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- Vasiliy Usatyuk
- 2013

This article present a concise estimate of upper and lower bound on the cardinality containing shortest vector in a lattice reduced by block Korkin-Zolotarev method (BKZ) for different value of the block size. Paper show how density affect to this cardinality, in form of the ratio of shortest vector size and sucessive minimal. Moreover we give upper… (More)

- V. S. Usatyuk
- ArXiv
- 2010

This article presets a review of lattice problems. Paper contains the main eighteen problems with their reductions and referents to his cryptography application. As an example of reduction, we detail analyze connection between SVP and CVP. Moreover, we give an Ajtai theorem and demonstrate its role in lattice based cryptography.

- V. S. Usatyuk
- ArXiv
- 2013

This article present a parallel CPU implementation of Kannan algorithm for solving shortest vector problem in Block Korkin-Zolotarev lattice reduction method. Implementation based on Native POSIX Thread Library and show linear decrease of runtime from number of threads.

- V. S. Usatyuk
- ArXiv
- 2012

This article presets a review of lattice lattice basis reduction types. Paper contains the main five types of lattice basis reduction: size reduced (weak Hermit), c-reduced, Lovasz condition, Hermit-Korkin-Zolotarev, Minkowski reduced. The article provides references to applications in: information theory (decoding of coding group in MIMO), calculus… (More)

- V. S. Usatyuk
- ArXiv
- 2015

A) , (L J regular QC-LDPC code of length N is defined by a parity-check matrix L L p I p I p I p I p I p I p I p I p I H (1) where 1 1 J j , 1 1 L l and l j p I , represents the p p circulant permutation matrix obtained by cyclically right-shifting the p p identity matrix 0 I by l j p , positions, with. / L N p For a… (More)

- V. S. Usatyuk
- ArXiv
- 2014

This article present a application of Block Korkin---Zolotarev lattice reduction method for Lattice Reduction---Aided decoding under MIMO---channel. We give a upper bound estimate on the lattice reduced by block Korkin---Zolotarev method (BKZ) for different value of the block size and detecting by SIC.

- V. S. Usatyuk
- ArXiv
- 2010

This article presets a review of the achievements rapidly developing field of cryptography - public-key cryptography based on the lattice theory. Paper contains the necessary basic concepts and the major problems of the lattice theory, as well as together with the description on the benefits of this cryptography class - the properties of the reliability to… (More)

- Nikita Polyanskii, V. S. Usatyuk, Ilya Vorobyev
- ArXiv
- 2017

—In the given paper we present a novel approach for constructing a QC-LDPC code of smaller length by lifting a given QC-LDPC code. The proposed method can be considered as a generalization of floor lifting. Also we prove several probabilistic statements concerning a theoretical improvement of the method with respect to the number of small cycles. Making… (More)

- V. S. Usatyuk
- ArXiv
- 2012

We propose a practical algorithm for block Korkin-Zolotarev reduction, a concept introduced by Schnorr, using CPU arbitrary length Householder QR-decomposition for orthogonalization and double precision OpenCL GPU Finke-Post shortest vector enumeration. Empirical tests was used on random lattices in the sense of Goldstein and Mayer.

- V. S. Usatyuk
- ArXiv
- 2013

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