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A novel method for development of post-quantum digital signature schemes

Dmitry Moldovyan, Alexandr Moldovyan, Nikolay Moldovyan
2020 Information and Control Systems  
The first (second) form has allowed to use the finite commutative (non-commutative) algebra as algebraic support of the developed signature schemes.  ...  Results: A method for designing post-quantum signature schemes is proposed.  ...  Financial support This work was supported by the budget theme No. 0060-2019-010.  ... 
doi:10.31799/1684-8853-2020-6-21-29 fatcat:wfyhytr33ffx3cwscwllqbpd5i

Algebras and universal quantum computations with higher dimensional systems

Alexander Yu. Vlasov
2002 arXiv   pre-print
Here is discussed application of the Weyl pair to construction of universal set of quantum gates for high-dimensional quantum system.  ...  It is shown next, how for quantum computation with qubits can be used two-dimensional analog of this Cayley-Weyl matrix algebras, i.e.  ...  As an example of such a commutation law it is possible to mention AB = ζBA (A, B ∈ A, ζ ∈ C) (5) It is commutative algebra for ζ = 1 and anticommutative one for ζ = −1.  ... 
arXiv:quant-ph/0210049v1 fatcat:fvchjeeqc5d4fmpkoj6jassdc4

Candidate for practical post-quantum signature scheme

Nikolay A. Moldovyan, St. Petersburg Federal Research Center of the Russian Academy of Sciences, Alexandr A. Moldovyan, St. Petersburg Federal Research Center of the Russian Academy of Sciences
2020 Vestnik of Saint Petersburg University Applied Mathematics Computer Science Control Processes  
A 4-dimensional finite non-commutative associative algebra is applied as algebraic support of the cryptoscheme.  ...  A new criterion of post-quantum security is used to design a practical signature scheme based on the computational complexity of the hidden discrete logarithm problem.  ...  multiplication operation in the finite non-commutative associative algebra (FNAA) used as algebraic support of the signature scheme.  ... 
doi:10.21638/11701/spbu10.2020.410 fatcat:3khmribxk5gczclk6tehn4pfwe

A novel method for developing post-quantum cryptoschemes and a practical signature algorithm

Nikolay Andreevich Moldovyan, Dmitriy Nikolaevich Moldovyan
2021 Applied Computing and Informatics  
different finite commutative associative algebras as a single algebraic support of the digital signature scheme and setting two different verification equation for a single signature.  ...  Two new finite commutative associative algebras, multiplicative group of which possesses four-dimensional cyclicity, have been proposed as a suitable algebraic support.Originality/valueThe introduced method  ...  in non-commutative finite associative algebras (FAAs).  ... 
doi:10.1108/aci-02-2021-0036 fatcat:mtql7f7xe5gaxh4jgqgkicwr6m

Curious properties of free hypergraph C*-algebras [article]

Tobias Fritz
2019 arXiv   pre-print
We show that they coincide with the class of finite colimits of finite-dimensional commutative C*-algebras, and also with the class of C*-algebras associated to synchronous nonlocal games.  ...  As special cases, the class of free hypergraph C*-algebras comprises quantum permutation groups, maximal group C*-algebras of graph products of finite cyclic groups, and the C*-algebras associated to quantum  ...  Up to isomorphism, the class of hypergraph C*-algebras coincides with the class of finite colimits in C * alg 1 of finite-dimensional commutative C*-algebras.  ... 
arXiv:1808.09220v3 fatcat:7qdctzsjs5ge5l6bxzykqp5d2q

A post-quantum digital signature scheme on groups with four-dimensional cyclicity

Nikolay Moldovyan, Dmitry Moldovyan
2021 Information and Control Systems  
Purpose: Development of a new form of the hidden discrete logarithm problem set in finite commutative groups possessing multi-dimensional cyclicity, and a method for designing post-quantum signature schemes  ...  Two new four-dimensional finite commutative associative algebras have been proposed as algebraic support for the introduced computationally complex problem.  ...  One of attractive post-quantum primitives is the hidden discrete logarithm problem (HDLP) defined usually in non-commutative finite associative algebras (FAAs) .  ... 
doi:10.31799/1684-8853-2021-2-43-51 fatcat:zueeen24uzefrlyuzpnyr2egei

Post-quantum commutative encryption algorithm

A.A. Moldovyan, D.N. Moldovyan, N.A. Moldovyan
2019 Computer Science Journal of Moldova  
A candidate for post-quantum commutative encryption algorithm is proposed, using the computations in the 6-dimensional finite non-commutative associative algebra with a large set of the right-sided global  ...  The proposed algorithm is used as the base of the post-quantum no-key protocol.  ...  Preliminaries Algebraic carriers of the HDLP In a finite m-dimensional vector space defined over a finite field, for example, GF (p) there are defined two standard operations: addition of two vectors  ... 
doaj:0835f79b7caf44bda6240c26011f6821 fatcat:3h7umg45eja7zja3jjrzgdzizu

Fully graphical treatment of the quantum algorithm for the Hidden Subgroup Problem [article]

