes on Finite Algebras

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