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

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. ...

##
###
Algebras and universal quantum computations with higher dimensional systems

2002
*
arXiv
*
pre-print

Here is discussed application

arXiv:quant-ph/0210049v1
fatcat:fvchjeeqc5d4fmpkoj6jassdc4
*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. ...##
###
Candidate for practical post-quantum signature scheme

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. ...

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

2021
*
Applied Computing and Informatics
*

different

doi:10.1108/aci-02-2021-0036
fatcat:mtql7f7xe5gaxh4jgqgkicwr6m
*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). ...##
###
Curious properties of free hypergraph C*-algebras
[article]

2019
*
arXiv
*
pre-print

We show that they coincide with

arXiv:1808.09220v3
fatcat:7qdctzsjs5ge5l6bxzykqp5d2q
*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*. ...##
###
A post-quantum digital signature scheme on groups with four-dimensional cyclicity

2021
*
Information and Control Systems
*

Purpose: Development

doi:10.31799/1684-8853-2021-2-43-51
fatcat:zueeen24uzefrlyuzpnyr2egei
*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) . ...##
###
Post-quantum commutative encryption algorithm

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 ...

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

2017
*
arXiv
*
pre-print

Being fully diagrammatic, our proof extends beyond

arXiv:1701.08669v1
fatcat:x3chwcdpwnhtfdxcpg36eryf4y
*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. ...##
###
Abstract structure of unitary oracles for quantum algorithms

2014
*
Electronic Proceedings in Theoretical Computer Science
*

This gives an abstract understanding

doi:10.4204/eptcs.172.19
fatcat:nd6mkpompra2dpxjjq3lmgrrlm
*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. ...##
###
Quantum logic is undecidable
[article]

2020
*
arXiv
*
pre-print

It follows upon reinterpreting that result in terms

arXiv:1607.05870v4
fatcat:dllvashe7vbc5j4424ec57f7za
*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. ...##
###
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

2001
*
Bulletin des Sciences Mathématiques
*

We prove that any multi-filtered

doi:10.1016/s0007-4497(01)01090-9
fatcat:wrcdbxmxhvberk3j6nm7rn3gxu
*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*...##
###
A possible hypercomputational quantum algorithm

2004
*
arXiv
*
pre-print

We present

arXiv:quant-ph/0406137v1
fatcat:pa5cm2okb5hapgqxlgt444iilu
*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). ...##
###
A Novel Method for Developing Post-quantum Digital Signature Algorithms on Non-commutative Associative Algebras

2022
*
Information and Control Systems
*

Purpose: Development

doi:10.31799/1684-8853-2022-1-44-53
fatcat:5ktukb6wgfebxcetwtm2wuba5y
*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). ...##
###
Symmetry algebra of the planar anisotropic quantum harmonic oscillator with rational ratio of frequencies

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 ...

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