Stefano Gogioso, Aleks Kissinger
2017 arXiv   pre-print
Being fully diagrammatic, our proof extends beyond the traditional case of finite-dimensional quantum theory: for example, we can use it to show that Simon's problem can be efficiently solved in real quantum  ...  The traditional presentation of the quantum protocol for the abelian HSP is low-level, and relies heavily on the the interplay between classical group theory and complex vector spaces.  ...  The authors would like to thank Bob Coecke for comments and suggestions, as well as Sukrita Chatterji and Nicolò Chiappori for support.  ... 
arXiv:1701.08669v1 fatcat:x3chwcdpwnhtfdxcpg36eryf4y

Abstract structure of unitary oracles for quantum algorithms

William Zeng, Jamie Vicary
2014 Electronic Proceedings in Theoretical Computer Science  
This gives an abstract understanding of the structure of an oracle in a quantum computation, and we apply this understanding to develop a new algorithm for the deterministic identification of group homomorphisms  ...  We show that a pair of complementary dagger-Frobenius algebras, equipped with a self-conjugate comonoid homomorphism onto one of the algebras, produce a nontrivial unitary morphism on the product of the  ...  We are grateful to John Baez for useful discussions about signal-flow networks.  ... 
doi:10.4204/eptcs.172.19 fatcat:nd6mkpompra2dpxjjq3lmgrrlm

Quantum logic is undecidable [article]

Tobias Fritz
2020 arXiv   pre-print
It follows upon reinterpreting that result in terms of the hypergraph approach to quantum contextuality, for which it constitutes a proof of the inverse sandwich conjecture.  ...  This is a corollary of a recent result of Slofstra in combinatorial group theory.  ...  earlier version of this paper to prove a weaker result.  ... 
arXiv:1607.05870v4 fatcat:dllvashe7vbc5j4424ec57f7za

Page 4463 of Mathematical Reviews Vol. , Issue 2004f [page]

2004 Mathematical Reviews  
In the present work, the authors describe a similar algorithm for the computation of the global crystal bases for level-one basic representations of the quantum affine algebra of type es”.  ...  4463 description of the Fock space representations of the quantum affine algebras of type Ay’) in order to provide an algorithm for computing Kashiwara’s global crystal bases for their basic representations  ... 

Re-filtering and exactness of the Gelfand–Kirillov dimension

J.L. Bueso, J. Gómez-Torrecillas, F.J. Lobillo
2001 Bulletin des Sciences Mathématiques  
We prove that any multi-filtered algebra with semi-commutative associated graded algebra can be endowed with a locally finite filtration keeping up the semi-commutativity of the associated graded algebra  ...  As consequences, we obtain that Gelfand-Kirillov dimension is exact for finitely generated modules and that the algebra is finitely partitive.  ...  For the case of the quantum enveloping algebras associated to Cartan matrices of type A N McConnell [19] found an infinite dimensional N 2 -filtration with semi-commutative associated graded algebra  ... 
doi:10.1016/s0007-4497(01)01090-9 fatcat:wrcdbxmxhvberk3j6nm7rn3gxu

A possible hypercomputational quantum algorithm

Andrés Sicard, Mario Vélez, Juan Ospina
2004 arXiv   pre-print
We present a possible quantum algorithm for a classically non-computable decision problem, Hilbert's tenth problem; more specifically, we present a possible hypercomputation model based on quantum computation  ...  Our model exploits the quantum adiabatic process and the characteristics of the representation of the dynamical Lie algebra su(1,1) associated to the infinite square well.  ...  Kieu for helpful discussiones and feedback. This research was supported by COLCIEN-CIAS (grant #RC-284-2003) and by EAFIT University (grant #1216-05-13576).  ... 
arXiv:quant-ph/0406137v1 fatcat:pa5cm2okb5hapgqxlgt444iilu

A Novel Method for Developing Post-quantum Digital Signature Algorithms on Non-commutative Associative Algebras

Nikolay Moldovyan, Dmitriy Moldovyan, Alexandr Moldovyan
2022 Information and Control Systems  
Purpose: Development of a new method for designing post-quantum signature algorithms on finite non-commutative associative algebras.  ...  A new four-dimensional finite non-commutative associative algebra set over the ground field GF(p) have been proposed as algebraic support of the signature algorithms.  ...  One of attractive primitives of the post-quantum signature algorithms is the hidden discrete logarithm problem (HDLP) defined usually in finite non-commutative associative algebras (FNAAs).  ... 
doi:10.31799/1684-8853-2022-1-44-53 fatcat:5ktukb6wgfebxcetwtm2wuba5y

Symmetry algebra of the planar anisotropic quantum harmonic oscillator with rational ratio of frequencies

Dennis Bonatsos, C. Daskaloyannis, P. Kolokotronis, D. Lenis
2020 HNPS Proceedings  
The symmetry algebra of the two-dimensional quantum harmonic oscillator with rational ratio of frequencies is identified as a non-linear extension of the u(2) algebra.  ...  The finite dimensional representation modules of this algebra are studied and the energy eigenvalues are de- termined using algebraic methods of general applicability to quantum superintegrable systems  ...  From the algebraic point of view, however, while the many-dimensional analogue of the isotropic quantum oscillator can be studied using the su(N) or sp(2N,R) algebras, even for the two-dimensional anisotropic  ... 
doi:10.12681/hnps.2881 fatcat:ry5dazbc35ehrfknatndehkoia
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