Об использовании групп классов идеалов квадратичных полей для построения криптографических систем с открытым ключом

DOI10.4213/mvk3zbMath1469.94098OpenAlexW2793375719MaRDI QIDQ4958988

M. M. Glukhov

Publication date: 15 September 2021

Published in: Matematicheskie Voprosy Kriptografii [Mathematical Aspects of Cryptography] (Search for Journal in Brave)

Full work available at URL: http://mathnet.ru/eng/mvk3

zbMATH Keywords

discrete logarithm problemquadratic fieldclass groupkey exchange systemalgorithmic reduction of idealsring of integer numbers of quadratic fields

Mathematics Subject Classification ID

Algebraic coding theory; cryptography (number-theoretic aspects) (11T71) Quadratic extensions (11R11) Cryptography (94A60) Class numbers, class groups, discriminants (11R29)

Related Items

RSA cryptosystem for Dedekind rings

Cites Work

• The distance between ideals in the orders of a real quadratic field
• A key distribution system equivalent to factoring
• A key-exchange system based on imaginary quadratic fields
• A key-exchange protocol using real quadratic fields
• Efficient undeniable signature schemes based on ideal arithmetic in quadratic orders
• Kangaroos, monopoly and discrete logarithms
• On the computation of units and class numbers by a generalization of Lagrange's algorithm
• A signature scheme based on the intractability of computing roots
• A new public-key cryptosystem over a quadratic order with quadratic decryption time.
• An improved real-quadratic-field-based key exchange procedure
• The class-number of real quadratic number fields
• On the Integrability and Exact Solutions of a Generalized Korteweg-de-Vries Equation
• A Rigorous Subexponential Algorithm For Computation of Class Groups
• Breaking the Ong-Schnorr-Shamir Signature Scheme for Quadratic Number Fields
• A Probabilistic Factorization Algorithm with Quadratic Forms of Negative Discriminant
• SOME PUBLIC-KEY CRYPTO-FUNCTIONS AS INTRACTABLE AS FACTORIZATION
• A modification of the RSA public-key encryption procedure (Corresp.)
• Worst-case complexity bounds for algorithms in the theory of integral quadratic forms
• A Note on NUCOMP
• On Real Quadratic Number Fields Suitable for Cryptography
• Über die Klassenzahlen algebraischer Zahlkörper
• Cryptography based on number fields with large regulator
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